Modeling and Design of RobustDigital Controller for Gimbal Control

Actuator of a Launch Vehicle

Preliminary Thesis Report

Submitted in partial fulfillment of the requirements for the award of M.Tech

Degree in Electrical Engineering

(Control Systems)

University of Kerala

Submitted by

Aparna S

M3 CS

No : 12400004

DEPARTMENT OF ELECTRICAL ENGINEERING

COLLEGE OF ENGINEERING TRIVANDRUM

THIRUVANANTHAPURAM-16

2014

2

Department of Electrical Engineering

College of Engineering, Trivandrum

Thiruvananthapuram-16

2014

Certificate

This is to certify that this report entitled “Modeling and Design of Robust DigitalController for Gimbal Control Actuator of a Launch Vehicle ” is a bonafide recordof the preliminary project work done by Aparna S. of 3rd Semester, M.Tech under ourguidance towards the partial fulfillment of the requirements for the award of M.Tech Degreein Electrical & Electronics Engineering (Control Systems) of the University ofKerala during the year 2014.

Dr. Dinesh Pai A. Ms. Revathy H Ms. Preethisree G.Professor Division Head Scientist/Engineer-SDDepartment of Electrical Engineering AEMD/CEAG CED/CEAGCollege of Engineering, Trivandrum LPSC, Valiamala LPSC, ValiamalaInternal Guide External Guide External Guide

Dr. S. Ushakumari Prof. A.S. ShajilalProfessor ProfessorDepartment of Electrical Engineering Department of Electrical EngineeringCollege of Engineering, Trivandrum College of Engineering, Trivandrum(Group Head) (P.G Co-ordinator)

Prof. S. LylaHead of the DepartmentDepartment of Electrical EngineeringCollege of Engineering, Trivandrum

2

Acknowledgement

I have great pleasure in expressing my gratitude and obligations to Ms. Revathy H.,,

Group Head, CGDG/CGSE,LPSC andMs. Preethisree G.,,Scientist/Engineer,CED/CEAG,LPSC

for their valuable guidance and suggestions to make this work a great success.

I express my thanks to Dr. Dinesh Pai A., Professor, Department of Electrical En-

gineering, College of Engineering, Trivandrum, for all necessary help extended to me in the

fulfillment of this work.

I extend my gratitude to Dr. S. Ushakumari, Group Head, Department of Electrical

Engineering, College of Engineering Trivandrum for being a source of constant support and

encouragement.

I express my sincere thanks to Prof. A. S. Shajilal, Professor & PG Co-ordinator,

Department of Electrical Engineering, College of Engineering Trivandrum.

I express my gratitude to Prof. S. Lyla, Professor & Head of the Department, Depart-

ment of Electrical Engineering, College of Engineering Trivandrum.

I also acknowledge my gratitude to other members of faculty in the Department of Elec-

trical Engineering, my family, friends and seniors for their whole hearted cooperation and

encouragement. Above all, I thank GOD Almighty, without whose help, I wouldn’t have

reached this far.

Trivandrum Girija S.

i

Abstract

Compared with analog controllers, digital ones are more stable and easier to adjust

parameter. Digital controllers are usually implemented with FPGA for its fast and stable

performance. The process of converting analog controllers to digital one is studied in depth.

Implementation of digital controllers in embedded environment suffers from the inherent

problems associated with analog-digital signals interfacing in hard real-time, therefore, the

control algorithms are invariantly subjected to approximations. This work presents a tech-

nique for implementation of an efficient FPGA based robust digital controller for the position

control of a permanent magnet DC high torque motor. The implementation technique cir-

cumnavigates the problem of interfacing analog and digital systems in real-time.

Contents

1 Introduction ii

2 Literature Review iv

3 System Modeling vii

3.1 System Description . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . vii

3.2 Nomenclature . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . viii

3.3 System Modeling . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ix

3.3.1 PMDC Motor . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ix

3.3.2 Gear Mechanism . . . . . . . . . . . . . . . . . . . . . . . . . . . . . x

3.3.3 Engine . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . x

3.3.4 Feedback Section . . . . . . . . . . . . . . . . . . . . . . . . . . . . . x

3.4 Limitations of the System . . . . . . . . . . . . . . . . . . . . . . . . . . . . xi

4 Simulation Results xii

4.1 Modeled System Simulation . . . . . . . . . . . . . . . . . . . . . . . . . . . xii

4.2 Modeled System with Existing System Simulation . . . . . . . . . . . . . . . xiv

4.3 Digital Implementation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . xv

5 Conclusion xvi

i

Chapter 1

Introduction

DC motors are commonly used as actuators in all manner of industries. They offer

precise position and speed control. DC motors have changing dynamics caused by parameter

variations such as inertia changes. The changing dynamics and other nonlinear effects can be

suppressed by the use of high gear ratios. However, the high gear ratios have the disadvan-

tages of higher friction, deflection and backlash. Therefore, the ability to design DC motor

controllers with fast drive performance and reduced sensitivity to parameter variations that

do not rely on high gear ratios is desired. An important feature of this controller is that it

does not need a precise analytical model of the system to be controlled.

