Improving robustness of a PID-controlled measurement system through Design of Experiments

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Improving robustness of a PID-controlled measurement system through Design of

Experiments

A DMAIC case study at Atlas Copco BLM

Eira Siljeström Hansson Emil Hellström

Industrial and Management Engineering, master's level 2020

Luleå University of Technology

Department of Business Administration, Technology and Social Sciences

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Preface

The spring of 2020 will probably always be remembered because of the outbreak of Covid-19, which put the whole world on lock-down. We, the authors of this master thesis, will remember the spring of 2020 as challenging and turbulent, but also fun, enlightening and exciting. The spring of 2020 represents the end of our five years of studies to finally become engineers. It started in Milan, Italy and even though we were forced to return to Sweden earlier than expected, we were able to finish our master thesis for Atlas Copco BLM.

We would like to thank everyone at Atlas Copco BLM for their support and trust but there are a few people that were especially valuable to us. Gianmaria for helping us to perform the experiments and believing in our methods as well as his patience with all our questions. Nunzio for supporting us in setting up the experiments and solving all the problems we created with the tools and the bench. We would also like to thank Marcello for taking the time to help us with the PID-controllers, his patience and inputs to the work.

Our instructor from Luleå University of Technology, Mahdieh Sedghi, also deserves a huge thanks for the feedback, patience and encouragement. We have probably been in contact with everyone who works at the Department of Quality at LTU and would like to thank all of them for taking their time to answer our questions.

However, the accomplishment of our master thesis is because of our supervisor Nicolo’ Fioretti who both before, during and after our stay in Milan supported us with both knowledge, contacts and valuable inputs to the report. He has continuously shown a great interest in our work, both in successes and set-backs. In addition to the support, we have also learned that the best olive oil is from the southern part of Italy, the best wine from Sicily and that a walk after lunch with coffee included is essential for a good work ethic.

Even though our stay in Italy did not go as planned, we are very grateful for all the support we received.

Grazie mille

Eira Siljeström Hansson Emil Hellström

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Abstract

Companies within the manufacturing industry are often aiming to increase productivity and simultaneously maintain the quality of their products. To achieve higher productivity and quality it is imperative to have tools with a high speed and accuracy. Atlas Copco BLM’s STbench is a measurement system which enables manufacturers to validate their tools during different situations. The purpose of this case study was to improve the robustness of the STbench so it would operate well during situations with both low and high tool speed. To define and investigate how to improve the STbench, a modified DMAIC-approach was used. During the investigation it was found that the area with the largest improvement possibilities was the STbench’s PID-controllers. Design of Experiments was used as the method to optimize the P- and I-element of the PID-controllers; hence, increase the robustness. The optimal settings could improve the robustness of the STbench with approximately 50%, but the result has not been verified. This case study presents results that can increase the robustness of the STbench; thus answering the purpose. Furthermore, this master thesis presents several revelations regarding using experimental plans while optimizing control systems, an area that has not been extensively investigated in previous literature.

Keywords: Robustness, Design of Experiments, PID-controller, Control system, Measurement system

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Sammanfattning

Företag inom tillverkningsindustrin har ofta som mål att öka deras produktivitet och samtidigt behålla en hög kvalitet hos deras produkter. För att uppnå en högre produktivitet och kvalitet är det viktigt att ha verktyg med hög hastighet och tillförlitlighet. Atlas Copco BLMs STbänk är ett mätverktyg med ändamålet att tillverkare ska kunna validera kapabiliteten hos deras verktyg under varierande omständigheter. Syftet med denna fallstudie var att förbättra robustheten hos STbänken för att den skulle prestera väl under både låga och höga verktygshastigheter. För att definiera och undersöka hur robustheten kunde förbättras användes en modifierad DMAIC-strategi som tillvägagångssätt. Under fallstudiens gång framkom det att det område med störst förbättringspotential var STbänkens PID-regulatorer. Försöksplanering användes för att optimera P- och I-elementen hos PID-regulatorerna och därmed öka robustheten. De optimala inställningarna förbättrade robustheten hos STbänken med ungefär 50% men resultatet har inte blivit verifierat. Denna fallstudie presenterar resultat som förbättrar robustheten hos STBänken och besvarar därmed syftet. Dessutom visar detta examensarbete på flera insikter angående användandet av experimentella designer vid optimering av kontrollsystem, ett område som inte har utretts i stor utsträckning i tidigare litteratur.

Nyckelord: Robusthet, Försöksplanering, PID-regulator, Kontrollsystem, Mätsystem

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1 Introduction

The aim of the introduction is to provide the reader with a background of the master thesis and a problematization. Furthermore, it presents the chosen case study approach to fulfill the purpose of the thesis. Finally, the limitations are described and their implications.

Background

High-quality performance and high productivity are imperative for companies to gain a greater market share (Deming & Edwards, 1982). Disturbances within processes are a common problem that can cause a decrease in quality performance and therefore decrease productivity (Ingemansson & Bolmsjö, 2004). Robust processes and products can minimize the impact of disturbances (Ingemansson & Bolmsjö, 2004) and also reduce cost as well as increase productivity (Fuentes, Benavent, Moreno, Cruz & Pardo del Val, 2000).

The disturbance of processes can occur due to everything from variation in temperature during manufacturing to changes in process parameters (Kackar & Shoemaker, 1986; Arvidsson &

Gremyr, 2008). A process which is sensitive to these kinds of variations also becomes expensive to control (Kackar & Shoemaker, 1986). The goal of robust processes is to reduce variation within the functional characteristics of a process, in other words to find the optimal process settings where the disturbance has the least effect on the output (Kackar & Shoemaker, 1986;

Arvidsson & Gremyr, 2008).

Control systems can increase the robustness of a process by decreasing the variations within quality performance measurements (Vlachogiannis & Roy, 2005; Lee & Kim, 2000; Goodwin, Graebe & Salgado, 2001). Control systems are often used in industrial settings (Capaci, Bergquist, Kulachi & Vanhatalo, 2017; Vlachogiannis & Roy, 2005; Lee & Kim, 2000) because of their inexpensiveness and low cost (Tang, Man, Chen & Kwong, 2001). A robust controller is defined as the controller's tolerance towards changes in process parameters (Luyben, 1989).

