El-Kébir Boukas and Fouad M. AL-Sunni. Mechatronic Systems. Analysis, Design and Implementation ABC

Transcription

1 Mechatronic Systems

2 El-Kébir Boukas and Fouad M. AL-Sunni Mechatronic Systems Analysis, Design and Implementation ABC

3 Authors Prof. El-Kébir Boukas Mechanical Engineering Department Ecole Polytechnique de Montreal P.O. Box 6079, Station centre-ville" Montreal, Quebec, H3C 3A7 Canada Prof. Fouad M. AL-Sunni Department of Systems Engineering King Fahd University of Petroleum and Minerals Dhahran, Saudi Arabia ISBN e-isbn DOI / Library of Congress Control Number: c 2011 Springer-Verlag Berlin Heidelberg This work is subject to copyright. All rights are reserved, whether the whole or part of the material is concerned, specifically the rights of translation, reprinting, reuse of illustrations, recitation, broadcasting, reproduction on microfilm or in any other way, and storage in data banks. Duplication of this publication or parts thereof is permitted only under the provisions of the German Copyright Law of September 9, 1965, in its current version, and permission for use must always be obtained from Springer. Violations are liable to prosecution under the German Copyright Law. The use of general descriptive names, registered names, trademarks, etc. in this publication does not imply, even in the absence of a specific statement, that such names are exempt from the relevant protective laws and regulations and therefore free for general use. Typeset & Cover Design: Scientific Publishing Services Pvt. Ltd., Chennai, India. Printed on acid-free paper springer.com

4 Preface Nowadays most of the systems are computer controlled among them we quote mechatronic systems where the intelligence is implemented in microcontrollers. The discipline that deals with such systems is mechatronics that we define as the synergistic combination of mechanical engineering, electronic engineering, and software engineering. The purpose of this interdisciplinary engineering field is to control complex systems by providing hardware and software solutions. The engineers working in this field must master concepts in electronics, control and programming. Examples of such systems can be found in different industrial areas ranging from aerospace to automobile industries. In the mechanical part, the engineer must follow a rigorous procedure to design the mechatronic system. He must build the mechanical part of the system and choose the appropriate sensors and actuators that have to be used in the functioning of the mechatronic system. At this phase we must think about the place where the electronic circuit will be integrated. In the electronics part, the engineer must design the electronic circuit around microcontrollers that will assure the functioning of the mechatronics systems. It covers the integration of the required electronics components such as resistors, capacitors, integrated circuits, sensors and the chosen microcontrollers. The required regulated voltage for the different components is also part of this step. In the control part, the engineer must analyze the system under study and design the appropriate controller to get the desired performances. In the analysis part, we should start by establishing an acceptable model that gives the relationship between the inputs and the outputs. Once the dynamics is mastered a sampling period is chosen and the model is converted to a discrete-time form and an appropriate controller can be chosen among the classical proportional integral and derivative (PID)

5 VI controller or the state feedback controller or any other controller that can give the desired performances. In the programming part, the engineer must develop the code of the appropriate algorithms and then upload it in the memory of the chosen microcontroller. Many languages can be used for this purpose. In the rest of this volume, the C language is used to implement the developed algorithms. The field of mechatronics is blooming and due to its interdisciplinarity many universities around the world have introduced complete programs on mechatronics in their curriculum. Also the number of students that are attracted by this field is also blooming and many research directions related to this have emerged recently. Huge efforts have been done to structure research in this discipline and we have seen recently many international conferences totally dedicated to this. Also some journals have been created to report interesting results on the subject. Unfortunately the number of book dealing with such discipline is limited and sometimes inappropriate for some courses in the different programs around the world. This book provides some tools that engineers working on the mechatronics discipline can use. It can be considered as a reference for a second course in mechatronics curriculum where the students are supposed to have a prerequisite course in which the structure and the different components on mechatronics systems have been presented. It focuses only on the analysis, design and implementation of continuoustime systems controlled by microcontrollers using advanced algorithms to get the desired performances. The hardware design of the mechatronic systems represents the hearth of the mechatronics field. It consists of designing the different parts of the mechatronic systems. Mainly beside the electronic circuit, we should select the appropriate sensors and actuators that we can use for our mechatronic system. The choice of the microcontroller is also important for the success of the desired system. In the modeling part a model to describe the behavior of the system is developed either using the transfer function or the state space representation. In the transfer function approach part, the model of the continuous-time systems is converted to a discrete-time system and different techniques for analysis and synthesis of controllers to guarantee some desired performances are developed. In the state space approach part, the model of the continuous-time systems is converted to a discretetime state space representation and different techniques for analysis and synthesis of controllers to assure some desired performances are developed. The part on implementation will focus on how we can implement the control algorithm we developed either using the transfer function tools or the ones based on state space. Both the hardware and software parts will be covered to give an idea for the reader on how to deal with such problems. Mainly the selection of the sensors and the actuators that may be used in the mechatronic system will be covered. In the advance control part, a flavor of how to design controllers that handle uncertainties and external disturbances in the dynamics is presented. This will give an idea to the reader on robust control technique and get familiar with implementation of these techniques. Stability and stabilization problems and their robustness are covered. Different controllers (state feedback, static output feedback and dynamic

