Driver Circuit for an Ultrasonic Motor

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Institutionen för systemteknik

Department of Electrical Engineering

Examensarbete

Driver Circuit for an Ultrasonic Motor

Examensarbete utfört i Elektroniksystem vid Tekniska högskolan vid Linköpings universitet av

Henrik Ocklind

LiTH-ISY-EX–13/4659–SE 2013 TEKNSIKA HÖGSKOLAN LINKÖPINGS UNIVERSITET

Department of Electrical Engineering Linköpings tekniska högskola Linköpings University Institutionen för systemteknik S-581 83 Linköping Sweden 581 83 Linköping

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Driver Circuit for an Ultrasonic Motor

Master thesis performed in Electronics Systems at Linköpings Institute of technology

By:

Henrik Ocklind

Supervisor: Ove Gustafsson Flir Systems

Anders Wistrand

Flir Systems

Joakim Alvbrant

ES, ISY

Examiner: Oscar Gustafsson ES, ISY

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Abstract

To make a camera more user friendly or let it operate without an user the camera objective needs to be able to put the camera lens in focus. This functionality requires a motor of some sort. Due to its many benefits the ultrasonic motor is a preferred choice. The motor requires a driving circuit to produce the appropriate signals and this is what this thesis is about. The main difficulty that needs to be considered is the fact that the ultrasonic motor is highly non-linear.

This report will give a brief walk through of how the ultrasonic motor works, its pros and cons and how to control it. How the driving circuit is designed and what role the various components fills. The regulator is implemented in C-code and runs on a microprocessor while the actual signal generation is done on a CPLD (Complex programmable logic device). The report ends with a few suggestions of how to improve the system should the presented solution not perform at a satisfactory level.

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Acknowledgements

I would like to extend my gratitude to Flir Systems for the opportunity to do this project, it has been very rewarding. Furthermore I would like to thanks my supervisors at Flir, Ove Gustafsson and Anders Wistrand, for their support and help to make things run smoothly. I would also like to thank my supervisor at ISY, Joakim Alvbrant and my examiner Oscar Gustafsson for their valuable insights. A special thanks goes out to my objector, Gustav Wallin for having the patience of an angel.

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Chapter 1 Introduction

This chapter presents the background, purpose, goals and delimitations of the thesis along with the method and necessary tools.

1.1 Background

This thesis project was performed at Flir Systems. Flir is a company that works with thermal imaging and more specifically they design and manufac-ture infrared cameras. A lens made out of germanium will look solid black to the human eye, but to infrared light the lens is transparent. However the rules of optics still apply so the lens needs to be in focus to get a clear image. One way of doing that would be to let the user manually tune the lens position, but this is time consuming and not always a practical solution since some of the cameras made at Flir need to operate on its own or need to be controlled remotely, for example in surveillance scenarios. That is why the camera objective usually has a built in autofocusing system which is a driving circuit paired with a regulator. The purpose of this system is to place the lens at the appropriate position by controlling a motor that is connected to the lens. In this case the motor used is an ultrasonic motor. These motors are very popular for this kind of application because they are ring shaped and thus fit very well into the design since most camera objectives are cylin-drical. Other advantages include low noise, quick response and the fact that it is a more durable solution compared to a regular electrical motor.

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1.2 Purpose

Ultrasonic motors comes in different shapes and sizes as well as with different properties. The company that makes the motors do not sell the associated electronic driver circuits so it is up to customer to create their own. The project presented in this report is a continuation of a previous project where a driver circuit was developed for a motor with a diameter of 65 mm. Fukoku is the company that made this motor and they also manufacture a motor with a diameter of 12 mm. The smaller motor has a number of advantages, for example, it requires less space (which can be seen in figure 1.1), weighs less, has a lower power consumption and is cheaper. In theory it should be possible to modify the existing circuit board for the larger motor to control the smaller one. However, the motors works in different frequency ranges, has different properties and ultrasonic motors (USM) suffers from non-linearities. This project will find out if it is possible and how it is done.

Figure 1.1: Stators for the big and small motors.

1.3 Goal

The goal of this thesis is to develop a driving circuit for a 12 mm ultrasonic motor that performs on the same level regarding speed and response time as the circuit for the bigger motor. What this means is that new code for the microprocessor and the complex programmable logic device (CPLD) will be developed, specifically the code that regulates the system. Furthermore there will be a theoretic study into possible improvements in the architecture of the circuit board.

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1.4 Delimitations

The circuit board is already made and the overall architecture will not be altered, thus the components are predetermined. The microprocessor is a Texas Instruments MSC1202Y2 which has a built in analogue to digi-tal converter(ADC), it belongs to the 8051 family. The CPLD is a Xilinx XCR3064XL, which has 64 macro cells. The whole circuit is synchronised by a crystal oscillator which oscillates at 40 MHz, this clock will be referred to as the system clock.

1.5 Method

The first phase of this project will be to get a basic understanding of how the ultrasonic motor works. This will be followed by an analysis of the previous project, in essence that means that all the written code (C++, assembler and VHDL) and all the components in the circuit will be scrutinized and analysed. There is no existing coding environment so as a part of the project the necessary programming tools needs to be selected and then implemented into the environment. These tools will be described later in this chapter. To verify the code an I2_C_{-communication between a computer and the circuit}

needs to be established. Most of the work concerning the regulator will be done through simulations in Matlabs Simulink.

1.6 Devices

This section gives a short explanation of the microprocessor and the CPLD.

1.6.1 Micro Processor

Texas Instrument MSC1202Y2 is the processor used in the circuit, it has a built in ADC/DAC and a 4 kB flash memory The processor core is based on the 8051 architecture which was developed by Intel in the early 1980s. However, the processor used in this thesis is an improved version, it does accept the same instruction set, but it processes data approximately three times faster [1]. The 8051-architecture is a widely used standard and because of this there exists a large number of different compilers and the generated code can be downloaded to any 8051-controller if needed. Some properties worth mentioning for the controller includes the 8 bit CPU, 8 bit data bus and the 16 bit address bus [2] and the general core can be seen in figure 1.2.