Within the design of control systems there is often a trade-off between performance and robustness, where an improvement in performance decreases the possibility for the controller to operate well during disturbance (Luyben, 1989; Shinskey, 1990).

PID-controllers are the most used type of controllers within industrial control systems (Dewantoro, 2015; Vlachogiannis & Roy, 2005; Lee & Kim, 2000). A well-tuned PID- controller can manage most of the disturbance that affects the system and changes in process parameters; in other words, ensure that the system is robust (Vlachogiannis & Roy, 2005; Lee

& Kim, 2000). However, tuning the PID-controllers is difficult and can result in poorly functioning processes if not done correctly (Vlachogiannis & Roy, 2005; Dewantoro, 2015;

Goodwin et al., 2001).

Problem description

In the manufacturing industry the most common form of mechanical connections is the use of threaded fasteners (e.g. screws) (Milani & Hamedi, 2008). The usage of threaded fasteners is primarily due to their inexpensiveness and ability to easily assemble and disassemble the connection. The goal of joining two parts with threaded fasteners (e.g. joint) is to reach the proper clamping force, see Figure 1, to avoid joint failures (Housari, Alkelani & Yocum, 2012).

However, there is a current trend going towards tighter tolerances in industries (Archenti, 2011).

Therefore, within tightening strategies, more focus has to be put upon torque control, angle control, and stretch control to be accurate (Housari et al., 2012).

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Figure 1. Descriptive picture of clamping force.

With permission from Atlas Copco BLM.

With plenty of factors affecting the desired clamping force, manufacturers must assure that their tools can tighten the joints with the required accuracy. Atlas Copco BLM is based in Italy and specializes in the development of tightening tools and solutions for quality control and assurance. One of their products is a joint simulation bench (STbench), see Figure 2, where customers can validate the capability of their tools without interfering with their manufacturing processes. In other words, they can assure that their tools can tighten with the desired accuracy.

The bench is a moveable measurement system and can be positioned where it is needed. It can also reproduce different joints that are used within the manufacturing, allowing for a more time and cost efficient quality assurance process. To simulate a wide range of joints, the STbench has several brakes with different torque ranges. These brakes create resistance towards the tool when tightening; hence simulating how a bolt would react in a real tightening operation. The brakes on the STbench are hydraulic and they are regulated by a control system, consisting of two PID-controllers, one for pressure-control and one for torque-control.

Figure 2. The STbench.

With permission from Atlas Copco BLM.

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The STbench’s robustness depends on the type of joint it is aiming to simulate as well as the speed of the tool. For example, on a joint with a target angle of 90° and a target torque of 40 Nm¹, the maximum tool speed the bench can handle was approximately 468 RPM ² (see section 5 for calculations). Since manufacturers are aiming to increase their productivity, the speed of the tightening tools is increasing as well. Increased tool speed is mainly seen at manufactures in the United States while European manufactures are more conservative (personal communication, Federico Fraschini, March 5 2020). At the same time, the demand for the tools to perform with high quality remains the same. However, since the bench is not able to operate well during certain situations with high tool speed, some customers had to use other solutions for testing the capability of their tools (personal communication, Federico Fraschini, March 5 2020). For Atlas Copco BLM to keep and potentially increase their market share, they must ensure that the STbench is robust enough to operate well with both high- and low-speed tools to meet the demand.

The DMAIC-approach was chosen as the problem-solving process, since the case study was an improvement project for the robustness of the STbench. The DMAIC-approach was useful since it helped to identify and define the problem which was affecting the robustness as well as disintegrate the problem into subcategories. Montgomery (2013b) mentions that when using the DMAIC-approach, the value opportunity of the case study must be clear and that an improvement project should result in financial benefits for the company. Hence, the approach ensured that the focus of the case study also was on providing results that were valuable for Atlas Copco BLM and their customers, which gave incentive for the case study within the company.

Purpose

The purpose of this case study was to improve the robustness of the STbench, in other words ensure that it could handle changes in process parameters without sacrificing performance.

More specifically, the case study was imperative for Atlas Copco BLM to ensure that the STbench would meet the customers’ demands of higher tool speed but at the same time continue to operate well with low tool speeds.

In the beginning of the DMAIC-process, it was determined that the components to be optimized were the two PID-controllers within the STbench. It was concluded to use Design of Experiments as the method for analysis and optimization. Since control systems increase the complexity of experimental designs (Capaci, 2019), it was also of interest in this case study to explore the practical challenges faced while using Design of Experiments on control systems.

The choosing of Design of Experiments as the method for analysis resulted in the following research question:

How can the robustness of a PID-controlled measurement system be improved through Design of Experiments?

1 Newtonmeter

2 Rounds per minute

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4 Limitations

This case study was limited to only focus on the PID-controllers due to the time resources and scope of the thesis. Within the chosen scope, only the 50 Nm brake on one STbench was investigated since this type of brake was the most used and therefore provided the most value for Atlas Copco BLM’s customers and the company with the most utility. The time frame of the case study was from 2020-01-27 until 2020-06-01 but because of Covid-19, the authors of this master thesis only had access to the bench between 2020-01-27 until 2020-03-11.

Furthermore, the case study was limited to only include testing with one tool, Tensor ST Electric Nutrunner, and one type of joint, a 90° target angle and a target torque of 40 Nm. Since the quality of a joint can be different depending on the type of tool (Milani & Hamedi, 2008) the result might not be applicable to other joints.

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2 Theoretical background

The aim of the theoretical background is to provide the reader with the necessary knowledge to understand the experiments and analysis. It begins by describing robustness of control systems and the function of controllers. How to apply Design of Experiments on control systems is thereafter discussed and the theoretical background ends with an introduction to tightening technique.

Robustness and control systems

Control systems are often used for industrial process control due to their inexpensive maintenance, ease of design, low cost, and possible quality improvements to processes (Tang et al., 2001; Goodwin et al., 2001). The controllers in a control system aim to ensure that the process is robust (Luyben, 1989) and performing well, more specifically, that the controllers are able to correct the output to a target value while the system is disturbed by external factors (Goodwin et al., 2001). Robust controllers are in this thesis defined as the controller’s tolerance towards changes in process parameters (Luyben, 1989). According to Luyben (1989) and Shinskey (1990) there is a trade-off between robustness and performance in control systems, where improving performance (e.g. tighter control of process) causes the robustness to decrease since it becomes more sensitive to changes.