6 VII output feedback) are used and linear matrix inequality (LMI) condition is developed to design such controllers. In the case studies part, a certain number of practical examples are presented to show how the concepts we presented earlier are implemented to obtain a functional mechatronics systems. More detail is given to help the reader to design his own mechatronic system in the future. The rest of this book is organized in seven parts and divided in eleven chapters and one appendix. In the introduction, a general overview of the mechatronics fields is given and the main concepts are recalled to make the book self-contained. In Chapter 2, the structure of mechatronic systems are detailed and some examples are given. Chapter 3 which is a part of the modeling part, deals with the modeling problem of the class of linear continuous-time systems. Both the physical laws and identification approaches are covered. The concepts of transfer function and state space representations are presented. Chapter 4 treats the Z -transform and its properties and how the transfer function is obtained from a model that is given in a set of differential equations. Other techniques for analysis of such systems are also covered. In Chapter 5, some design approaches based on transfer function are developed. Chapter 6 deals with the state space approach for analyzing linear discrete-time systems. The concepts of stability, controllability and observability are covered. In Chapter 7, the state feedback, static output and dynamic output stabilization techniques are tackled. Chapter 8 deals with the implementation problem of the control algorithm we may develop for controlling a given continuous-time system. The focus will be made on all the steps. Mainly the hardware and software parts are covered in detail to help the reader to develop his own expertise. Chapter 9 presents some ideas on robust control. Stability and stabilization problems for systems with uncertainties and external disturbancesare tackled. Chapter 10 covers the guaranteed cost control problem. Different types of controllers are used for this purpose. In Chapter 11 some selected systems are considered and all the concepts we developed in this book are applied to give the whole picture for the reader. An appendix that contains some relevant tools is also provided to try to make the book self-contained. El-Kébir Boukas Fouad M. AL-Sunni

7 In Memory of Prof. El-Kébir Boukas Missing a very dear friend Born in Morocco in 1954, Prof. Boukas obtained his BS Electrical Engineering degree from Ecole Mohammadia des Ingenieurs with excellent standing and with an early focus on control and application on large scale systems. Since then, he was fascinated by the area of control and its application. To fulfil his design of knowing more about it, he moved to Canada to pursue his higher studies. A decision which proved rewarding, he finished his MS and PhD in Electrical Engineering from Ecole Polytechnique of Montreal, and established himself as an authority in his area of specialization of control and automation with specialization in the use of control tools in manufacturing, maintenance and inventory control. In his mid- fifties, he left us while still active in his research and very productive. In fact, the manuscript of this book was with him while in hospital during the last few weeks of his life. He left behind an excellent profile of accomplishments in the form of 167 High caliper International Journals, more than 8 books and many educational software and materials, and very visible presence in internationalconferences with more than 125 papers and presentations in conferences and involvements in organizations, and international technical committee of several of conferences over the years. After fighting for his life, he passed away peacefully and he left behind his loyal wife, two daughters (A dentist, and an MD) and one son (soon to-be physical therapist). I have known him since 1996, and since his visit to us in King Fahd University of Petroleum and Minerals, I have known him to be a kind, nice, helpful, and dear friend to all. He has been one of my best friends that I will always remember. He left me with the job of completing this manuscripts and then to translate it to Arabic to be the first textbook on the subject. The English version is now out, and the Arabic version is being scheduled at a later time. Fouad M. AL-Sunni

8 Contents 1 Introduction MechanicalPartDesign ElectronicCircuitDesign Real-TimeImplementation OrganizationoftheBook I Mechatronic Systems 21 2 Mechatronic Systems Mechatronics MechanicalPart Sensors Actuators ElectronicCircuit Real-TimeImplementation ExamplesofMechatronicSystems DcMotorControl Two Wheels Robot MagneticLevitation Conclusions Problems... 40

9 XII Contents II Modeling 43 3 Mathematical Modeling MathematicalModelingBasedonPhysicsLaws ConceptofTransferFunction StateSpaceDescription Identification TransferFunctionApproach StateSpaceDescriptionApproach Conclusions Problems III Transfer Function Approaches 69 4 Analysis Based on Transfer Function Introduction SamplingProcess TransferFunctionConcept Time Response and Its Computation Stability and Steady-State Error RootLocusTechnique BodePlotTechnique Conclusions Problems Design Based on Transfer Function Introduction FormulationoftheControlDesignProblem Design Based on Empirical Methods DesignBasedonRootLocus DesignBasedonBodePlot CaseStudy Proportional Controller Proportional and Integral Controller Proportional and Derivative Controller Proportional Integral and Derivative Controller PhaseLeadController PhaseLagController PhaseLead-LagController Conclusion Problems