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Figure 1.2: The standard 8051 core.

Probably the most defining feature of this chip is the ADC and it is a rather central part of this project, more on this later. The ADC utilizes a Sigma delta converter with a 16 bit resolution.

1.6.2 Complex Programmable Logic Device

Xilinx XCR3064XL is the CPLD chip used. A CPLD unlike a FPGA does not require an external configuration memory to boot and is therefore suitable for this type of circuit. VHDL is the chosen language for programming the CPLD.

1.7 Environment

This section will list the various programs and tools needed to for implemen-tation, simulations and validation.

1.7.1 SDCC

SDCC is an abbreviation for Small device C compiler and as the name im-plies it is an ANSI C compiler and includes other functionalities as linker, assembler, debugger and simulator [3]. It is an open source project and is distributed under the GNU general public license. It is possible to use with a wide variety of processors including processors of the 8051 architecture.

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1.7.2 Modelsim

Used to debug and simulate VHDL code before it is downloaded to the CPLD.

1.7.3 ISE Webpack

ISE Webpack is a free of charge program developed by Xilinx. It is used to synthesize and download code to the CPLD.

1.7.4 Matlab

The regulator will be tested and verified in Matlab before it is implemented in the actual system.

1.7.5 Other Tools

In addition to previously mentioned tools there are some other required tools which have no need to be described in detail. Those include an oscilloscope, a voltage meter, some circuits developed by Flir to program the microprocessor and the CPLD and also equipment needed to communicate with the driving circuit through I2_C.

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Chapter 2 The Ultrasonic Motor

This chapter will explain how the ultrasonic motor (USM) works and how it differs from a regular electromagnetic motor.

2.1 The Piezoelectric Effect

To get a grasp of how the USM works the principle of the piezoelectric effect needs to be understood. The discovery of piezoelectricity is attributed to the Curie brothers who made the discovery in the late 19th century while studying Rochelle salt [5]. Piezo is Greek and translates into pressure so in pure English the effect would be called pressure-electric. There are a number of materials that exhibit piezoelectric properties, but they all work the same. If pressure is applied to the material, or more specifically if the material is deformed, an electric field is generated and thus an electric potential. For this project the opposite is desired and since the effect is reversible that can be achieved. An electric field with a positive potential will make the material expand, this is illustrated in figure 2.1. The short version of the piezoelectric effect would be that it describes a material that can convert mechanical to electrical energy and vice versa.

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Figure 2.1: How an applied voltage affects the piezoelectric material.

2.2 The Barth Motor

The human ear can detect sound waves ranging from 20 Hz to 20 kHz which is commonly known as the audible frequency range. Signals with a higher frequency operates in the ultrasonic region and those kind of signals are rather easy to create using a piezoelectric vibrator of some sort. It has been known for some time that the energy density of such a vibrator is higher than that of an electromagnetic motor, up to ten times higher [4]. However there would be a while before anyone attempted to construct a motor using the piezoelectric principle. In 1973 H.V. Barth published his work on an USM, it

m

Figure 2.2: H.V. Barth’s motor

consisted of one rotor and two vibrators. It is a fairly straight forward design, when the left vibrator is excited the rotor moves clockwise and in the opposite direction when the right vibrator is excited [4], a model is illustrated in figure 2.2. Since then many different motors have been developed, including the wedge-type, the twist coil, various linear motor designs and also the motor used in this project, the travelling wave motor.

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2.3 The Travelling Wave Motor

The travelling wave motor was developed by Toshiiku Sashida in 1982. There are some variations of this type of motor and the one used in this project is of ring type.

2.3.1 Architecture

The overall architecture of this motor is pretty similar to an ordinary elec-tromagnetic motor. It consists of two main parts, the stator and the rotor. The stator is stationary in the sense that it does not move along the rotation axis (cylindrical coordinates), it does however move up and down, but more on that in the next section. The stator is made by combining two parts, the piezoelectric part and on top of that an elastic body which is recognisable by its saw tooth silhouette.

Figure 2.3: Left: The different parts of the USM. Right: A motor, the stator is clearly visible.

The rotor is the moving part of the motor, the spring pushes the stator and rotor assembly together and the oscillations in the piezoelectric material causes the rotor the rotate, hence the name. In an ordinary electromagnetic motor the rotor is not in physical contact with the stator, however the driv-ing principle of the USM depends on friction between the stator and rotor. Therefore a thin lining is applied to the rotor to increase friction and thus decrease sliding energy loss. Also the lining increases the durability of the motor. Thus forming the rotor assembly.

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and that is why there is a spring in the bottom. Then there are a number of plates to equalize pressure in the design and some protective sheets to protect against wear and tear. What the motor looks like under the hood is illustrated in figure 2.3.

2.3.2 Operating Principle

The piezoelectric material is connected to a two-phase sinusoidal voltage with a 90 degree phase shift, in other words a sine and a cosine phase. The un-shifted voltage will be called phase A and the other one phase B henceforth. As described in figure 2.4 there are alternating nodes with different polar-ization spread out around the ring, when a positive voltage is applied to a node it will cause positive nodes to expand and negative nodes to shrink, the opposite is true for a negative voltage.

If only one phase is active a standing wave will be created, even though the voltage is only applied to a little less than half of the ring the wave will propagate through the entire ring. When the other phase is activated the wave will move which is called a travelling wave. Imagine a fixed point on the surface of the piezoelectric disc, this point will move up and down in an elliptical trajectory which is illustrated to the right in figure 2.4. There are two main stages to convert the electrical energy to mechanical ditto. In the first stage the piezoelectric electrodes becomes excited which causes vi-brations in the material, in the later stage these vivi-brations are transmitted through to the rotor which, given enough pressure, will move the rotor in the opposite direction of the travelling wave.

Figure 2.4: Left: Piezoelectric disc. Right: Driving principle of an USM.

