Slide 1Slide 2Slide 3Slide 4Slide 5Slide 6Slide 7Slide 8Slide 9Slide 10Slide 11Slide 12Slide 13Slide 14Slide 15Slide 16Slide 17IllustrationsIn this chapter we extend the ideas of modeling to include control system characteristics, such as sensitivity to model uncertainties, steady-state errors, transient response characteristics to input test signals, and disturbance rejection. We investigate the important role of the system error signal which we generally try to minimize.We will also develop the concept of the sensitivity of a system to a parameter change, since it is desirable to minimize the effects of unwanted parameter variation. We then describe the transient performance of a feedback system and show how this performance can be readily improved. We will also investigate a design that reduces the impact of disturbance signals. Chapter 4: Feedback Control System CharacteristicsObjectivesIllustrationsOpen-And Closed-Loop Control SystemsAn open-loop (direct) system operates without feedback and directly generates the output in response to an input signal.A closed-loop system uses a measurement of the output signal and a comparison with the desired output to generate an error signal that is applied to the actuator.IllustrationsOpen-And Closed-Loop Control SystemsH s( ) 1Y s( )G s( )1 G s( )R s( )E s( )11 G s( )R s( )Thus, to reduce the error, the magnitude of 1 G s( ) 1H s( ) 1Y s( )G s( )1 H s( ) G s( )R s( )E s( )11 H s( ) G s( )[ ]R s( )Thus, to reduce the error, the magnitude of 1 G s( ) H s( ) 1Error SignalIllustrationsSensitivity of Control Systems To Parameter VariationsGH s( ) 1Y s( )1H s( )R s( )Output affected only by H(s)G s( )G s( )Open LoopY s( )G s( ) R s( )Closed LoopY s( )Y s( )G s( )G s( ) 1 G s( )G s( ) H s( )R s( )Y s( )G s( )1 GH s( ) GH s( ) 1 GH s( )( )R s( )GH s( )GH s( )The change in the output of the closed systemis reduced by a factor of 1+GH(s)Y s( )G s( )1 GH s( )( )2R s( )For the closed-loop case ifIllustrationsSensitivity of Control Systems To Parameter VariationsT s( )Y s( )R s( )S T s( )T s( ) G s( )G s( )STTddTGGddGTTddGGddGTT s( )11 H s( ) G s( )[ ]SGTTTddGGddGTTTddGGddGT11 GH( )2GG1 GH( )SGT11 GH( )Sensitivity of the closed-loop to G variations reducedSensitivity of the closed-loop to H variationsWhen GH is large sensitivity approaches 1Changes in H directly affects the output responseSHT GH1 GH( )IllustrationsExample 4.1Open loop Closed loopvoKa vinR2R1RpR1 R2T kaTKa1 KaSKaT11 KaSKaT1If Ka is large, the sensitivity is low.Ka104 0.1 SKaT11 1039.99 104IllustrationsControl of the Transient Response of Control Systems s( )Vas( )G s( )K11s 1where,K1KmRab KbKm1RaJRab KbKmIllustrationsControl of the Transient Response of Control Systems s( )R s( )KaG s( )1 KaKt G s( )KaK11s 1 KaKt K1KaK11s1 KaKt K1 1IllustrationsControl of the Transient Response of Control SystemsIllustrationsDisturbance Signals In a Feedback Control SystemsR(s)IllustrationsDisturbance Signals In a Feedback Control SystemsIllustrationsG1 s( ) KaKmRa G2 s( )1J s b( )H s( ) KtKbKaE s( ) s( )G s( )1 G1 s( ) G2 s( ) H s( )Td s( )G1G2H s( ) 1E s( )1G1 s( ) H s( )Td s( )If G1(s)H(s) very large the effect of the disturbancecan be minimizedG1 s( ) H s( )Ka KmRaKtKbKaapproximately Ka Km KtRasince Ka >> KbStrive to maintain Ka large and Ra < 2 ohmsDisturbance Signals In a Feedback Control SystemsIllustrationsSteady-State ErrorEos( ) R s( ) Y s( ) 1 G s( )( ) R s( )Ecs( )11 G s( )R s( ) H s( ) 1Steady State Error0te t( )lim 0ss E s( )limFor a step unit inputeoinfinite( )0ss 1 G s( )( )1slim 0s1 G 0( )( )limecinfinite( )0ss11 G s( )1slim 0s11 G 0( )limIllustrationsThe Cost of FeedbackIncreased Number of components and ComplexityLoss of GainInstabilityIllustrationsDesign Example: English Channel Boring MachinesY s( ) T s( ) R s( ) Td s( ) D s( )Y s( )K 11 ss212 s KR s( )1s212 s KD s( )IllustrationsDesign Example: English Channel Boring MachinesStudy system for differentValues of gain KSteady state error for R(s)=1/s and D(s)=0infinitete t( )lim 0ss11K 11 ss2s1slim0Steady state error for R(s)=0 D(s)=1/sinfinitety t( )lim 0ss1s212 s K1slim1KGTdIllustrationsStudy Examples of 4.9 - Control Systems Using MATLABAndApply concepts performing Lab
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