10 Contents XIII IV State Space Approaches Analysis Based on State Space Introduction StateSpaceConcept Time Response and Its Computation Stability Controllability and Observability CaseStudy Conclusion Problems Design Based on State Space Introduction FormulationoftheControlDesignProblem StateFeedbackControllerDesign OutputFeedbackControllerDesign LinearQuadraticRegulator CaseStudy Conclusions Problems V Implementation Design and Implementation of Mechatronic System Introduction DesignPhase ElectronicDesign SoftwareDesignandReal-TimeImplementation dspic30f Pusle Width Modulation Interrupts DesignandImplementationBasedofTransferFunction DesignandImplementationBasedonStateSpace Conclusions Problems VI Advanced Control Robust Control Stability Problem Stabilization H Stabilization

11 XIV Contents State-FeedbackControl Static Output Feedback H Control Output-FeedbackControl Conclusion Problems Guaranteed Cost Control Problem Introduction ProblemStatement StateFeedbackControlDesign OutputFeedbackControl Conclusion Problems VII Case Studies Case Studies Introduction VelocityControlofthedcMotorKit Position Control of the dc Motor Kit Balancing Robot Control MagneticLevitationSystem Conclusion Problems A C Language Tutorial 487 References 495 Index 497

12 List of Figures 1.1 Loaddrivenbyadcmotorkit Electroniccircuitofthedcmotorkit Signalconversionmadeintheforwardpath Signalconversionmadeinthefeedbackpath Partition of the sampling period T Trafficsystem Type of light used in the trafficlightsystem Mechatronicdesignapproach Real-timeimplementationsetup Electroniccircuitofthedcmotorkit Balancing robot Electronic circuit of the balancing robot Magneticlevitatiossystem Block diagram of continuous-time system Block diagram of continuous-time linear system Blockdiagramofadcmotor Tilt dynamics free body diagram Wheels and linear displacement free body diagram Heading dynamics free body diagram Signalconversionismadeintheforwardpath Signalconversionismadeinthefeedbackpath Samplingprocess... 77

13 XVI List of Figures 4.4 Samplingperiodchoice Transformationofthes-planeintoz-plane Transformationofthes-planewhentherealpartisconstant Forwardintegration Backwardintegration Trapezoidalintegration Pulse transfer function definition Cascadetransferfunctionswithsamplerbetween Cascade transfer functions without sampler between Transferfunctionsinfeedback Transferfunctionsinfeedback Transferfunctionsinfeedback Transferfunctionsinfeedback Transferfunctionsinfeedback Transferfunctionsinfeedback Transferfunctionsinfeedback Transferfunctionsinfeedback Behavior of the time response for a step input Blockdiagram(BD) Blockdiagramoftheclosed-loop BD of the system with characteristic eqn: 1 + K (z+1) = 0... (z 1) RL of the system with characteristic eqn: 1 + K (z+1) = (z 1) 2 z 4.26 BD of the system with characteristic eqn: 1 + K (z 1)(z 0.368) = z 4.27 RL of the system with characteristic eqn: 1 + K (z 1)(z 0.368) = Speedcontrolofmechanicalpartdrivenbyadcmotor Bode diagram of (1 0.05w) 1+w Transferfunctionsinfeedback Blockdiagramoftheclosed-loop Blockdiagramoftheclosed-loop Ziegler-Nichols methods: stable case Step response of a stable dynamical system Step response of the closed-loop dynamics with a PID controller Ziegler-Nichols: unstable case (a) and determination of T c (b) Step response of the closed-loop dynamics with a PID controller Step response of the closed-loop dynamics with a PID controller Root locus of 1 s(s+1) 5.9 Step response of 0.5 s(s+1)+0.5 s+z 5.10 Root locus of s(s+1) 5.11 Step response of , z = K P s+5k I s 2 +(1+5K P )s+5k I s+z 5.12 Root locus of s(s+1), z = s+z 5.13 Step response of s(s+1), z = Root locus of s+a 2 s(s+3), a 2 = Step response of s+a 2 s(s+3), a 2 =