One type of controller to ensure robustness is the feedback control-loop which is characterized by a behavior that, based on the current output, adjusts the input of the controller to compensate for disturbances on the system. A feedback control-loop system, as shown in Figure 3, is often designed and modelled as a PID-controller.

Figure 3. A feedback-controller.

Modified from Capaci et al. (2017).

There are different elements of a PID-controller and how they decrease the effect on the response caused by disturbance are described by Goodwin et al. (2001) as follows and shown in Figure 4:

 The proportional element (P) is proportional to the error that is looped back, which can be interpreted as an amplification of the current state.

 The integral element (I) is proportional to the integral of the error, which can be interpreted as the accumulation of the “past” error, to the target, and therefore not allow the system to overshoot the target.

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 The derivative element (D) is proportional to the derivative of the error, which can be interpreted as the prediction of the “future” error, to the target, and therefore will stabilize the system.

Figure 4. Conceptual example over how the system response is affected by elements of PID-controllers.

Modified from Control system animation.

The graph P) shows what occurs to the system response when only the proportional element is used. The response will increase and probably miss the target value. When an integral element is included, shown in PI), the response will correct itself according to the error (distance between the target value and actual value). The last graph PID) displays how the system responds if a derivative element is added. The derivative element reduces overshoot and improves the transient response of the system response; hence, predicting when the system will reach the target and result in a more stable system.

The tuning of PID-controllers is essential to ensure that the system is robust and has minimal unpredictable behavior (Vlachogiannis & Roy, 2005). Even though PID-controllers are prominent in control system design and widely used, the tuning is both challenging and difficult (Dewantoro, 2015; Vlachogiannis & Roy, 2005). There are several methods for tuning PID- controllers with various results and resource demands. One popular approach is the Ziegler- Nichols method, which evaluates the system’s stability limits. This method is only applicable to systems that are secure when operating close to the region of system’s instability (Lee &

Kim, 2000; Vlachogiannis & Roy, 2005). Another method which also can be used for tuning is the relay feedback method (Lee & Kim, 2000; Vlachogiannis & Roy, 2005). However, it is not

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appropriate for all types of systems, such as those with long reaction time on the measured output or systems with several outputs (Lee & Kim; 2000).

The Taguchi method can also be used to tune PID-controllers and is the most commonly used to optimize industrial machines and other electrical systems (Dewantoro, 2015). It is based upon fractional factorial designs (e.g. Design of Experiments) but uses only orthogonal arrays to reduce the number of needed experiments. Nevertheless, the method presumes that interactions between factors are known, in contrast to the normal fractional factorial design, and does not investigate all interactions between factors (Islam & Pramanik, 2016).

Design of Experiments on control systems

In processes there are several different types of inputs (e.g. factors), which can be used as experimental factors in Design of Experiments (DoE). For an open-loop process, see Figure 5, controllable inputs could be used as experimental factors since their values are changeable to get a reaction on the output (e.g. response). Other types of inputs that are not controllable because of difficulty or expensiveness are called nuisance or disturbance factors (Capaci, 2019).

Figure 5. An open-loop system with inputs and outputs.

In contrast to an open-loop, a closed-loop system can consist of a feedback control-loop, see Figure 6. Some of the inputs to the system will pass through the controller and are manipulated to provide a correct output in regards to the target. The settings of the controllers are often based upon previous experience and understanding of how the input affects the response (Capaci et al., 2017). Therefore, if the inputs are used as experimental factors, the response value will not change substantially since they are manipulated by the controller. Thus, it is important to take the impact of the controller into account when deciding the experimental factors to get useful results (Capaci et al., 2017).

Figure 6. A closed-loop system.

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For closed-loop systems (e.g. PID-controllers), Capaci et al. (2017) describes two different approaches for choosing experimental factors and responses. The first approach is to use the disturbance factors and inputs not passing through the controller as experimental factors and further use the manipulated variables or the controlled variable (e.g. output) as responses. The second approach is to use the elements of the controller (e.g. set-points) as experimental factors and vary their value. The response variable in the second approach should be an indication of process performance, such as error measurements, cost or time.

A widely used response variable of process performance when tuning PID-controllers is the integral-squared error (ISE) (Vlachogiannis and Roy, 2005). The ISE is mathematically defined as equation 1 where y (α) is the output and the ysp is the target output (Vlachogiannis & Roy, 2005; Luyben, 1989; Clark, 1961).

𝐼𝑆𝐸 = ∫ 𝑒(𝛼)²𝑑𝑡

∞ 0

= ∫ (𝑦(𝛼) − 𝑦_𝑠𝑝)²𝑑𝛼

∞ 0

(1)

ISE is a performance measurement showing the size of the error (Clark, 1961). Luyben (1989) emphasizes that ISE is a reasonable compromise between performance and robustness of the process when evaluating a control system. Minimization of the ISE means a minimization of the error. By squaring the error (see equation 1), the points which are further away from the target will be weighted higher compared to those being close to the target. Also, if the variables are not equally distributed, using only a summation of the error, instead of the integral formulation, would cause some values to be weighted higher than others. ISE is therefore a response variable which provides a fair and accurate interpretation of a process performance (Clark, 1961). However, only analyzing ISE can cause the analyzer to miss small oscillations, disguising instability within a system (Clark, 1961; Shinskey, 1990).

Tightening strategies

The aim of mechanical connections is for the joint to reach the correct clamping force.

However, the clamping force is difficult to apply or measure (BLM, 2004), and tightening strategies are instead focused on torque control, angle control and/or stretch control (Housari et al., 2012). The most used tightening strategy is torque control because of its simplicity and the direct correlation between torque and clamping force, the torque tension relationship (Housari et al., 2012). When tightening, the aim is usually to reach at least 80% of a joint’s yield point, see Figure 7. Higher torque than the yield point can result in joint failures, such as permanent deformation on the threaded fastener. A torque below 80% of the yield point might cause the joint not to fulfill its purpose of connecting components (BLM, 2004).

