西安理工大学自动化与信息工程学院自动控制理论Chapter3 Time-Domain Analysis of the Linnear Systems(3).pptVIP

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西安理工大学自动化与信息工程学院自动控制理论Chapter3 Time-Domain Analysis of the Linnear Systems(3).ppt

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3.4 Transient response analysis of the linear control system 2. The performance criteria 3.4.2 step response of the first-order systems 3.4.2 step response of the first-order systems 3.4.2 step response of the first-order systems 3.4.3 step response of the second-order systems The system could be described by a second-order differential equation. 3. step response of the typical second-order systems 4. The transient performance analysis of the second-order system Example 3.1 Solution: * * 3.4.1 Time-Domain transient performance specification of the linear control systems. 1. Step response The step response of the general control systems is shown in Fig.3.4.1 Step Response 1) Rise time tr for the curve① for the curve ② k1/s α 2. Why and How to research the first-order system? The system could be described by a first-order differential equation—the first-order system . Typical first-order system Why---many actual systems can be expressed as a first-order system. How---solve C(t) and analyze C(t). 3. The step response of the first-order system 1. What is the first-order system? The step signal r(t)=A0·1(t) Graphic representation Step response Pole distribution Re Im performance 2. Why and how to research the second-order system? 1. What is the second-order system? Why---many actual systems can be expressed as a second-order system. How---solve C(t) and analyze C(t). 3. step response of the typical second-order systems Here: Here: Three case: 1) ξ1 over damping case Poles distribution c(t) t Unit step response 2) ξ=1. critical damping case Poles distribution t c(t) Unit step response 3) 0ξ1. Under damping case Im S-plane Re Poles distribution c(t) t 1 Unit step response 4) ξ≤0. Zero or negative damping case system is unstable Poles distribution: Unit step response: c(t) t 1 ① Rise time tr ② Peak time tr ③ Setting time ts ④ maximum overshoot σp Note: 3.4.5 The response of t