Chapter 5 The Performance of Feedback Control Systems

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Chapter 5 – The Performance of Feedback Control Systems
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Presentation transcript:

Chapter 5 The Performance of Feedback Control Systems Test Input Signals Performance of a Second-Order System Effects of Third Pole and a Zero on the Second-Order System Response Estimation of the Damping Ratio The Steady-State Error of Feedback Control Systems Performance Indices

Preview The ability to adjust the transient and steady-state response of a feedback control system is a beneficial outcome of the design of control systems. Input signals such as step and ramp are used to test the response of the control system. In this chapter, common time-domain specifications are introduced: Transient Response and Steady-State Response Percent overshoot Settling time Time to peak Time to Rise Steady-State Tracking Error. The concept of a performance index that represents a system’s performance by a single number (or index) will be considered..

Test Input Signals

Performance of a Second-Order System + E(s) Y(s)

Standard Performance Measures

The Steady-State Error of Feedback Control Systems Ea(s) G(s) K1 + Y(s) - H(s)

Performance Indices A performance index is a quantitative measure of the performance of a system and is chosen so that emphasis is given to the important system specifications. A system is considered an optimum control system when the system parameters are adjusted so that index reaches an extremum value, commonly a minimum value. A performance index, to be useful, must be a number that is always positive or zero

Table 5.5 Summary of Steady-State Errors Number of Integrations in G(s), Type Number Step R(s)=A/s Input Ramp A/s2 ess=1/1+Kp Infinite 1 ess= 0 A/Kv 2

E5.1: In order to get ess = 0; When the input is a step we require one integration (type 1 system). For a ramp input we require type 2 system. G(s) H(s) Y(s) R(s) + - E(s)

The Optimum Coefficients of T(s) Based on the ITAE Criterion for a Step Input

E5.2: 100/(s+2)(s+5) Y(s) R(s) + -

E5.3 K / s(s+14) Y(s) R(s) + -

E5.8:

E5.10 The system is a type 1 (Table 5.5). The error constants are G(s) H(s) Y(s) R(s) + - E(s)

E5.13 GP(s) + E(s) K/s(s+2) R(s) Y(s) - K = 4 (s+3)/(s+0.1)