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Figure 7. Graph over torque showing the yield point.

Modified from BLM (2004).

Nevertheless, the clamping force can vary up to ±35% if only the torque is controlled.

Therefore, torque control is often complemented with angle control that provides a more accurate clamping force, which only varies up to ±7% (Housari et al., 2012). See Figure 8 for a visualization of torque and angle control.

Figure 8. Torque and angle control.

Modified from BLM (2004).

The tightening strategies are also dependent on the stiffness of the joint, in other words if it is a soft or hard joint. This is often defined based on the type of material that is mechanically connected and the material of the screw (Wang et al., 2017). Furthermore, the category of the joint is also dependent on the torque-rate, see Figure 9. A soft joint has a low torque-rate and the tightening usually demands a full turn or more, an angle of +360°. While a hard joint has a high torque-rate and only requires a fraction of a full turn, an angle up to approximately 60°

(International Organization for Standardization, 2017; Milani & Hamedi, 2008).

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Figure 9. Visualization of hard and soft joints.

The target line for the joint behavior is in many cases linear and based upon the target torque and target angle, ^𝑑𝑇

𝑑𝛼, see Figure 10. Improvement of the tightening is done by controlling the behavior of the joint, so it follows the target line as much as possible (BLM, 2004). Hence, the tools need to be tested regularly to ensure that they are capable of performing a correct tightening.

Figure 10. Joint behavior over angle.

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3 Methodology

The methodology of this case study is explained in this section with the purpose of providing a transparent description of how the case study evolved and how the experiments were performed.

The methods used and assumptions made are built upon the theoretical background and, therefore, continuously refer to it.

Research approach

This research was based upon a mostly quantitative case study with an explorative and deductive research approach. A case study is usually focused on a single situation (Patel &

Davidson, 2019) where this case study investigated the improvement opportunities for the STbench at Atlas Copco BLM. Case studies often have a holistic perspective in order to gather as comprehensive information regarding the researched subject as possible (Patel & Davidson, 2019); hence an explorative and deductive research approach was suitable for this case study.

Using an explorative approach was beneficial since it aims to gather information with different techniques, both qualitative and quantitative (Patel & Davidson, 2019), and the purpose of the approach is to gain more knowledge and new insights to the specific area (Saunders, Lewis &

Thornhill, 2009). A large part of this case study was quantitative where experiments were performed. Experiments are effective when the aim is to understand the relationship between independent and dependent variables (Patel & Davidson, 2019). The qualitative parts were mainly focused on gathering background information regarding the problem area (Patel &

Davidson, 2019) with help from literature, seminars, presentations and different types of meetings. The research and experiments of this case study was based upon general principles and existing theory when making decisions and drawing conclusions, therefore a deductive approach was appropriate (Patel & Davidson, 2019).

Approach for case study

The chosen approach for this case study was the DMAIC problem-solving-process. According to de Mast and Lokkerbol (2012), DMAIC is suitable for extensive problem-solving tasks where the problem needs to be defined and categorized into subcategories. The problem in this case study needed to be disintegrated since the areas affecting the robustness of the STbench was not completely determined and thoroughly investigated. Furthermore, the value opportunity was clear and aligned with the company’s business objectives; helping customers increase productivity with high quality performance (Atlas Copco, 2020), which is a key factor when using DMAIC (2013b). However, the DMAIC-approach used in this case study was modified according to Tanco, Viles, Ilzarbe and Alvarez (2007) because of the chosen method for analysis, Design of Experiments. Design of Experiments demands careful planning and trial experiments to ensure valuable final results (Montgomery, 2013a) and in order to allocate resources to these vital parts, the two phases Pre-analyze and Experiment, were added. In Figure 11, the modified DMAIC-approach is presented, also showing which phases that were mostly qualitative and quantitative.

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Figure 11. Modified DMAIC-approach for Design of Experiments.

Modified from Tanco et al. (2007).

Because the aim of this case study was not to change or redesign any part of the STbench but to find factors and interactions influencing the output and suggest improvements, Design for Six Sigma (DFSS) was not a suitable approach (Sokovic, Pavletic & Pipan, 2010; Montgomery, 2013b). As the case study has a clearly defined scope and goals, the PDCA-cycle was also not reasonable (Sokovic et al., 2010).

3.2.1 The DMAIC-approach

The first part of the case study was the Define phase where the opportunity for Atlas Copco BLM to improve was identified and validated together with them. The need for investigating the limitations of the STbench and improving the operability was known before the start of the case study but how it should be done was not. Hence, a thorough introduction of the bench was performed, at the start of the project, with the individuals responsible for each part to ensure that the authors of the master thesis (from now on called authors) fully understood the structure and complexity of the bench and the system behind it. In Table 1, a summary of each segment in the introduction is presented. Another aspect of the introduction was to create an incentive for the case study and involve the necessary people who could provide valuable inputs. A final meeting, consisting of 2 x 90 min sessions with discussions and brainstorming, was held where the objective of the case study was set. The people involved in these sessions were the people in bold text in Table 1. The result from the final meeting was that the case study should focus on improving the robustness of the STbench in order for it to operate well during both high and low tool speeds.

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Table 1. Summary of each segment in the introduction.

Segment Duration Leader Type of meeting Description

Torque

introduction 8 x 45 min Competence team

manager Seminar Introduction to tightening methods

STbench platform 2 x 150 min

Firmware developer

& R&D consultant Demonstration Functionality of the bench, usage, limitations etc.

Quality challenges 60 min Quality manager Presentation Quality claims and challenges of the bench STbench

production process

120 min Production manager Tour Production tour of the bench

Introduction to

testing 150 min

Validation lab engineer &

manager

Demonstration Usage of the bench

The brake system

modeling 150 min Control systems

engineer Presentation

Introduction to the control system and PID-

controllers Mechanical

design 60 min Mechanical

designer

Presentation &

Demonstration

The brake system from a mechanical perspective Standards 60 min Senior technical

advisor Presentation The ISO and VDI

standards of the STbench

Customer

perspective 120 min Marketing manager

& Product manager Presentation

The customer’s viewpoint of the STbench and their

demands

When the scope of the case study was determined, the objective of the previous phase, the case study moved on to the Measure phase. A cause-and-effect diagram was composed by the authors to identify all components that could affect the robustness of the STbench. The diagram was based upon the learnings and outcomes of the introduction and validated together with the competence team manager, senior firmware engineer and control systems engineer. The selected component to focus on was the control system, more specifically the two PID- controllers. During this phase it was investigated how the controllers were operating as well as the inputs and outputs of the system. Making the PID-controllers more robust would make the STbench more robust; hence it was aligned with the purpose of the case study. Furthermore, during the first two phases, Define and Measure, a literature review was conducted in parallel, described more in section 3.3. When the limitations of the system were identified the project continued to its next phase Pre-analyze.