H∞ control framework is well suited for designing optimal and robust controllers

for linear time-invariant (LTI) systems [1]. It provides a straightforward methodology to

achieve all design objectives that guarantee stability and optimal performance. The ability

to redesign the controller by changing the software (rather than hardware) is an important

feature of digital control against analog control. Digital control systems have become very

popular due to the rapid advancement and consequent reduction in cost of digital computer

and embedded systems technology. They are not susceptible to environmental noise and

very easy to reconfigure. Introduction of the speed and position control loops in the motion

control systems, to achieve fast response and high accuracy, is a very popular technique in

industry. Therefore, digital control techniques are becoming very popular in motion control

systems and they are replacing their analog counterparts.

ii

Implementation of controllers has gone through several stages of evolution, from the

early mechanical and pneumatic designs to the Microprocessor based systems[13]. Recently,

Field Programmable Gate Array (FPGA) have become an alternative solution for the real-

ization of digital control systems, previously dominated by the General purpose micropro-

cessors. FPGA based controllers offer advantages such as high speed computation, complex

functionality, real time processing capabilities and low power consumption[5, 11]. The recent

advancements in the area of FPGA[6, 7, 9] has provided many useful techniques and tools

for the development of dedicated and reconfigurable hardware employing complex digital

circuits at the chip level. Therefore, FPGA technology can be gainfully utilized in order

to develop digital circuits so that the problem of realizing efficient, flexible and fast control

systems could be solved at the hardware level.

In the system under consideration, roll control of a launch vehicle is carried out

by controlling the angle of deflection of the engine. The gimballed engine is controlled by

the gimbal control actuator. The actuator used in the system is a high torque permanent

magnet DC motor. In the next chapter we go through the literature review. Chapter 3 deals

with system modeling. The simulation results are shown in chapter 4. Chapter 5 is the

conclusion.

iii

Chapter 2

Literature Review

The design and experimental implementation of a discrete-time fixed-order H∞ controller

for a DC motor speed and position control. To provide a model for the DC motor, two

system identification techniques are employed. In the first one a model for DC motor speed

control is identified in open-loop based on black box modeling whereas in the other one

a model for position control is identified in closed-loop based on grey box modeling. An

extension of HIFOO toolbox to discrete-time controller design developed recently is used

to synthesize the controller. The performance of the designed controller in comparison

with various control strategies is demonstrated. The paper aims at demonstrating simple

modeling and control synthesis techniques with the help of available software tools to design

low-complexity controllers in terms of design and implementation.

DC motors are commonly used for precise position and speed control in gimballed sys-

tems. The gimbal control of the launch vehicle is done by the gimbal control actuator. The

actuator used in high torque DC motor controls the angle of deflection of the engine. The

nonlinear model of the system is to be completed first. The design of the robust controller

is carried out [1,12-15]. The obtained analog controller is converted to digital for which the

process of converting analog controllers to digital ones is used [10].

The PID controllers are commonly used for DC motor speed and position control

due to simple structures and comprehensible interpretation of operation. However, design-

ing and tuning PID controllers using conventional methods or with the help of optimization

iv

tools might not be adequate to achieve specified design objectives [2]. However H∞ control

framework is well suited for designing optimal and robust controllers for linear time-invariant

(LTI) systems[1]. It provides a straightforward methodology to achieve all design objectives

that guarantee stability and optimal performance.

Nowadays most of controllers are implemented digitally on microcontrollers. Digi-

tal control systems have become very widely popular due to the rapid advancement and

consequent reduction in cost of digital computer and embedded systems technology. They

are not susceptible to environmental noise and very easy to reconfigure. Introduction of the

speed and position control loops in the motion control systems, to achieve fast response and

high accuracy, is a very popular technique in industry. Therefore, digital control techniques

are becoming very popular in motion control systems that involve various sources of noise

and demand reconfiguration of the controller as and when a new job is to be performed with

guaranteed control performance.