14 List of Figures XVII s+ 1 at 5.16 Root locus of s(s+2)(s+ 1 T ) 2aK 5.17 Step response of F(s) = P(s+ 1 at ) s 3 +(2+ 1 T )s 2 +( 2 T +2aK P)s+ 2K P T Root locus of s(s+2) s Root locus of s(s+2)(s+0.06) aK 5.20 Step response of F(s) = P(s+ 1 at ) s 3 +(2+ 1 T )s 2 +( 2 T +2aK P)s+ 2K P T 2aK 5.21 Step response of F(s) = P(s+ 1 at ) s 3 +(2+ 1 T )s 2 +( 2 T +2aK P)s+ 2K P T s+ 1 a 5.22 Root locus of 1 T ( 1 ) s(s+2) s+ 1 T 1 ( )( ) s+ 1 a 1 T s+ 1 1 a 2 T ( )( 2 s(s+2) s+ 1 T s Root locus of )... T Step response of F(s) Bode plot of T(s), with K = 1, and K = kk P Step response of F(s) Bode plot of T(s), with K = Step response of F(s) Bode plot of T(s), with K = Step response of F(s) Bode plot of T(s) Step response of F(s) Bode plot of T(s) Step response of F(s) Bode plot of T(s) Step response of F(s) Bode plot of T(s) K 5.38 Bode plot of T(s) s(τ m s+1), with K = 1, and K = K mk P Root locus of T(s) = s(τ m s+1) K 5.40 Step response of F(s) = m K P τ m s 2 +s+k m K P Bode plot of T(s) K(0.5s+1) s 2 (τ m s+1), with K = 1, and K = K mk P Root locus of T(s) = 0.25s+1 s 2 (τ m s+1) 5.43 Step of F(s) with two controllers for two design methods Bode plot of T(s)(compensatedandnoncompensatedsystem Step of F(s) with two controllers for two design methods Root locus of T(s) = ( 1 13 s+1)( 1 15 s+1) s 2 (τ m,... s+1) Bode plot of T(s) = 100( 1 12 s+1)( 1 15 s+1) s 2 (τ m s+1) 5.48 Step response of F(s)withthetwocontrollers at s Root locus of T(s) = s(τ m s+1)(ts+1) Bode plot of T(s) s(τ m s+1)

15 XVIII List of Figures 5.51 Step of F(s) with two controllers for two design methods Bode plot of T(s) (τ m s+1) Step of F(s) with two controllers for two design methods Root locus of T(s) K(0.5s+1) s 2 (τ m s+1), with K = 1, and K = K mk P Bode plot of T(s) K(0.5s+1) s 2 (τ m s+1), with K = 1, and K = K mk P Step of F(s) with two controllers for two design methods Blockdiagramofdiscrete-timelinearsystem Blockdiagramofdiscrete-timelinearsystem Behavior of the output versus time with state feedback controller Behaviorofstatesvstimewithstatefeedbackcontroller Blockdiagramofdiscrete-timelinearsystem Behavioroftheoutputvstimewithstatefdkcontroller Behavioroftheoutputvstimewithstatefdkcontroller Behaviorofthecontrollergainsversusiteration Behavioroftheoutputvstimewithstatefdkcontroller Behavioroftheoutputvstimewithstatefdkcontroller Behaviorofthestatesvstimewithstatefdkcontroller Behaviorofthestatesvstimewithstatefdkcontroller Behaviorofthestatesvstimewithstatefdkcontroller Two wheels robot dspic30f4011 pins description ExampleofPWMsignal Blockdiagramoftheclosed-loop Root locus of the dc motor with a proportional controller Output of the load driven by a dc motor vs time with p controller Time response for a step function with 1 as amplitude Time response for a step function with 1 as amplitude Behavior of the output for a non null initial conditions Behaviorofthesystem sstates Behavioroftheobserver sstates Electroniccircuitofdcmotorkit Real-timeimplementationsetup Root locus of the dc motor with a proportional controller Time response for a step function with 30 degrees as amplitude Time response for a step function with 30 degrees as amplitude Time response for a step function with 30 degrees as amplitude Outputversustime System sstatesversustime Observer sstatesversustime Balancing robot Electronic circuit of the balancing robot

16 List of Figures XIX Outputsversustime Statesversustime Magneticlevitatiossystem Time response for moving object

17 List of Tables 3.1 Variables definition Variables definition Dataofthemagneticlevitationsystem Z-transformtable Poles in the z-plane using z = e j 2πω ωs Ziegler-Nichols methods: controller parameters Ziegler-Nichols method: case of unstable systems ZieglerNicholsmethodinfrequencydomain ComparativestudyofthedesignofPcontroller Difference equations for the differentcontrollers:dcmotorkit Conventionfordcmotormovement Dataofthemagneticlevitationsystem A.1 List of C language keywords A.2 Numberrepresentations A.3 Integerrepresentations A.4 Decimalrepresentations A.5 Arithmeticoperations A.6 Logicoperations A.7 Logicoperations A.8 Logicoperations