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continueSteady-state errorThe cost of feedbackExamples and simulationMain content:3.1 Open-loop and closed-loop control systemsReview the concepts and structure A closed-loop systemThe roles of feedbackReduce error(eliminating the error)Reduce sensitivity to Parameter variationsDisturbance rejection or eliminationImprove dynamic performance or adjust the transient response(such as reduce time constant)Benefits:3.2 Sensitivity of system to parameter variationsSystem are time-varying in its nature because of inevitable uncertainties such as changing environment,aging,and other factors that affect a control process.All these uncertainties in open-loop system will result in inaccurate output or low performance.However,a closed-loop system can overcome this disadvantage.A primary advantage of a closed-loop feedback control system is its ability to reduce the systems sensitivity to parameter variation.Sensitivity analysis Robust controlContinueEffect of parameter variationsIf process is change as Open-loop system Closed-loop systemSystem sensitivitySystem sensitivity is defined as the ratio of the percentage change in the system transfer function to the percentage change of the process transfer function.It is defined as continueIn the limit,for small incremental changes,last formula isSensitivity comparisonOpen-loop systemClosed-loop systemSensitivity to parameters If system TF is System sensitivity to isExample of sensitivityFeedback amplifierGoal:Reduce the sensitivity to parameters variation,that is enhance the robustness to change in amplifier gain.3.3 Transient response of systemTransient response is the response of a system as a function of time.It is one of the most important characteristics of control system.If transient response is not satisfying,what shall we do?Control of transient response(Take speed control system as example)Open-loop speed control systemClosed-loop speed control system and its realizationResponse of open-loop and closed-loop system 3.4 Disturbance in a feedback control systemDisturbance signal is an unwanted extraneous input signal that affects the systems output signal,such as noise for amplifier,wind gusts for radar antennas,etc.Feedback control can completely or partially eliminate the effect of disturbance signal.Example of steel rolling millLoad changes or disturbances+NoiseOpen-loop without external feedbackClosed-loop speed tachometer control sysytemSpeed-torque curves for the closed-loop systemFeedback can alleviate the effects of disturbances and noise signal occurring within the feedback loop.If system exists noise at the input point,we can design a low-pass filter to improve SNR(signal-noise ratio)Remarks:3.5 Steady-state errorSteady-state error is the error after the transient response has decayed,leaving only the continuous response.Feedback can reduce the steady-state error of control systemHow to define the error?From input point:From output point:E a(s)=R(s)-H(s)Y(s)E(s)=R(s)-Y(s)Only for unit feedback H(s)=1,We have E a(s)=E(s)Comparison of error Open-loop system Closed-loop systemcontinueOpen-loop system under unit step inputClosed-loop system under unit step inputExample illustrationRefer to P207-208An example of first-order system3.6 The cost of feedbackIncrease of complexityLoss of gainRisk of Instability An unrealistic dreamWhy not simply set G(s)=Y(s)/R(s)=1?Transfer function represent the physical system or process,Therefore G(s)=1 is unrealizable.3.7 Design examplesEnglish channel boring machines(P209)PD controller,and how to select K?Block diagram model Unit step response for K=100Unit step response for K=20 Mars rover vehicleTo compare the sensitivity and steady-state error between open-loop and closed-loop systemControl system for rover:a)open-loop b)closed-loop3.8 Simulation using MATLABRefer to P214-224Self-learning after classSummaryDecrease the sensitivity to parameter variationImprove transient or dynamic performanceEnhance the robustness or disturbance rejectionReduce the steady-state errorThe fundamental reasons for using feedback are as follows:AssignmentE4.1E4.3E4.4E4.6P4.2,P4.5,P4.7
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