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2.4 Advantages of the Ultrasonic Motor

This section will explain the various advantages of the USM.

2.4.1 No Influence of Magnetic Fields

This is perhaps one of the most important aspects of the USM since an electromagnetic motor may not function properly while under the influence of a magnetic field. The principle of electromagnetic induction states that a fluctuation in the magnetic field will create an electric field and the USM is no exception, however the effects are negligible. Assume a 1 T fluctuation in the magnetic flux density at about 60 Hz, this will create an electric field of about 100 V m−1 which is 100 times lower than the normal field strength of

the piezoelectric material [4]. Since the motor does not utilize a magnet nor a coil it will not generate magnetic fields either.

2.4.2 Driving Properties

Since the motor operates at a frequency range above the audible range the motor is very quiet. Compared to an electromagnetic motor the USM has considerable higher torque, a factor of somewhere between 10 and 100 com-pared to a electromagnetic motor of a similar size [6]. The difference is largest at low speeds. Moreover the drive does not need any gears and because of this and the low inertia of the rotor the motor has a very quick response for both start and stop (about 1 ms [4]). As soon as the ceramic starts to vibrate the rotor will start moving and the moment it stops the stator will work as a brake. This makes the motor easy to control and suitable for machines where high precision is needed.

2.4.3 Structural Properties

The motor is ring shaped and thus hollow, this makes the motor easy to fit in your design. Furthermore the USM is very light The structure is rather simple and therefore easy to manufacture.

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2.5 Disadvantages of the Ultrasonic Motor

Besides the listed advantages in section 2.4 the USM has its drawbacks.

2.5.1 Friction

The rotor is pressed down onto the stator and it is the friction between these two parts that makes the motor work. However, this also generates a lot of heat. The motor is therefore not suitable for a continuous workload since the temperature would rise to extreme levels.

2.5.2 Non-Linear

It is hard to derive a mathematical model of the motor. This is due to the fact that the motor parameters are hard to obtain. To complicate matters further the values changes over time. As mentioned above the motor gen-erates a lot of heat while running and the change in temperature will effect the performance of the motor. Furthermore the travelling wave can only be considered ideal at the resonance frequency (more on this in chapter 4), the farther the driving frequency strides from resonance the harder it is to pre-dict the motors behaviour. Finally the speed of the motor depends on the input frequency, however the relation is not linear.[6]

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Chapter 3 The System

This chapter will give a description of the driver circuit developed in the previous project.

3.1 Overview

To get an understanding of the circuit the first thing that needs to be done is to figure out what its role is in the system. The whole system can commu-nicate through a I2_{C-bus, other signals include inputs to the circuit, current}

position and wanted position. The output consists of the signals needed to control the motor. In between the circuit converts the input signals to a format that makes sense, put the signals through a regulating algorithm and finally outputs a sinusoidal waveform.

Since the driving circuit is the last step before the motor and the only part of the system that communicates directly with the USM, the circuit is placed around the camera objective on top of the motor. This also means that the circuit board is shaped like a ring. Its position relative to the camera can be seen in figure 3.1.

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Figure 3.1: A somewhat complete camera, the circuit is clearly visible around the lens.

3.2 Circuit Design

This section will describe the three main parts of the system. Also present in the design are a temperature indicator, electrostatic discharge protection and a crystal oscillator that oscillates at 40 MHz and is the clock for the CPLD.

Figure 3.2: The main blocks in the design.

3.2.1 Microprocessor

As in most embedded systems the microprocessor is responsible for most of the computations in the system. In this case the MCU has a built in ADC which comes in handy since the current position (labelled Pos in figure 3.2)

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is an analogue signal. The signal is generated by a potentiometer that is physically attached to the lens and thus will change value when the lens moves. The signal is then converted to a discrete number and sent to the regulator. The regulator in question is a traditional PID-regulator. The regulator computes in which direction the motor needs to spin and how fast, this is done by outputting a six bit number to the CPLD. This number tells the CPLD at what frequency to run the motor, this is explained more in section 3.2.2 This means that the speed of the motor, measured in Hz, can only be one of 64 (26_{) predetermined values. So using a lookup table the}

computed value is rounded to the nearest value.

The I2_{C-bus makes it possible for a user to communicate with the circuit}

while the system is running. The bus makes it possible to manually set the lens position or the running speed of the motor, it is also possible to change the regulator’s coefficients, in essence the proportional (P), integral (I) and derivative (D) coefficients.

3.2.2 Complex Programmable Logic Device

The CPLD block is basically a state machine with four states. When the system is running and the wanted position does not equal the current posi-tion the CPLD loops through the states and each state means that one of four output channels is set to logical one. The system clock runs at 40 MHz, this means that one clock pulse has a time period of 25 ns. An easy way of creating a square wave generator is to let the output signal be high for a predetermined number of clock pulses. Let the square wave be logical one for 284 clock pulses and with 25% duty the that corresponds to a square wave that runs at approximately 35 kHz. Add the six bit number from the MCU and the output signal can range from 28 kHz to 35 kHz which is suitable for the 65 mm motor. The output frequency can be expressed as a function of this 6-bit number:

fout(n) = _{(284+n)∗4∗25∗10}1 −9, {n = 0, 1, 2, 3, ..., 63}

Figure 3.3 shows the output patterns generated from the CPLD while run-ning, why this particular pattern is desired is covered in the next section. It is also worth noting that if you reverse the order in which the signals goes high, the motor will spin the other way.

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Figure 3.3: Output signals from the CPLD while running.

3.2.3 The Inverter Stage

The CPLD will generate a digital signal, however the motor needs a analogue signal to run. That is why there needs to be an inverter stage. There are two identical inverters working in parallel where one generates phase A and the other phase B.