Although there are numerous developments in advanced control theory, the Propor-

tional Integral Derivative (PID) controller are still dominating in the motion control systems

in the industry due to the well acquaintance of the operating personnel with PID controllers

[2, 3,4]. Therefore, digital PID controllers are taking the place of their analog counterpart

in the motion control systems due to the widespread popularity of digital control as stated

above.The ability to redesign the controller by changing the software (rather than hardware)

is an important feature of digital control against analog control. Here we consider the im-

plementation of various digital PID controller architectures using FPGA [8].

An important feature of this controller is that it does not need a precise analyt-

ical model of the system to be controlled. Implementation of PID controllers has gone

through several stages of evolution, from the early mechanical and pneumatic designs to the

Microprocessor based systems [13]. Recently, FPGA have become an alternative solution

for the realization of digital control systems, previously dominated by the General purpose

microprocessors. FPGA based controllers offer advantages such as High speed computation,

v

complex functionality, real time processing capabilities and low power consumption [5,11].

The recent advancements in the area of Field Programmable Gate Array [6,7,9] has

provided many useful techniques and tools for the development of dedicated and reconfig-

urable hardware employing complex digital circuits at the chip level. Therefore, FPGA

technology can be gainfully utilized in order to develop digital circuits so that the problem

of realizing efficient, flexible and fast control systems could be solved at the hardware level.

Digital controllers implemented with DSP or FPGA have been conceived and designed to

improve performance. Implemented with these fixed point devices, floating point arithmetic

is usually converted to fixed point format. However fixed point format can not offer high

precision and wide dynamic range. At the same time, the process of a float-fixed conver-

sion is complex and the period is long. In order to improve accuracy and minimize error,

and to reduce speed and complexity of conversion of floating point format to fixed point,

best-precision fixed point arithmetic is conceived and applied to implementation of PID

controllers by FPGA circuitry because it excels one with DSP in speed and stability [14].

vi

Chapter 3

System Modeling

Accurate model building is a crucial stage in practical control problems. An ade-

quately developed system model is essential for reliability of the designed control. When

the plant has uncertainties or time dependencies, or cannot be parameterized, a model for

the system may be hard to obtain. For such systems, the system parameters should be de-

termined using system identification techniques. However, an appropriate model structure

should be obtained before the identification procedure can be executed. Consequently, the

system modeling process is vital for control and identification problems.

3.1 System Description

The plant is an engine gimbal control system of a launch vehicle. The plant consists

of the actuator, gear system, engine, rotary potentiometer, error amplifier, PWM generator,

H-bridge power amplifier etc. The block diagram of the system is shown in Fig.3.1. The

input is a command signal in the range of 0 to 6V from the main processor board and

the feedback signal is from the actuator. The error signal is then fed to the pulse width

modualted (PWM) power amplifier used to drive the DC torque motor. The actuator is

connected to the engine via the gear assembly. The rotary potentiometer is used to obtain

the feedback signal from the gear system output. The optocoupler is used for isolating the

control and power sides. The power amplifier is modelled as a one dimensional look up table.

vii

Figure 3.1: Block Diagram of the Engine Gimbal Control System

3.2 Nomenclature

Va - Applied voltage

Ra - Armature resistance

La - Armature inductance

Jm - Rotor inertia

Bm - Rotor damping

Eb - Motor backemf

Kb - Backemf constant

Ia - Motor current

θm - Rotor angular deflection

θa - Actuator angular deflection

Kt - Torque constant

Tm - Generated motor torque

Td - Disturbance torque

Jn - Engine inertia

Bn - Engine damping

θn - Engine angular defection

Td1 - Disturbance torque at the engine

Tn - Generated torque

Ks - Mounting bracket stiffness

Kf - Feedback gain

Vf - Feedback voltage

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3.3 System Modeling

3.3.1 PMDC Motor

The permanent magnet DC motor is a high torque motor. It is connected to the engine

via a gear system. In modeling the DC motor, the aim is to find the governing differential

equations that express the motor characteristics and relate the applied voltage to the torque

produced by the rotor. A schematic diagram of the DC motor built with regard to the aim

expressed above is given in Fig. 1. The diagram shows the electrical components of the

overall rotational system[16]. The equations that describe the motor electrical components

are as follows:

Va = Eb +RaIa + LadIadt

(3.1)

Eb = Kbθ̇m (3.2)

Tm = KtIa (3.3)

Taking Laplace Transform of (3.1),(3.2) and (3.3) and simplifying

θ̇m(s) =Tm(s) − Td(s)

sJm +Bm

(3.4)

Eb(s) = Kbθ̇m(s) (3.5)

Ia(s) =Va(s) − Eb(s)

Ra + sLa

(3.6)

Tm(s) = KtVa(s) − Eb(s)

