Adaptive Robust Control of Uncertain Nonlinear Systems

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1.A Brief History of Feedback ControlsBin YaoIntelligent and Precision Control LaboratorySchool of Mechanical EngineeringPurdue UniversityWest Lafayette, IN47907, USA

2.History of Feedback Controls Feedback Controls have been implicitly usedthroughout human civilization; Automatic ControlSystems were first developed over two thousandyears ago (Ktesibios’ water clock)The first feedback control device on recordis thought to be the ancient water clock ofKtesibios in Alexandria Egypt around thearound 270 B.C. It kept time by regulatingthe water level in a vessel using a float (justlike the flush toilet used today) and,therefore, the water flow from that vessel.Cornelius Drebbel (1572–1633), developedthe first automatic temperature regulator,i.e. the thermostat, of a furnace.

3.History of Feedback Controls Automatic Control Systems have been an essentialfactor in the spread of industrialization (Watt’s steamengine)James Watt (1736–1819) did not invent thesteam engine as many so often claim.Steam engines had been around fordecades before Watt saw one for the firsttime. Watt did, however, improve the steamengine in many different ways, the mostrevolutionary being Watt’s “flying balls”, i.e.the motor’s rotation speed regulator (fly-ballgovernor), which Watt made public in 1769.Before Watt’s invention, the rotation speedof steam engines varied significantly andcontrolling the motors was extremelydifficult. clip&id mm gi steam broadband

4.History of Feedback Controls The need for a formal Mathematical Control Theoryappears with the invention and industrial use ofsophisticated Automatic Control SystemsIn his 1868 paper "On Governors", J. C. Maxwell (who discovered theMaxwell electromagnetic field equations) was able to explaininstabilities exhibited by the flyball governor using differentialequations to describe the control system. This demonstrated theimportance and usefulness of mathematical models and methods inunderstanding complex phenomena, and signaled the beginning ofmathematical control and systems theory. Elements of control theoryhad appeared earlier but not as dramatically and convincingly as inMaxwell's analysis.Formal Stability Analysis Techniques:Routh Stability Criterion (1877) (Hurwitz 1895) for LTI systemsLyapunov’s Stability Theorems (1893) for general nonlinear systemsNyquist Stability Criterion (1932) in frequency domainoriginally developed for the design of feedback amplifiers byBlack at Bell Lab, a critical element to telecommunications()

5.History of Feedback Controls Classic Control Theory was developed in conjunctionwith the ability to implement simple linear controllersusing analog operational amplifiers (analog computer)around the World War IIThe realization that feedback described common phenomena in avariety of settings did not crystallize until World War II, when newinstitutions brought engineers from diverse backgrounds together toconstruct military control systems. Only then were the techniquesdeveloped at BTL to deal with feedback, frequencies, and noise appliedto mechanical and hydraulic systems, and to the human operatorsthemselves. Only then did feedback become prominent as a generalprinciple in engineering, and only afterward, with the work of Wiener,Shannon, and numerous others, did Black’s, Bode’s, and Nyquist’sideas move beyond amplifiers and into a broad range of disciplinesVarious Classical Control Techniques for LTI Systems:PID control: Callender et al (1936) (time-domain)Root Locus: Evans (1948) (time-domain)Frequency Domain: Bode (1945) (gain and phase margin)

6.History of Feedback Controls The fundamental role of Feedback Controls to moderntechnology was well recognized after World War IIBenefits of Feedback Controls:-Stabilize Unstable Systems-Improve System Performance (e.g., speeding up systemresponse) to meet stringent performance requirements-Reduce (Attenuate) the effect of modeling uncertainty andvarious disturbances for consistent performance

7.History of Feedback Controls The fundamental role of Feedback Controls to moderntechnology was well recognized after World War IIVarious Professional Societies Formed:-The ASME Dynamic Systems and Control Division (DSCD)was founded in l943 ( IEEE Control Systems Society (CSS) was founded inl954 ( American Automatic Control Council (AACC), anassociation of the control systems divisions of eightmember societies: AIAA, AIChE, AISE, ASCE, ASME, IEEE,ISA, and SCS, was formed in 1956 (中国自动化学会( Chinese Association of Automation) 于1961 年成立 ( International Federation of Automatic Control wasfounded in 1957 (

8.History of Feedback Controls Modern Control Theory was developed based onstate-space representations of dynamic systems.More sophisticated mathematical and computationaldesign tools were developed with the advent of digitalcomputersControl theory made significant strides in the next 100 years. Newmathematical techniques made it possible to control, more accurately,significantly more complex dynamical systems than the original flyballgovernor and feedback amplifiers.Samples of Modern Control Theory Design Techniques:– Observer Design and Filtering (50s)– Optimal Control (Bellman’57, Pontryagin’58, Kalman’60)– Stochastic, Robust, and Adaptive Control of LTI systems(70s and 80s)– Digital Controls (70s and 80s)

9.Current Status of Control Theory Rapid advances in microelectronics and microprocessortechnologies during the past decades have made thecomputer based control implementation platform ratheraffordable and a standard choice for any modernmachines. Such a hardware configuration enablescontrol algorithms to be constructed in the same way aswhat a human brain normally does – a decision makingprocess making full use of all information availableincluding feedback signalsDiverse Advanced Control Design Techniques:– Computation based Multivariable Linear Controls (since 80s)– Nonlinear Control Theory (since 80s)– Nonlinear Robust and Adaptive Controls (since 90s)– Control of Discrete Event and Hybrid Systems (since 80s)–…

10.General Structure of ControllerIn general, a controller is nothing but a strategy to determine a control actionbased on all available information; information not only comes from themeasured output but also from the measured internal state variables, measureddisturbance, reference trajectory, and plant model structure. It can have anyform and is illustrated below:ˆ(t)dd(t)DisturbancesSensorMeasuredDisturbanceReferenceTrajectoryr(t)OtherAvailableInformationInformationSynthesisu(t)Plant DynamicsControl StrategyMeasuredStateVariablesSensorsMeasuredOutputSo there will be no end to new control schemes !y(t)

11.Control Applications Feedback is fundamental to our technology world.Applications of control methodology have helpedmake possible space travel and communicationsatellites, safer and more efficient aircraft, cleanerauto engines, cleaner and more efficient chemicalprocesses, to mention but a few.

12.Examples of FeedbackControlRobotics

13.Examples of FeedbackControlManufacturing

14.Examples of FeedbackAutomotive ApplicationsControlActive Suspension SystemsBrake-by-Wire

15.Examples of FeedbackControlAerospace & Astronautics

16.Examples of FeedbackControlNon-CircularTrack ProfilePivotFrictionEccentricityExternal VibrationsFlow-inducedAero-elasticForcesHard-Disk Drive Control Issues

17.Examples of FeedbackMedical and Daily Life ApplicationsControlCyberKnife full-body radiosurgery using Image-guided robotics

18.More Information can be downloaded from: byao


Such a hardware configuration enables control algorithms to be constructed in the same way as what a human brain normally does – a decision making process making full use of all information available including feedback signals Computation based Multivariable Linear Controls (since 80s) Nonlinear Control Theory (since 80s) Nonlinear Robust and ...

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