The outputs from the CPLD are connected to the gate of a NMOS transistor, in essence the transistor works as an ordinary switch. When the signal at the gate is high the transistor is open and current flows through it. These drain of these transistors are wired each respective end of a transformer with a middle tap where the circuits power supply is connected. Consider the schematics in figure 3.4, when channel 1 is logical one it will make current flow upwards through the transformer and onwards through transistor N1. This will create an amplified square wave in the right side of the transformer according to the laws of inductance. When channel 2 is logical one the current will flow downwards instead creating a negative square wave. The output can be seen in figure 3.5.

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Figure 3.4: The schematics of the inverter stage.

The outputs from the transformers are starting to resemble a sinusoidal waveform and it will be more apparent once the motor is connected. As it turns out the motor has a clear capacitive behaviour and will thus work as a capacitive load, effectively creating a LC-filter. As mentioned in section 2.4.2 it is hard to pin point an exact value of this capacitance and it will change overtime. However the closer the wave is to the resonance frequency the more sinusoidal the inputs to the motor will become. Luckily the motor does not require a perfect wave to run and with this set up the LC-filter is good enough to provide a valid signal for all the relevant frequencies.

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Figure 3.5: Inducted voltages at the secondary coil.

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Chapter 4 Driving the Motors

This chapter will cover how the input frequency correlates with the speed of the motor and as well similarities and differences between the two motors. Furthermore it will also discuss the changes needed in the circuit design.

4.1 Speed Characteristics

Figure 4.1: Rotor speed versus drive frequency, fr marks the resonance fre-quency.

A typical frequency response of a non-specified USM is shown in figure 4.1. In other words, the graph will look like this no matter the properties of the motor. However the exact numeric values will be unique for every type of motor and to some degree even every individual motor. To get some perspective, the range of input frequencies that will make the motor spin allows 4f to range from somewhere between 2 to 6 kHz depending on the specific motor. The resonance frequency can be at just the edge of the audible sound (20 kHz) up to 5 MHz.

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The speed of the motor is proportional to the amplitude of the vibrations in the piezoelectric material. As mentioned in section 2.4.2 the generated friction heat will affect the amplitude of these vibrations causing a drop off in speed, it may be as much as 20%. To complicate matters further not only do the speed decrease the resonance frequency (fr) will change as well, it may

decrease by as much as 400 Hz [7]. Temperature will not decrease speed with an equal amount over the whole frequency spectra, it will have a different effect on each frequency level. Below is a rough illustration of how the rise in temperature due to friction decreases the speed, the data was presented in the Journal of power electronics [8]. The measurements have been performed on a USM with a resonance frequency of around 40 KHz.

Figure 4.2: How temperature affect the output speed.

One further thing worth noting is that the load torque will also affect the system. Load torque is the minimum amount of force the motor needs to apply to the system to keep it stable. For example, imagine a motor in a crane that lifts some kind of weight, the load torque is the force required to keep the weight in place. If the load torque is increased the internal impedance of the motor will increase and thus the input voltage needs to be increased in order to make the system perform at the same level. The speed of the motor will naturally decrease since the amount of work the motor has to do has increased. This is however fairly linear, so it is possible to predict the outcome beforehand with some accuracy. Since the required force to move the camera objective is fairly predictable the load torque is constant for this purpose.

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4.2 Motor Diameter and Performance

This section will explain how the diameter of the ring motor affects the performance. Figure 4.3 gives a graphic presentation of the results here.

4.2.1 Torque

The torque when the motor starts up is roughly some constant multiplied with the diameter cubed. It can be assumed that the rated torque or in other words the running torque is the starting torque times a constant. So the torque is proportional to the diameter cubed [4].

T orque_{∝ (Diameter)}3

4.2.2 Speed

The speed is measured in revolutions per minutes (RPM). When there is no load attached to the motor the speed is approximately inversely proportional to the diameter. As in the previous section it is assumed that speed changes due to different loads are the no-load speed times a constant. Hence the speed is inversely proportional to the diameter.[4]

Speed∝ Diameter1

4.2.3 Output Power

The output power of an electrical motor is the product of the motors torque and the angular speed. Given the results from the two previous sections the output power in relation to the diameter of the motor will not be to difficult to derive. The output power is proportional to the diameter squared. The maximum output power is obtained at half the no-load speed since the motor is most efficient then. Due to sliding and deformation the output power decreases after this.

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Figure 4.3: The diameter of the motor and how it effects performance.

4.3 A Comparison of the Two Motors

This section will examine how the two motors differs. Both motors are man-ufactured by the Fukoku company. The larger motor bears the name High torque 65 and will be referred to as HT65 in the following text, the other motor is the Pencil 12 and will be labelled P12.

Specification HT65 P12 Diameter [mm] 65 12 Weight [g] 27 5 Resonance frequency [KHz] :31 :59 Driving voltage [Vrms] 30 70 Power consumption [W] ≤ 1 ≤ 1.2 Idling speed [rpm] ≥ 65 ≥ 500 Rated speed [rpm] ≥ 60 ≥ 400 Max torque [gcm] ≥ 800 ≥ 50 Efficiency [%] ≥ 20 ≥ 10

Table 4.1: Some notable specifications for the two motors

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4.3.1 Frequency

If the nodes in the piezoelectric material is placed with the same interval for a smaller and a larger ring it falls naturally that the resonance frequency will increase since the wavelength will decrease. The frequency range will also increase if the stator thickness increases and since HT65 has a stator thickness of 7 mm compared to the P12 which is 12 mm across the steep rise of the resonance frequency is mitigated somewhat. In the end the value of P12 is approximately double that of the HT65, this means that the CPLD needs to work at double the speed compared to the original circuit. This is not a problem per se, however it is an obstacle to overcome, especially concerning the system clock. More on that in chapter 5.

