1. Automatic Control Theory School of Automation NWPU Teaching Group of Automatic Control Theory

2. Exercises (5) 2 — 8, 9 Automatic Control Theory

3. Review §2.3.3 Properties of transfer functions §2.3.1 Definition of Transfer Functions §2.3.2 Standard form of transfer functions §2.3.4 Limitations of Transfer Function Mathematical Model of Control Systems Differential Equation (Time-Domain) Transfer Function (Complex Domain) (1) G(s) is a complex function ； (2) G(s) only depends on the structure and parameters of the system (3) G(s) has direct relation with differential equation. (4) G(s) = L[ k(t) ] ； (5) G(s) corresponds to zero-pole plot on s-plane.

4. Transfer function （ 1 ） Example 1 Consider the system shown in the right figure. Its differential equation of the plant is Obtain the transfer function  s  of the system. Solution.(1) Obtain G 0 (s),we have (2) By the op-amp,we have

5. Transfer function （ 2 ） Thus

6. Automatic Control Theory （ Lecture 5 ） Chapter 2 Mathematical Model of Control Systems §2.1 Introduction §2.2 Time-Domain Mathematical Models of Control Systems §2.3 Complex Domain Mathematical Models of Control Systems §2.4 Block Diagrams of Control Systems §2.5 Signal Flow Graphs of Control Systems §2.6 Transfer Functions of control systems

7. §2.3.2 Transfer Functions for Common Components Common components

8. §2.3.3 Basic Factors (1) Factor ： representing different components with same transfer function. Typical factors Different components may have the same transfer function. The same component may have different transfer function if selections of input and output are different. Every transfer function may be regard as the combination of typical factors

9. §2.3.3 Basic Factors (2) Transfer function may be regard as the combination of typical link Problem of load effect

10. Mathematical model of control system

11. §2.3.2 Transfer Functions for Common Components of Control Systems （ 1 ） Potentiometer （ 2 ） Bridge type error angle detector （ 3 ） Synchro （ 4 ） Tachogenerator （ AC ， DC ） （ 5 ） Armature control DC motor （ 6 ） Two-phase Asynchronous Motor （ 7 ） Gear train Summary （ 1 ）

12. §2.3.3 Basic Factors （ 1 ） Gain 比例环节 （ 2 ） Derivative factor 微分环节 （ 3 ） Integral factor 积分环节 （ 4 ） First-order factor 惯性环节 （ 5 ） Quadratic factor 振荡环节 （ 6 ） Reciprocal first-order factor 一阶复合微分 （ 7 ） Reciprocal second-order factor 二阶复合微分 Summary （ 2 ）

13. Excises （ 5 ） 2 — 8, 9 Automatic Control Theory