Ra + sLa

(3.7)

Like most rotational systems, the system in consideration can be modeled as a

multi-mass system with the masses connected with flexible shafts or springs. The model can

be simplified further as a two mass system connected by a mass or inertia free flexible shaft,

where the first mass represents the DC motor, and the second mass represents the total

load that the motor rotates. In modeling the dynamics of the simplified two mass system,

considering only the linear dy- namics or approximating the model as a linearized one is

a common approach.the system can be accurately modeled without considering the major

nonlinear effects by the speed dependent friction, dead time and time delay, a linear model

for the two mass mechanical system can be obtained using the conventional torque balance

ix

rule:

Jmd2θmdt2

+Bmdθmdt

= Tm − Td (3.8)

Taking Laplace Transform of (3.8)

sJm ˙θm +Bmθ̇m = Tm(s) − Td(s) (3.9)

Substituting (3.9) in (3.7) and simplying further

˙θm(s)

Va(s)=

Kt

KtKb + (sJm +Bm)(sLa +Ra)(3.10)

θm(s)

Va(s)=

Kt

s(KtKb + (sJm +Bm)(sLa +Ra))(3.11)

3.3.2 Gear Mechanism

The gear mechanism is employed between the DC torque motor and the engine to

match the speed torque requirements of the engine with that of the DC machine.

θa(s) =1

nθm(s) (3.12)

where n is the gear ratio.

3.3.3 Engine

The engine dynamics is considered as that of a second order system. We can model

the engine dynamics as follows:

Jnd2θndt2

+Bndθndt

= Tn + Td1 (3.13)

where Tn = Ks(θa − θn). Substituting Tn and taking Laplace Transform of (3.13)

and simplifying we have

θ̇n(s) =Td1 +Ks(θa(s) − θn(s))

sJn +Bn(3.14)

3.3.4 Feedback Section

The actuator angular deflection θa is measured using the rotary potentiometer. The

sensor output is scaled and fed to the negative input of the input error amplifier.

Vf (s) = Kfθa(s) (3.15)

x

3.4 Limitations of the System

The model of the system so obtained is the linear model of the system. For accurate

modeling we need to consider the nonlinear aspects that come into play as well. Currently

the system has an analog lead lag compensator as shown below below.

35(1 + s

12.5)

(1 + s37.5

)

(1 + s2)

(1 + s0.12

)

Even in the presence of this compensator the system has the following limitations:

1. Loop stiffness is less. This results in oscillation of the engine even at null condition

2. System is not immune to power supply variations

3. Changes in shaft coupling due to oscillations and hence requires fine tuning of the com-

pensator

4. Gear backlash error

5. Expected response of the system should be similar to that of a second order system. This

is not the case and hence it also needs to be changed.

A robust compensator should be designed and it should be digitally implemented

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Chapter 4

Simulation Results

4.1 Modeled System Simulation

The modeled linear system is simulated in MATLAB. Simulation step size is taken

as 1ms. It is as shown in Fig.4.1 below.

Figure 4.1: Simulation of Actuator System

xii

The results are shown below as in 4.2, 4.3.

Figure 4.2: Actuator Position

Figure 4.3: Engine Position

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4.2 Modeled System with Existing System Simulation

The system is modeled with the compensator and simulated. It is as shown in Fig.4.4 below.

The results are shown below as in 4.5, 4.6.

Figure 4.4: Simulation of Actuator System with Compensator

Figure 4.5: Actuator Position

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Figure 4.6: Engine Position

4.3 Digital Implementation

The digital implementation of the existing compensator is being carried out using

DSP chip TMS320F2812. This is to be done by first converting the analog compensator into

itds digital equivalent with T = 100µs. Then it is implemented along with error amplifier

and PWM power amplifier in the DSP chip.

xv

Chapter 5

Conclusion

The problem has been identified. Literature survey in progress. System linear mod-

eling is complete. Case study for digital implementation is progressing.Nonlinear modeling

of the system is progressing. Design of robust analog compensator is to be done. Digital

implementation of the robust compensator is also to be completed. The many system limi-

tations are to be properly addressed in the design of the compensator.

In the implementation phase of the project we need to aim for FPGA as it is

used to develop digital circuits so that the problem of realizing efficient, flexible and fast

control systems could be solved at the hardware level. The aim of the work is to implement

the robust compensator using FPGA. It can be extended to accomodate other advanced

controllers that may also result into superior, reliable and flexible systems. Furthe studies

on nolinear robust control of the system is currently under developement. The motivation

is to handle the effects if wider range of uncertainties and operating conditions efficiently.

xvi

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