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1、Ch4 The Performance of Feedback Control Systems,4.6 Steady-state error of feedback control systems,For unity negative feedback system, the steady-state error is:,Closed-loop control system,Steady-state error for the three standard test inputs (H(s)=1),Step input (r(t)=A) Ramp input (r(t)=At) Acceler
2、ation input (r(t)=At2/2),Type number of system,The general form of open-loop transfer function is:,The number of integration v reflect the tracking ability of the system, which is called type number,Open-loop transfer function:,Steady-state error:,Steady-state error is dependent on 3 factors:,Type n
3、umber DC Gain Input (amplitude & form),Definition of three error constants,Position error constant Velocity error constant Acceleration error constant,Step input:,Steady-state error:,Ramp input:,Steady-state error:,Acceleration input:,Steady-state error:,The relationship between error constant and t
4、ype number,0 K p 0 0 1 infinite K v 0 2 infinite infinite K a,Type number position velocity acceleration,Refer to table 5.5 (P263),An example and illustration,Mobile robot steering control P controller and PI controller,The three error constants describe the ability of a control system to reduce or
5、eliminate the steady-state error.The designer try to increase the error constants while maintaining an acceptable transient response. A compromise is needed.,Steady-state error of non-unity feedback system,Conversion into unit feedback system From the error definition,Refer to Example 5.4,Refer to E
6、xample 5.5,4.7 Performance indices,ISE: IAE: ITAE: ITSE:,Optimum performance indices J,performance indices:,Goal of Controller design,The general form of the performance integral is,The goal of control system design is to minimize the performance indices by selecting suitable controller parameters.,
7、Refer to some examples (P269-276),4.8 Examples and simulation,Hubble telescope pointing control Aircraft roll control using Simulink Sequential design example:disk drive read system,Self-learning after class,Refer to P286-291,Pay attention to design process,Summary,Transient and steady-state performance Performance indices and evaluation Steady-state error evaluation Concept of compromise or trade-off Dominant poles and model simplification Optimization performance indices,( especially for 1st-order and 2nd-order system ),Assignment,E5.10 E5.12 E5.13 E5.17 P5.19,