As mentioned previously, a modified DMAIC-approach was used in this case study. Therefore, the data in this case study was mostly gathered during the Pre-analyze and Experiment phase as recommended by Tanco et al. (2007) and not during the Measure phase recommended by Montgomery (2013b) and Sokovic et al. (2010). The process of Measure, Pre-analyze, Experiment and Analyze was iterative due to new insights during these phases which forced changes in the other phases.

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In the Pre-analyze phase, different response variables were discussed and assessed in relation to their measurement simplicity and relevance for the case study. Furthermore, the experimental factors were chosen based upon earlier studies and expert knowledge from the control systems engineer. Factors to hold constant and nuisance factors were also evaluated by help from the cause-and-effect diagram and together with the competence team manager, senior firmware engineer and control systems engineer, see appendix A and B. Furthermore, experimental plans were discussed, a trial experimental plan was designed and when the experimental environment was determined as satisfactory for the trial experiments the project continued to its next phase Experiment. From the results and insight of the trial experiments, the final experimental plan could be fine-tuned. The duration of the final experiment was approximately six hours, where two hours were used to collect the raw data and four hours were used to clean and calculate the response of each run. The data collection process is described more in section 3.4.1. When enough data was gathered to provide an accurate description of the process performance, the case study continued to its following phase Analyze.

During the Analyze phase the response values were analyzed in the software Design-Expert 11.

The first analysis could not describe the process accurately so more data was collected and the process started again from Measure since the DMAIC-approach was used iteratively. The process of the analysis is presented more in section 3.4.2. When a final model was found and no obvious further evaluations could be investigated the next phase was initiated.

In the Improve phase, based upon the results from the previous phase, the optimal settings to ensure robustness of the STbench was determined. The response surfaces for the interactions were studied to understand the behavior of the models; hence, the PID-controllers. With the optimization tool in the software, the optimal settings for three different tool speeds were determined. Since there was no possibility to test the new settings on the bench, Design-Expert 11 was used to calculate a prediction interval instead. When these calculations were done and conclusions from them drawn, three recommendations were summarized before the case study moved on to the last and final phase.

The recommendations together with a plan for further experiments and controls was completed in the last and final phase of the case study: Control. A process control plan was created for the R&D unit to use while performing the validation tests with the new optimized settings. The documentation of the DMAIC-project was handed over to the company after it was accepted by Luleå University of Technology.

Frame of references

To gather relevant knowledge and theory within the scope of the case study, a literature review was conducted during the Define and Measure phase. The purpose of the literature review was to find similar studies where the DMAIC-approach and/or Design of Experiments had been used. Another aspect of the literature review was to understand more about control systems and PID-controllers and how it is used in the manufacturing industry. The gained knowledge helped to plan and perform the experiments and draw correct conclusions. The literature was primarily found on Google Scholar and Scopus where emphasis was on finding highly cited articles from well-renowned journals. Out of the 21 articles presented in section 13, eight of them were published in journals recommended by the Quality Technology and Management Department at Luleå University of Technology or had a ranking of three or higher at the Academic Journal Guide in 2018 (CABS, 2015). Of the remaining 13 articles had eight been cited above 100

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times. The remaining five articles had below 100 citings. Because of the case study’s specific scope, articles from conferences were used. Books were also used in order to describe general concepts that are well-known. Patents and standards (e.g. ISO) from Atlas Copco BLM were used in the problem description and theoretical background to narrow it to the defined problem area.

The articles have been found by combining the keywords below. The combinations together with the amount of hits on Google Scholar and Scopus are presented in Table 2. The articles were first evaluated based upon their title’s relevancy for this thesis and secondly on the abstract. Thirdly, it was investigated if the articles were published in any well-renowned journal. If the article was considered to have potential to contribute to the thesis, it was valued higher than if it belonged to a well-renowned journal or had many citings and the article was downloaded. The article was further studied by searching after keywords to once again validate if the article could contain valuable inputs to the case study. Lastly, if the article contained the desired keywords it was read completely. As seen in Table 2, there were few hits on combinations that included Design of Experiments which could indicate that the research done on control systems with Design of Experiments was sparse. Further, the articles which included Design of Experiments were mostly within areas such as medical technology or pharmaceutical technology, showing that this case study could be valuable for the research of PID-controllers within manufacturing and measurement systems.

Keywords: PID-controller, Tuning, Robust controllers, Design of experiments, Tightening strategies

Table 2. Combination of keywords and the amount of hits in 2020-05-04.

Combination of keywords Amount of hits Google Scholar

Amount of hits Scopus

PID-controller AND Tuning 93 000 6 746

PID-controller AND Tuning AND Design of Experiments 677 7

PID-controller AND Design of Experiments 1 420 17

Robust controllers AND Design of Experiments 62 6

Tightening strategies 323 35

The creator of Design-Expert, Stat-Ease, is continuously used as a reference in the data analysis section. Stat-Ease is mainly used to reference general concepts within Design of Experiments to explain phenomenons or decisions made in the section. For a statistician who is used to Design of Experiments, the referencing might be trivial but since this master thesis has a broad target group, it is of interest to show the reader where more information about the method can be found. Furthermore, since Stat-Ease is the supplier of the used software, their knowledge within Design of Experiments were considered reliable.

