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Ch4 The Performance of Feedback Control Systems

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:. Refer to Figure 5.18 (P241). Steady-state error for the three standard test inputs ( H(s)= 1). Step input ( r(t)= A)

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Ch4 The Performance of Feedback Control Systems

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  1. Ch4 The Performance of Feedback Control Systems

  2. 4.6 Steady-state error of feedback control systems For unity negative feedback system, the steady-state error is: Refer to Figure 5.18 (P241)

  3. Steady-state error for the three standard test inputs (H(s)=1) • Step input (r(t)=A) • Ramp input (r(t)=At) • Acceleration input (r(t)=At2/2)

  4. 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

  5. Definition of three error constants • Position error constant • Velocity error constant • Acceleration error constant

  6. The relationship between error constant and type number Type number position velocity acceleration • 0 K p 0 0 • 1 infinite K v 0 • 2 infinite infinite K a Refer to table 5.5 (P243)

  7. 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 eliminate the steady-state error.The designer try to increase the error constants while maintaining an acceptable transient response. A compromise is needed.

  8. Steady-state error of non-unity feedback system • Conversion into unit feedback system • From the error definition Refer to Example 5.4 Refer to Example 5.5

  9. 4.7 Performance indices Optimum performance indices J • ISE: • IAE: • ITAE: • ITSE:

  10. 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. Refer to some examples (P249-256)

  11. 4.8 The Simplification of linear systems • A reduced-order model by dominant poles • An approximation formula are the numerator and denominator polynomials of H(s)/L(s).

  12. 4.9 Examples and simulation • Hubble telescope pointing control • Aircraft roll control using Simulink • Sequential design example:disk drive read system Pay attention to design process Refer to P266-271 Self-learning after class

  13. 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 )

  14. Assignment • E5.10 • E5.12 • E5.13 • E5.17 • P5.19

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