4.3.2 Speed and Frequency

On the next page there are two graphs of motor speed and how it relates to input frequency. Figure 4.1 showed a graph for a general motor, for the purpose of this thesis the left side of the resonance frequency is not interest-ing. This is due to the fact that it is much harder to control the motor with a regulator that works in that area. It has also been previously mentioned that the resonance frequency is rather fickle and is prone to change while running. Therefore it is advisable to only use frequencies 500 Hz or more over the specified resonance frequency for your control algorithm. The motor is fast enough without running it at maximum speed and the drawback of having a situation arise where the regulator think it is increasing the speed while it is in fact decreasing it makes it an unnecessary risk. Worth noting about the graphs is that the one for HT65 was supplied by the manufacturer and the one for P12 is measurements made during this project. Some imme-diate observations include the faster speed of P12 and that its active range is about twice as large as for the HT65. The measurements where performed with a minor load of a small metallic screw.

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Figure 4.4: RPM vs. frequency, measurements of P12.

Figure 4.5: RPM vs. frequency, supplied by the manufacturer (HT65).

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4.3.3 Torque and Efficiency

A look at table 4.1 shows that the torque is considerable smaller for P12 and while this is a fact it does not have that large impact on the system. The P12 has enough torque to move the camera lens however it will reduce the speed of the motor by a larger fraction than for the HT65.

The power consumption is larger for the smaller motor and according to figure 4.3 the output power is smaller. It follows that the power efficiency will be worse than for the larger motor. Since the camera for which this project is aimed at is a handheld device this is possible the biggest drawback with P12.

4.3.4 Mechanical Differences

The P12 is lighter and smaller and while this looks good on paper the size of the motor causes a mismatch in regards to the size of the motor and the size of the camera lens. The HT65 is roughly the same size as the camera lens and so they are assembled directly to each other. The P12 needs some sort of mechanical help. While the HT65 is clearly a ring structure the P12 looks more like a disc at a first glance. There is a little hole though where a screw can be fitted, this screw can be fastened directly to the camera lens or it could be connected to a cog wheel, essentially creating a gear.

In the case without gears the inertia of the camera lens would be greater than that of the motors rotor, this will reduce the motors acceleration and retardation. In the other case where a gear is placed between the motor and the camera lens it will reduce the overall speed of the system, but will maximize the possible torque[4]. The latter case is preferred here since the system will become quicker and stronger and that is more valuable than pure speed. There is however another drawback with this design and that is space, a gear will need more space which will force the motor to be placed outside the ring and the camera objective.

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Figure 4.6: A possible gear solution.

4.4 Changes in the Circuit

The driving voltage for the P12 is more than twice the amount of the required voltage for HT65. This means that the transformers in the circuit will need to be replaced by new ones with a larger ratio between the number of turns on each coil. If for some reason it is desired to use the same circuit to drive a number of different motors the new transformers will not stand in the way. A higher Vrms will make the larger motor go faster, since the expansions and contractions in the piezoelectric material will be stronger. So this will need to be adjusted for, otherwise this is not a problem.

There is a small difference when it comes to the FPC. P12 has the three normal inputs, phase A, phase B and ground, the same is true for HT65. HT65 has one additional output as well, a feedback node which is used to determine the speed of the rotor. This node is not connected in the original design though so it will not make this project any harder. However the three inputs are not in the same order on the two motors which means that some rewiring is required.

Changes and additions in the VHDL- and C-code and the electronic design will be discussed in later chapters.

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Figure 4.7: The circuit board after the necessary changes.

4.5 End of Applied Study

Due to some restructuring at Flir Systems there has been a lack of necessary equipment and material to finish the thesis as it was originally intended. Ev-erything so far has been tested on a real camera objective and works well, the motor can spin in either direction and the circuit board can communi-cate with the camera system. However, it has not been possible to test the regulator while downloaded into the microprocessor and thus the rest of this report is based on simulations and a theoretic study.

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Chapter 5 The Regulator

At this point it is possible to drive the motor in both directions and at some predetermined frequencies. Since the aim of the project is to develop a circuit that can put the lens in focus without human intervention there needs to be a regulator. This chapter will give a brief explanation of the PID controller and how it was implemented.

5.1 PID Controller

PID stands for proportional, integral and derivative and is a common way to regulate a system. One does not need to have complete knowledge about the underlying system to create a working PID controller and that is one of its strengths. Even if it is not possible to measure noise affecting the system the controller will handle it since there is a feedback loop. The three parts of the PID controller are more or less independent and it is possible to create a working regulator with only one or two parts, in some cases it is even desired.

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5.1.1 Proportional Regulating

u(t) is the desired output signal and y(t) is the actual one, subtract those

two signals and you get the current error signal e(t). Proportional regulating simply means that the error signal is amplified by a constant Kp(or reduced).

This is the most commonly used feedback controller and have been around since ancient times [9]. For the application of this thesis this part of the regulator means that the farther away the lens is from the target position the faster the motor spins. This type of regulating requires a non zero error and thus the term P0 is introduced. The proportional part is given by:

Pout = Kpe(t) + P0

5.1.2 Integral Regulating

By just using proportional regulating it is not possible to completely elimi-nate noise or disturbance. The integral term is the sum of the past errors. For the purpose of this thesis it calculates how much closer the lens is to the target point now than it was in the beginning, compares that with how much distance left and adjusts speed accordingly. The integral term speeds up the system, but there are some dangers. Set the Ki value too high and there is a

risk that the regulator will overshoot its target, that is not necessarily a bad thing, but if the overshoots becomes bigger and bigger that means trouble. Overuse of past values will as a rule lead to instability [9]. Its greatest con-tribution is that it eliminates the steady state error, or the error when the regulator has made its target. The integral term is given by:

Iout = KiR0te(t) dt.

5.1.3 Derivative Regulating

Relying too much on measured values can lead to instability, that is why a derivative term is introduced. This term gives the regulator a chance to predict future errors and therefore it can adjust for those errors before they happen. What happens is that this term slows down the rate of change and tries to decrease or eliminate overcompensating of the system. This term can also cause instability, since the term is derivative it is sensitive to transients caused by noise. This term is given by:

Dout = Kd_dtde(t)

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If the proportional part is added the following terms are obtained through Taylor series [9]:

x(t) = Kpe(t) + Kd_dtde(t) ≈ Kpe(t + τD)

τD = K_Kd_p

Where τD is how far the system can plan ahead.

