自动控制原理-运动对象的微分方程描述.ppt

Chap2: Math. Models of Systems * 2.7 The Simulation of Systems Using MATLAB (Cont.) Chap2: Math. Models of Systems * 2.7 The Simulation of Systems Using MATLAB (Cont.) Chap2: Math. Models of Systems * 2.8 Summary Derive ordinary differential equations for simple physical systems. Transform DEs into Transfer Functions. Simplify system models by using the Block Diagrams or the Signal Flow Diagrams. Use Matlab for system modeling. End of Chapter 2 Mathematical Models of Systems Next Chapter ? The Time-Domain Analysis of Linear Systems Lecture Notes of Chaper 2, PAC Copyright by Dr Jun WANG, Tsinghua Univ. * Chap2: Math. Models of Systems * 2.5.2 The Transfer Functions of LRC Circuits Similarly, by Laplace transformation to the above DE under zero initial conditions, we have Chap2: Math. Models of Systems * 2.5.2 The Transfer Functions of LRC Circuits (Cont.) Is there an easier way of deriving transfer functions for LRC circuits? Yes!!! Why not use ‘Complex Impedances’ in Circuit Theory R (Resistance R) Ls (Inductance L) 1/Cs (Capacitance C) The impedance approach is valid only if the initial conditions involved are ALL zero. Chap2: Math. Models of Systems * 2.5.3 The Transfer Functions of Op-Amp Circuits The operating conditions for an ideal op-amp are i1 = 0 and i2 = 0 ? The input impedance is infinite. v2 ? v1 = 0 or v1 = v2 The input-output relationship for the ideal op-amp is vo = K (v2 ? v1) = ? K (v1 ? v2), K? ? The output voltage is not affected by the load connected to the output terminal. ? The output impedance is zero. Chap2: Math. Models of Systems * 2.5.3 The Transfer Functions of Op-Amp Circuits (Cont.) Chap2: Math. Models of Systems * 2.5.3 The Transfer Functions of Op-Amp Circuits (Cont.) Chap2: Math. Models of Systems * 2.5.3 The Transfer Functions of Op-Amp Circuits (Cont.) Chap2: Math. Models of Systems * 2.5.3 The Transfer Functions of Op-Amp Circuits (Cont.) —— An Exercise PID Controller Chap2: Math. Models of Systems * 2.5.3