6.1 What Is Control?,Fig.6-1 Components of a computer-controlled system,6.2 Feedback,6.2.1 Introduction 6.2.2 Drawbacks of Feedback,6.2.1 Introduction,Fig.6-2 Open and closed loop systems a) Closed loop b) Open loop,6.2.2 Drawbacks of Feedback,While feedback has many advantages, it also has some drawbacks. Chief among these is the possibility of instability if the system is not designed properly. We are all familiar with the effects of positive feedback when the amplification on a microphone is turned up too high in a room. This is an example of feedback instability, something that we obviously want to avoid. This is tricky because we must design the system not only to be stable under nominal conditions but also to remain stable under all possible perturbations of the dynamics.,6.3 PID Control,The reason why on-off control often gives rise to oscillations is that the system overreacts since a small change in the error makes the actuated variable change over the full range. This effect is avoided in proportional control, where the characteristic of the controller is proportional to the control error for small errors. This can be achieved with the control law u=umax if eemaxkpe if emineemaxumin if eemin(6-1),6.4 Adaptive Control,6.4.1 Introduction 6.4.2 Formulation of Adaptive Control Problem,6.4.1 Introduction,1) the use of algebraic approach in control design, 2) the parameterization of controllers, 3) the use of rational fraction functions, 4) the digitalization of signals and models.,6.4.2 Formulation of Adaptive Control Problem,1) their state or structure may change, 2) we may influence the state or output of the system.,Fig.6-3 Inner structure of an adaptive system,6.4.2 Formulation of Adaptive Control Problem,1) Recursive identification -i.e. the creation of a mathematical description of the controlled process using self-adjusting models. 2) The control of systems about which we know too little before starting up to predefine the structure and parameters of the control algorithm, and also systems whose transfer characteristics change during control. 3) Recognition of subjects or situations (scenes) and their classification. Adaptive and learning systems are then components of so-called classifiers. 4) Manipulation of subjects -i.e. change of their spatial position. Adaptive and learning systems are then components of robots.,6.4.2 Formulation of Adaptive Control Problem,Fig.6-4 General block diagram of adaptive control system,1) pole and zeros assignment of a closed loop system,6.4.2 Formulation of Adaptive Control Problem,2) the required overshoot of the step response of a closed loop system to reference and input disturbances, 3) the settling time, 4) the minimum value of various integral or summing criteria, 5) the amplitude and natural frequency of oscillations in nonlinear loops, 6) the frequency spectrum of a closed loop control system, 7) the required value of gain and phase margins, etc. 1) by making a suitable alteration to tile adjustable parameters of controller, 2) by altering the structure of the controller, 3) by generating a suitable auxiliary input signal (an adaptation by signal).,6.4.2 Formulation of Adaptive Control Problem,1.setpoint 2.fly-by-wire 3.router 4.autonomous 5.attenuation 6.game 7.control-oriented 8. fidelity 9.be 10. crucial 11.causal 12.counterintuitive,6.4.2 Formulation of Adaptive Control Problem,13. governor 14. flyball 15.throttle 16.resilient 17.perturbation 18.on-off 19.over-react 20.extrapolation 21.proportional-integral-derivative 22.stochastic 23.autopilot 24.aeronautics,6.4.2 Formulation of Adaptive Control Problem,25.cybernetic 26.heterogenous 27.diversity 28.fuzzy 29.matrix 30.lemma 31.rational 32.monograph 33.harsh 34.accumulation 35.learning 36.recursive,6.4.2 Formulation of Adaptive Control Problem,37.identification 38.self-adjusting 39.criteria 40.frequency,