5.1.4 The whole regulator

Figure 5.1 and the previous sections gives the following expression for the whole regulator:

x(t) = Kpe(t) + KiR0te(t) dt. + Kd_dtde(t)

5.2 Tuning the System

The ground rules are now established, but we still need some way to de-termine the values of Kp, Ki and Kd. A good start is the Ziegler-Nichols

method.

5.2.1 Ziegler-Nichols Method

The Ziegler-Nichols method was developed by John G. Ziegler and Nathaniel B. Nichols and was published in their book Optimum settings for automated

controllers from 1942. To determine appropriate values for the PID

con-trollers coefficients begin by disconnecting the integral and derivative terms, in essence setting Ki and Kdto zero. Now by set the value of Kp on the edge

of a stability or in other words make the signal oscillate at a constant am-plitude around its target value. Note which value was obtained, in the table denoted as Ku, and what the time period of the oscillation was, denoted Tu.

There is no guarantee that this will produce a good regulator, but in most cases it will be a good starting point. At least one of the proposed set of values will. [9] Regulator Kp Ki Kd Normal PID 3Ku 5 6K5Tuu 3KuTu 40 Some overshoot Ku 3 6K5Tuu KuTu 5 No overshoot Ku 5 6K5Tuu KuTu 5

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5.2.2 Manual Tuning

Chances are that the solution provided by Ziegler-Nichols is not perfect so some tuning will be required. So below is a list of all the coefficients and how an increase in the coefficients value will affect the system.

Coefficient Rise time Overshoot Settling time

Kp Decrease Increase Small increase

Ki Decrease Increase Increase

Kd Minor increase Decrease Decrease

Coefficient Steady state error Stability

Kp Decrease Degrade

Ki Eliminate Degrade

Kd No effect Improve (if Kd is small)

Table 5.2: How an increase in a coefficients value will affect the system

5.3 The Model

The system was simulated in Simulink. However, to do that a model of the system needs to be created. The model in itself is rather simple, just a lookup table that outputs a certain speed given a certain frequency based on figure 4.4. There are some complications however, since the regulator is implemented on the MCU that regulator can not be continuously running since the processor has other tasks that also needs be taken care of. This means that the regulator needs to function in the discrete time domain, the principle for the discrete PID-controller is the same as for time continues controller. This is the obtained expression:

u[n] = Kpe[n] + Ki n

P

i=−∞e[i] + Kd(e[n] − e[n − 1])

Note that Kd is a coefficient divided by the sample time. In the frequency

domain the expression looks like:

U[z] = E[z](Kp+ Ki_z₋₁z + Kdz−1_z )

This type of expression can be handled by Simulink which will be used to simulate the system. To directly translate this expression into C-code can be quite awkward so the expression will be rewritten so the system can be

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realized using only the input and output signals, adders, multipliers and unit delays. U[z] E[z] = Kpz(z−1)+Kiz2+Kd(z−1)2 z(z−1) U[z] E[z](z2− z) = Kp(z2− z) + Kiz2+ Kd(z2− 2z + 1) U[z] = E[z](Kp(1 −1_z) + Ki+ Ki(1 −2_z + _z12)) + U_z[z] From the above expression the model in figure 5.2 is obtained.

Figure 5.2: The model used for simulating the motors behaviour during regulation.

5.4 Regulating the Motor

Ziegler-Nichols method can still be used even though the system operates in the time discrete domain. By replacing Tu in table 5.1 with Td = T_Tu_s where

Ts is the sample time of the system making Td the number of samples in a

period. The sample time chosen for the simulation is 0.05 seconds and the target signal for the regulator is the unit step. In reality the sample time will be smaller than the one chosen, the reason for this rather large value is to really test the performance of the regulator. It will therefore most likely perform better than the results of these simulations indicate.

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The first step is as previously mentioned to set Ki and Kd to zero and

find a value for Kp which makes the ouput signal oscillate at a constants

amplitude. The signal oscillates between zero and two and with the target signal at one the amplitude has to be considered very large. This was ob-tained at Ku = 201.9 and the measured Td = 6 and can be seen in the figure

5.3.

Figure 5.3: The first stage of Ziegler-Nichols method.

Using the values for a normal PID-controller from table 5.1 the newly ac-quired values of Ku and Td will calculate the values of the controller

coeffi-cients. These values gives a raw regulator pictured in figure 5.4.

Figure 5.4: Result after Zeigler-Nichols method. 41

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The result after Ziegler-Nichols is a crude regulator, it might be enough for the purpose of this thesis, but there are a lot of room for improvement. Table 5.2 explains how an increase in a coefficient affects the regulator, using this the regulator can be improved. The performance values most in need of a boost seems to be to decrease settling time and the overshoot. This can be achieved by increasing Kd and maybe decreasing the other two coefficients.

Figure 5.5: The simulation result after some manual tuning.

The overshoot has been drastically improved, there are also some improve-ments regarding rise time and stability. The settling time seems to be about the same and may be hindered by the system, in essence the motor, to im-prove beyond the current value.

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5.5 Poles and Phase Margin

The pole placement and phase margin of the open loop system is of interest. The feedback in figure 5.2 needs to be removed and then by using the lin-earisation tool provided in Simulink the poles and phase margin can easily be computed. Simulink provides the following pole zero diagram in the con-tinuous time domain: There is a pole in origin, since this model is based on

Figure 5.6: The pole zero diagram of the open loop.

approximations and ideal behaviour that means that there is a risk that the real part of the pole is larger than zero and thus making the system unstable. Simulink also provides a bode plot which is shown below.

Figure 5.7: The bode plot of the open loop. 43

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The circuit amplifies signals with low frequencies, as the frequency in-crease the gain dein-creases and levels out at around 11 rad/s where the gain is -18 dB. The phase margin is approximately 40 degrees, this paired with the behaviour of the system makes it likely that the system is indeed stable.