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16 The usage of Design of Experiments

As mentioned in the theoretical background, Design of Experiments can be used as a method for tuning PID-controllers (Dewantoro, 2015). It was found useful since both knowledge about the interactions between the elements of the PID-controllers was of interest as well as finding their optimal values. It could be argued that the Taguchi method should have been used instead but since this method assumes that interactions were known in advance, it was not suitable (Islam & Pramanik, 2016). Capaci et al. (2017) also emphasized that Design of Experiments can provide valuable insights on how the values of the set-points of the controllers can affect process performance measurements. With this in mind, Design of Experiments was therefore used as the method for analyzing the collected data. The following section will further describe how the data collection and analysis were performed and motivate the used experimental plan.

3.4.1 Data collection and cleaning

To collect the data, a 2^5-1 randomized experimental plan with five repeats, two replicates and five center points was used, meaning that 37 runs were conducted and in total 185 tightenings.

The resolution of the experimental plan was V which implies that no main effects or two-factor interactions were aliased with other main effects or two-factor interactions (Montgomery, 2013a). It was considered sufficient for this case study since if higher-order interactions were significant, it was expected that they could be easily identified and explained. The center points were added to detect if there was any curvature in the model (Montgomery, 2013a; Stat-Ease, 2020a). The design generator was E = ABCD with the defining relation I = ABCDE. The nine aliases between two-factor interactions and three-factor interactions are presented in Table 3.

The specific experimental factors for each letter are presented in section 6.

Table 3. Aliases for a 2^5-1 experimental plan.

AB = CDE BD = ACE AC = BDE BE = ACD AD = BCE CD = ABE AE = BCD CE = ABD BC = ADE DE = ABC

The raw data that was collected from every repeat of each run was composed of timestamps for each torque level and angle level the bench could measure until the tightening was completed.

Hence, the raw data consisted of more information than needed in the analysis since it was only of interest to investigate the points up until the maximum torque. Therefore, by using Excel, only the data up to the maximum torque was kept and analyzed. How the raw data was converted into the response variables are presented in section 6.1.

When calculating the average between the response values of each run, the data was trimmed with 20%, in other words the highest and lowest value of each sample group was removed, since there was variation within some runs, causing inaccurate results. The aim with the trimming was therefore to gain more accurate results and avoid measurement errors. Trimming the data was more suitable than other more standardized methods since the data could not be assumed to be normally distributed (Bryan, Cecchetti & Wiggins, 1997).

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17 3.4.2 Data analysis

A principle regarding hierarchy was considered when the data was analyzed and the selection of which effects that should be included in the model. According to the principle, low-order interactions are more likely to be the contributing factor compared to high-order interactions.

For example, A is more likely to be contributing than the interaction ABC (JMP & Proust, 2010). Another principle that was followed was the heredity principle which states that if a high-order interaction is significant, its main effects and interactions are probably also contributing to the response. To exemplify, if ABC is shown to be significant it is likely that A, B, C, AB, AC and BC are also significant (JMP & Proust, 2010). The third principle that was used was the principle of effect sparsity, which means that systems often are influenced by a few effects and interactions (JMP & Proust, 2010).

In this case study, the process of selecting which effects to include in the model was recommended by Stat-Ease (2020d) and is described below. As mentioned, the three principles presented above were also taken into consideration when performing the analysis.

1. Analyze the half-normal plot and select effects that are notably larger compared to others.

2. In the Pareto-chart, select the largest unselected effect to investigate if it is a true effect or not.

a. Effects above the Bonferroni limit are important factors and should be included in the model.

b. Effects that are above the t-value limit but not above the Bonferroni limit should be included in the model if they make sense to the experimenter.

c. Effects under the t-value limit should only be included to support the principles mentioned above.

3. Investigate the significance of effects by studying the p-value for each effect on the ANOVA-table. If an effect has a p-value below 0.05 it can be concluded that the effect is significant. A p-value above 0.1 usually indicates that it is not significant (Stat-Ease, 2020b).

Many of the standard statistical analysis methods rely on the data to be normally distributed (Feng et al., 2014) and the software Design-Expert 11, which is used for analysis in this case study, is not an exception. However, the collected data for one of the response variables was skewed and did not follow a normal distribution. If this was not taken into consideration when the data was analyzed, the result would have been invalid (Feng et al., 2014). Therefore, the data was transformed into a log-normal scale as recommended by Design-Expert, which uses the Box-Cox method to recommend which transformation is the most appropriate (Stat-Ease, 2020e). The transformation was performed since the usage of standard statistical methods during the Analyze phase was necessary (Feng et al., 2014).

Furthermore, to assess if the model suggested by the software described the data accurately, a lack-of-fit test was used (Box & Draper, 1982). The lack-of-fit test indicates how accurately the chosen model will predict response values compared to the actual measurements; hence describing how well-fitted the model is to the data (Stat-Ease, 2020c). For example, if lack-of- fit is significant it is an indication that the data is not well-fitted and vice versa. Lack-of-fit occurred when the transformed data was analyzed, which might have been due to the variation within the system being small (Montgomery, 2013a). To make the lack-of-fit insignificant, a

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response surface methodology (RSM) can be used, which investigates if high-order terms should be added to the model, which in turn could improve the lack-of-fit (Minitab, 2020).

To investigate if there was curvature in the response surface, five center points were added to the experimental plan (Box & Draper, 1982; Montgomery, 2013a). Curvature was shown to be present for both response variables and a model of a higher degree was therefore needed (Montgomery, 2013a). To find the most appropriate model, the RSM used was a central- composite-design (CCD), which is popular when fitting second-order models (Montgomery, 2013a). Since the ranges of the factors were close to the limits of the region of operability for the PID-controllers, a face-centered-composite-design (FCCD) was used. The benefits of a FCCD was that it did not move the levels outside of the limits; hence keeping the process within the region of operability. A FCCD is also easier to be used since it only requires three different levels of the factors (Verseput, 2000). Also, since it was presumed that the location of the optimum was within the ranges of the factors, the design did not need to be rotatable, which a FCCD is not (Montgomery, 2013a).

All things considered, it is important to remember that a model can almost never fully describe the functional relationship between factors and its response (Box, 1976). Therefore, the aim for this analysis was to find a model that is useful, not a correct description of reality.

