控制原理Chapter 2-3-3 linearization.pptVIP

Chapter 2-1 CHAPTER 2　Mathematical Models of Systems By Hui Wang Outline of this chapter Introduction Differential Equation of Physical Systems Transfer Function State Equation of Systems Block Diagram, Signal Flow Graphs Linearization The relation of various models ……… Linearization Linearization, why? How to do? Most physical systems in nature are nonlinear. Ex. Nonlinear System Example-1: AC servomotor(see P57, 2.14) An AC servomotor is shown as Fig.2.28(P58). As Fig.(b), the torque-speed curves are not straight line. So, a linear differential equation cannot be used to represent the exact motor characteristics. Nonlinear System Example-1: AC servomotor(see P57, 2.14) Nonlinear System Example-1: AC servomotor(see P57, 2.14) Nonlinear System Example-2: Pendulum 非线性方程的线性化 几乎所有元件或系统的运动方程都是非线性方程。但在比较小的范围运动来说，把这些关系看作是线性关系，是不会产生很大误差的。方程式一经线性化，就可以应用迭加原理。 非线性方程的线性化方法 设非线性函数 非线性方程的线性化方法 非线性方程的线性化方法 非线性方程的线性化方法：例题（参见P54） 磁场控制的直流电动机。电枢电压ua为常值，输出为w ，控制输入为uf 。研究它的小偏差过程，例如控制输入uf改变一个微量Δuf引起的变化过程。 非线性方程的线性化方法 经线性化后，得到激磁回路偏量间的线性关系，动态电感L’f为常值，但在不同平衡点有不同的值 。 非线性方程的线性化方法 Nonlinear System Example-1: AC servomotor(see P57, 2.14) Nonlinear System Example-2: Pendulum Nonlinear System Example-2: Pendulum Analysis and Design Loop Thanks. * * We describe a nonlinear physical system by the general differential equation 2) Ratio of Reagent to Influent Flow 　　　（反应物） 14 13 12 11 10 9 8 7 6 5 4 3 2 1 0 0 0.2 0.4 0.6 0.8 1.0 1.2 1.4 1.6 1.8 2.0 1) Highly Nonlinear (Titration Curve) 滴定曲线 Input ec Output ? Fig.2.28 (a) According to original AC servomotor equilibrium equation where torque-speed equilibrium equation is (1) (2) （伺服马达） （转矩） Input ec Output ? Fig.2.28 (a) Eliminating steady-state item from Eq. (3), then an AC servomotor dynamic model is obtained. When small changes appear, equilibrium equation will be where J is a moment of inertia. (3) Noted Eq.(1) From Eq.(1) Input ec Output ? Fig.2.28 (a) It is obviously that an AC serv