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Chapter 6 Improvements

At this point the system will be able to drive the motor and move the lens to a specified position. In theory it will at least perform adequately. There are still things that can be improved though which will be discussed in this chapter along with advantages and disadvantages of different solutions.

6.1 Evaluation of the Current Circuit

All in all the current circuit is well designed and there is no solution that is obviously better. The MCU lets the user interact with the system even while the system is running thus making the system versatile. It simplifies the development process since you can manually set position, motor frequency and regulator coefficients and also read those values. Furthermore the user is also capable of starting and stopping the system. Of course the MCU could be programmed to read and write other information as well as per the developers wishes. The CPLD is necessary since as mentioned in chapter 5, the processor has other tasks that needs doing and the signal generation is an ongoing process that should not be interrupted.

There is one thing that could use quite a lot of improvement in the current design though and that is the system clock. With the way the signal genera-tion works (explained in secgenera-tion 3.2.2) the period length of the driving signals is an integer multiplied by the period length of the system clock. However, since there are four signals that needs to be generated and only one can be active at a single time it follows that the smallest amount the period length of a given driving signal is 100 ns or in other words four times the system clock period length. This is fine for larger motor where there is approximately 50 valid values between 30 and 35 kHz and they will all make HT65 spin.

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Between 60 and 65 kHz which is the active frequency range for P12 there are only 13. This will negatively affect the regulators performance. Probably the best solution would be to just replace the crystal oscillator with one that oscillates at a higher frequency. If the system clock can not be changed for some reason there are other ways to mitigate this flaw. There are plenty of room left on the CPLD and below two solutions to double the number of valid values is presented.

6.1.1 Clock Doubler

Figure 6.1: The schematics for a simple clock doubler.

One way to solve the current problem is to create a new clock signal. The model in figure 6.1 is bases upon the fact that there is a propagation delay in every gate and flip-flop. When the system clock toggles it will take one Combinatorial logic delay (Tilo) for the new clock signal to go high, it will

remain high for the sum of the time clock to Q-delay on the flip-flop and another two Tilo due to the inverter and XNOR gate and the result should

be around 2 ns. Since there is 12.5 ns between toggles on the system clock it means that the duty cycle of the new clock signal will be small, but as long as the clock edges are detected by the CPLD this will not be problematic. To increase the duty cycle more inverters and flip-flops could be added to the design. This solution is not considered pretty since the quality of the clock signal will decrease and should therefore not be a designers first choice [10].

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Figure 6.2: The signals and how they affect each other.

6.1.2 Double Counter

The purpose of the clock on CPLD chip is to count clock pulses, it only counts the positive edges though. That means that a system could be designed where two counters work in parallel, with one counter counting the positive edges, one the negative edges and the add the results together. The CPLD can only handle flip-flops that triggers on either the rising or falling edge so one have to be chosen for the entire CPLD. This can be circumvented by introducing an inverter in front of one of the counters at the cost of a small delay which is manageable. The block diagram of the counter can be seen in figure 6.3, the wave generator is just a state machine.

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6.1.3 Results

The effects of the solutions proposed in section 6.1.1 and 6.1.2 are the same for the user. Figure 6.4 shows the results if one of these solutions are imple-mented, the solid line is the regular one and the dashed line is the output when the counter works at double the speed. Everything seems to improve, the rise time is slightly better, the overshoot is less and the settling time is de-creased. Notice that this simulations differs from the one presented in figure 5.5, this simulation was performed to emphasise the difference between the modified and the regular solution. These results may look a little better than they will appear in reality, however the previously mentioned improvements occurs for all simulations.

Figure 6.4: Solid line, unmodified; Dashed line, double counter speed.

6.2 Ideas for the Regulator

Simulations will only get you this far. The next step would be to hook up the motor to the camera objective and get a lot of measurements of how the system performs. The regular PID controller might not work at a satisfactory level even after some tweaking of the coefficients so below are two quick fixes that might improve the systems ability to regulate.

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6.2.1 Derivative Term

The purpose of the derivative term is to improve stability, it does just that in effect by dampening the system. However as a function of the regulator error the term is vulnerable to sudden changes in the input value which will create an abnormally large derivative term [11]. This can be remedied by letting the term be dependent on the current position instead, thus making the term measure the actual speed of the camera lens rather than by how fast the error is decreasing. This should make the system more stable and less erratic. So the new transfer function for the controller would be:

u[n] = Kpe[n] + Ki n

P

i=−∞e[i] + Kd(y[n] − y[n − 1])

U[z] = E[z](Kp(1 −1_z) + Ki) + Y [z]Kd(1_z − _z12) + U_z[z]

6.2.2 Limiting the Error

The integral term is the sum of all past errors, hence unusually large errors can affect the system and decrease performance. Therefore it can be benefi-cially to set a maximum limit for the error. The position is given by a 16 bit number and the error can potentially be of the same magnitude. By limiting the error to a number with less than 16 bits the overall performance of the system may improve.The regulator will experience a decrease in rise time, but hopefully an increase in settling time and decrease in overshoot.

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Chapter 7 Conclusion

The purpose of this thesis was to find it if it would be possible to modify an existing autofocusing system to make it work for a smaller motor. With a fair amount of certainty it can be concluded that, yes it is possible. The only doubt would be that the since the smaller motor is not as powerful as the larger one it may not be able to drive the lens at a satisfactory level. The effects of how heat affects the motors performance is not entirely clear. As long as the transformers are matched to the required input voltage of a specific motor it would be fairly easy to configure the circuit board for any motor, so the results are not just limited to the motors used in this thesis. Regardless of the size of the motor it should probably be placed outside the camera objective and thus make the motor drive geared. This will mean that the system will be quicker and stronger at the cost of maximum speed. A trade worth making in this case.