Validity and reliability

Within case studies, validity is often divided into three different aspects: internal validity, construct validity and generalizability (Gibbert, Ruigrok & Wicki, 2008). In effort to increase the internal validity of this case study a rigorous description of the data analysis is presented in the previous section. Furthermore, decisions made when analyzing the data are described and figures are shown before and after these decisions. To ensure that the experiments in this case study measured what they intended (construct validity) a continuous dialog with the engineers that created the system was held. They verified that the calculations and assumptions made during the case study was in line with the intended focus area.

During the data collection in the Experiment phase, it was imperative to keep the environment as homogeneous as possible. The purpose of setting up this environment was to minimize the variation within the repeated and replicated measurements used as response values. However, this homogeneity could affect the generalizability of this case study since future studies might find it difficult to achieve the same homogenous set-up.

In effort to increase the reliability of the case study the collected data was cleaned, described in section 3.4.1. A transparent data collecting procedure and cleaning procedure will increase the legitimacy and reliability of the case study; hence give more reliable results (van den Broeck, Cunningham, Eeckels & Herbst, 2005; Gibbert et al., 2008). The trimming of the collected data was done with the aim to reduce suspicious variations and measurement errors within the data sets in order to provide more accurate measurements. Furthermore, every experiment was repeated five times and randomly replicated once to ensure the instrument's consistency, which is similar to the test-retest methodology that is often used to increase the reliability of measurements (Weir, 2005).

To ensure the stability of the measurements over time, the addition of the FCCD was placed in a different block than the previous measurements since it was conducted one day later than the first experimental plan. By adding different blocks and performing five repeats of each run, it

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was possible to see if time affected the response values (Montgomery, 2013a). In this case study it was shown that the difference between the blocks was not significant, meaning that the measurements were stable over this period of time. To test the results over a longer period of time further studies are required.

The case study was performed with a deductive research approach that according to Patel and Davidson (2019) increases the objectivity. In an effort to increase objectivity and decrease bias the data collecting was performed by the authors since they did not have any prior connections to the system. Furthermore, the analysis of the data was performed by the authors with consultation from an independent adjunct professor which did not have any connections to the case study although had a vast knowledge of the methods used for the analysis.

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4 Define

Atlas Copco BLM is providing high-quality equipment to customers over several different industry segments. This equipment includes both high-accuracy instruments and quality assurance solutions to ensure the highest possible quality of tools and tightenings. One of these solutions is the STbench that provides the customer with an opportunity to test the capability of the tools without interrupting the manufacturing process. The bench simulates the characteristics of a real joint; hence, enables an accurate assessment of the tools performance.

The brakes on the bench simulates a joint by providing resistance towards the torque created by the operating tool. The created resistance is operating under a control system with two PID- controllers that aims to ensure that the behavior of the joint is linear and follows a target line based upon the target torque and angle, ^𝑑𝑇

𝑑𝛼, regardless of disturbance.

Since Atlas Copco BLM´s customers often are aiming to increase their productivity, it is natural that the speed of their tools are increased as well. However, the standards for the quality performance of the tools remains the same. The purpose of the STbench is for the customers to ensure that their tools are conforming to the demanded quality performance of tightening, the bench should therefore be robust enough to operate under high speeds. In certain situations of high tool speed, the bench was not able to simulate joints accurately and the customer was forced to use mechanical transducers or move over to an older version of the control system, which was not as accurate and demanded longer testing times. Furthermore, the older version cannot control angle divergence over time which in practical terms means that it is an open- loop system that does not correct itself for disturbance.

Therefore, it existed an opportunity to improve the robustness of the STbench so it could operate well during high and low tool speeds and for Atlas Copco BLM to meet the demands of their customers and keep their position as market-leader (Atlas Copco, 2020). The scope of the case study was to identify what components of the STbench affected the robustness during high tool speeds and how it could be improved. The goal was to increase the operability of the bench to a speed of 500 RPM, whilst not sacrificing performance.

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5 Measure

To evaluate and understand what components affected the robustness of the STbench a cause- and-effect diagram was useful (Montgomery, 2013b), see Figure 12. The diagram was created by the authors and validated with the R&D unit responsible for the bench. The cause-and-effect diagram visualizes components (underlined) of the STbench together with their contributing factors (italic).

Figure 12. Cause-and-effect diagram where the text in bold is the final selected component to improve.

During a meeting with the competence team manager, senior firmware engineer and control systems engineer regarding the cause-and-effect diagram it was realized that an investigation of the control system, more specifically the PID-controllers (bold in Figure 12) was of interest.

This investigation was of interest since during high tool speeds the bench was programmed to switch over to an older version of the control system. The switch was not desirable but the older system was able to handle the high tool speeds which the new version was not. The PID- controllers had not been extensively examined due to time resources but were known, according to the control systems engineer, to have an impact on the robustness of the STbench.

Vlachogiannis and Roy (2005), Lee and Kim (2000) and Goodwin et al. (2001) also mentions that PID-controllers affects the robustness of a control system. Furthermore, a robust controller is defined as a controller's tolerance towards changes in process parameters (e.g. tool speed) and it was thought that tuning of the PID-controllers might enable the new control system to handle higher tool speeds than previously and hence, it became the focus of this case study.

The switch between the two control systems was based upon the target torque (TT), target angle (TA), tool speed (v) as well as which type of brake that was used. Since this case study was limited to focus on the 50 Nm brake, the following reasoning will only be valid for that specific brake. The switch compares the maximum torque rate of the brake (^𝑑𝑇^{𝑏𝑟𝑎𝑘𝑒}

𝑑𝑡_{𝑏𝑟𝑎𝑘𝑒}) with the torque rate of the tool (^𝑑𝑇^{𝑡𝑜𝑜𝑙}

𝑑𝑡_{𝑡𝑜𝑜𝑙}). If the ^𝑑𝑇^{𝑡𝑜𝑜𝑙}

𝑑𝑡_{𝑡𝑜𝑜𝑙} was higher than the maximum torque rate of the brake, the bench switched over to the older version of the control system, otherwise it used the new version.

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Equation 2 shows the value for the maximum torque rate of the 50 Nm brake and equation 3 shows how to calculate the torque rate for the tool.

𝑑𝑇_{𝑏𝑟𝑎𝑘𝑒}

𝑑𝑡_{𝑏𝑟𝑎𝑘𝑒} = 625 (2)

𝑑𝑇_{𝑡𝑜𝑜𝑙}

𝑑𝑡_{𝑡𝑜𝑜𝑙} = 3 ∗ 𝑇𝑇 ∗ 𝑣 𝑇𝐴

(3)

Therefore, the aim was to find settings for the PID-controllers that made them robust enough to handle higher tool speeds. A target torque was decided to 40 Nm with a target angle of 90°, due to that it was a common joint used by customers and hence, the result would provide Atlas Copco BLM with the most value. According to the calculations this meant that with a speed above 468 RPM the bench would switch over to the old control system.

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6 Pre-analyze

The two PID-controllers, which are controlling the hydraulic brake, only use the P- and I- elements. The D-elements were not used due to problems regarding the systems instability. This means that there were a total of four factors influencing the controllers. Furthermore, since the purpose of this case study was to make the bench robust enough to handle both low and high tool speeds, the speed of the tool was also a potential factor. This sums up to five experimental factors, see Table 4. The range for the two levels of the P- and I-elements were decided based upon previous knowledge of the control systems engineer and trial experiments, described in section 7.1. The range for the levels of the tool speed were based upon equation 3, where the high level was high enough so that the bench normally would switch over to the old control system and the low level was at a speed where the bench used the new control system. The bench used during the experiments was programmed so the switch to the old control system would not occur and the collected data was therefore only from the new control system.

Table 4. Experimental factors and their levels.

Control variable Factor name Default Precision Low level Center points High level

P.Torque A 1.5 - 1 2 3

I.Torque B 80 - 40 100 160

P.Pressure C 2 - 1 2.5 4

I.Pressure D 50 - 25 62.5 100

Tool speed E 250 rpm ±5% 436 RPM 468 RPM 500 RPM

Response variables

The experimental factors were based upon the second approach recommended by Capaci et al.

(2017) where the set-points of the inputs were used. The adaption made in this case study was that the experimental factors are the set-points of the controllers. Therefore, it was recommended that the response variable should be a process performance measurement (Capaci et al., 2017). Hence, ISE was used as the first response variable, which was also used in a similar study by Vlachogiannis and Roy (2005). Equation 1 in section 2.2 presents the mathematical definition of ISE and Figure 13 shows a visual explanation of the response variable. Since the measured angles in the raw data were not equally distributed, it was of importance to use an integral formulation to avoid that some values would be weighted higher than others, which made the response variable ISE suitable in this case study. It would also provide a fair and accurate explanation of the joint’s behavior (Clark, 1961).

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Figure 13. Visual explanation of the error area measured in ISE.

The calculation of the ISE was performed with continuous variables because of the challenge of finding a well-fitted model for the raw data. Hence, the target function (ysp) was also transformed to discrete variables. The target function was defined as equation 4.

𝑦_𝑠𝑝 = 𝑚𝛼 + 𝑞 = 0.222𝛼 + 2.5 (4)

The slope (m) of ysp was calculated in relation to the target torque and angle, see equation 5. In this case study the target torque was 40 Nm and the target angle 90° (i.e. a hard joint). Moreover, the Start-Final-Angle (SFA) is 50% of the target torque and indicates where the measurement of the angle begins.

𝑚 =𝑑𝑇

𝑑𝛼 = 𝑡𝑎𝑟𝑔𝑒𝑡 𝑡𝑜𝑟𝑞𝑢𝑒 − 𝑆𝐹𝐴

𝑡𝑎𝑟𝑔𝑒𝑡 𝑎𝑛𝑔𝑙𝑒 − 𝑠𝑡𝑎𝑟𝑡 𝑎𝑛𝑔𝑙𝑒 =40 − 0.5 ∗ 40

90 − 0 = 0.222 (5)

The y-axis intersection (q) in equation 4 was 5% of the brake’s capacity. Since this case study was focusing on the brake which has a maximum capacity of 50 Nm, q was equal to 2.5, see equation 6.

𝑞 = 5% 𝑜𝑓 𝑚𝑎𝑥𝑖𝑚𝑢𝑚 𝑐𝑎𝑝𝑎𝑐𝑖𝑡𝑦 = 0.05 ∗ 50 = 2.5 (6)

As seen on Figure 13 there were also tolerance limits included. These limits were ±5% from a linear regression of the raw data, based upon the ISO 5393 (International Organization for Standardization, 2017) for hard joints, which is an important standard for Atlas Copco BLM and their customers. Furthermore, because of Clark’s (1961) and Shinskey’s (1990) reasoning about distinguished instability when only analyzing ISE, a second response variable (OK) was introduced which describes the percentage of data points which were outside of the 5%

tolerance limits. The response variable OK could therefore help to detect these small oscillations and investigate how well the joint was following ISO 5393. The data used to create the linear regression are from 10 to 100% of the target torque level. In this case study, the target torque was 40 Nm, which means that the linear regression was calculated from the data between 4 Nm to 40 Nm. A combination of the two response variables were analyzed, where both ISE and OK had to be minimized. Table 5 summarizes the response variables.

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Table 5. Response variables.

Response Tool speed Nominal

value Precision Comments

Integral-squared- error (ISE)

436 RPM 149.9793

Four decimals

Measured through integrating the squared error between the real data points and the desired data points.

468 RPM 174.5290 500 RPM 235.0606

OK

436 RPM 34.60%

Two decimals

Percentage of how many points are outside of the tolerance limits.

468 RPM 39.32%

500 RPM 41.04%

Other influencing factors

The factors that were not of interest for the case study but would affect the response were held constant during the whole experiment, as recommended by Montgomery (2013a). These factors and an explanation of their potential effect on the response are shown in appendix A, Table A 1. Moreover, the nuisance factors were the factors that could affect the result but were not possible to hold constant or control. Certain strategies were taken in order to avoid large disturbance on the response from the nuisance factors, which are described further in appendix B, Table B 1. Both the held-constant factor and the nuisance factors were identified during the workshop about the cause-and-effect diagram, shown in Figure 12.

Figure 14 is a visualization of the control system process with the experimental factors and the two responses. It also shows where the potential nuisance factors might have affected the process.

Figure 14. The process of the control system.

Improving robustness of a PID-controlled measurement system through Design of Experiments