The goal on the horizon was to make a circuit that performs on the same level as the original circuit, here the results are inconclusive. Due to limitations in tools and no possibility to connect the motor to an actual camera lens the results are in a large part theoretical. The concrete results have shown that the circuit board can drive the motor, but the circuits ability to regulate is not certain. The simulations and knowledge about the previous system indicates that it will not be a problem, but there is no way to be sure before real live tests.

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Bibliography

[1] Texas Instrument MSC1202 data sheet, available at http://pdf1.alldatasheet.com/datasheet-pdf/view/104509/BURR-BROWN/MSC1202.html (2012-07-15)

[2] MCS 51 Microcontroller Family User’s Guide, February 1994, Publication number 121517, Intel Corporation

[3] Homepage of the SDCC project, http://sdcc.sourceforge.net/ (2012-06-14)

[4] Toshiiku Sashida and Takashi Kenjo, An introduction to ultrasonic

mo-tors, Oxford university press, 2001

[5] Ilie Romaniuc, An introduction to ultrasonic piezoelectric motors, AGIR bulletin nr. 4/2011, available at http://www.agir.ro/buletine/1048.pdf (2012-07-16)

[6] Güngör Bal, A digitally controlled drive system for travelling-wave

ultra-sonic motor, Gazi University, 2003

[7] Tomonobu Senjyu, Katsumi Uezato and Hiroshi Miyazato, Adjustable

speed control of ultrasonic motors by adaptive control, IEEE Transactions

Power Electronics, vol. 10, no.5, 1995

[8] Tomohiro Yoshida, Tomonobu Senjyu, Mitsuru Nakamura, Naomitsu Urasaki, Toshihisa Funabashi and Hideomi Sekine, Sensorless control of

ultrasonic motors using neural network, Journal of Power Electronics, vol.

6, no.1, 2006

[9] Torkel Glad and Lennart Ljung, Reglerteknik, Grundläggande teori, Stu-dentlitteratur, 2006

[10] Peter Alfke, Six Easy Pieces,

http://www.pldworld.com/_xilinx/html/tip/sixeasypieces.htm (2013-01-10)

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[11] AVR221: Discrete PID controller, available at http://www.atmel.com/images/doc2558.pdf (2013-01-31)

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Typ av publikation Examensarbete ISBN (licentiatavhandling) ISRN LiTH-ISY-EX--13/4659--SE Serietitel (licentiatavhandling) Serienummer/ISSN (licentiatavhandling) Språk Engelska/English Antal sidor 54 Presentationsdatum 2013-04-25

Publiceringsdatum (elektronisk version)

Institution och avdelning

ISY

Department of electrical engineering

URL för elektronisk version

http://urn.kb.se/resolve?urn=urn:nbn:se:liu:diva-4659 (Ersätt xxxx med det korrekta numret)

Publikationens titel

Driver circuit for an ultrasonic motor

Författare

Henrik Ocklind

Sammanfattning

To make a camera more user friendly or let it operate without an user the camera objective needs to be able to put the camera lens in focus. This functionality requires a motor of some sort, due to its many benefits the ultrasonic motor is a preferred choice. The motor requires a driving circuit to produce the appropriate signals and this is what this thesis is about. The

main difficulty that needs to be considered is the fact that the ultrasonic motor is highly non-linear.

This paper will give a brief walk through of how the ultrasonic motor works,its pros and cons and how to control it. How the driving circuit is designed and what role the various components fills. The regulator is implemented in C-code and runs on a micro processor while the actual signal generation is done on a CPLD. The report ends with a few suggestions of how to improve the system should the presented solution not perform at a satisfactory level.

Antal sidor:

54

Nyckelord

Driver Circuit for an Ultrasonic Motor

Institutionen för systemteknik

Department of Electrical Engineering

Examensarbete

Driver Circuit for an Ultrasonic Motor

Henrik Ocklind

Driver Circuit for an Ultrasonic Motor

Contents

Acronyms

Chapter 1

Introduction

1.1 Background

1.2 Purpose

1.3 Goal

1.4 Delimitations

1.5 Method

1.6 Devices

1.6.1 Micro Processor

1.6.2 Complex Programmable Logic Device

1.7 Environment

1.7.1 SDCC

1.7.2 Modelsim

1.7.3 ISE Webpack

1.7.4 Matlab

1.7.5 Other Tools

Chapter 2

The Ultrasonic Motor

2.1 The Piezoelectric Effect

2.2 The Barth Motor

2.3 The Travelling Wave Motor

2.3.1 Architecture

2.3.2 Operating Principle

2.4 Advantages of the Ultrasonic Motor

2.4.1 No Influence of Magnetic Fields

2.4.2 Driving Properties

2.4.3 Structural Properties

2.5 Disadvantages of the Ultrasonic Motor

2.5.1 Friction

2.5.2 Non-Linear

Chapter 3

The System

3.1 Overview

3.2 Circuit Design

3.2.1 Microprocessor

3.2.2 Complex Programmable Logic Device

3.2.3 The Inverter Stage

Chapter 4

Driving the Motors

4.1 Speed Characteristics

4.2 Motor Diameter and Performance

4.2.1 Torque

4.2.2 Speed

4.2.3 Output Power

4.3 A Comparison of the Two Motors

4.3.1 Frequency

4.3.2 Speed and Frequency

4.3.3 Torque and Efficiency

4.3.4 Mechanical Differences

4.4 Changes in the Circuit

4.5 End of Applied Study

Chapter 5

The Regulator

5.1 PID Controller

5.1.1 Proportional Regulating

5.1.2 Integral Regulating

5.1.3 Derivative Regulating

5.1.4 The whole regulator

5.2 Tuning the System

5.2.1 Ziegler-Nichols Method

5.2.2 Manual Tuning

5.3 The Model

5.4 Regulating the Motor

5.5 Poles and Phase Margin

Chapter 6

Improvements

6.1 Evaluation of the Current Circuit

6.1.1 Clock Doubler

6.1.2 Double Counter

6.1.3 Results

6.2 Ideas for the Regulator