西安理工大学自动化与信息工程学院自动控制理论Chapter7 Nonlinear Control System.pptVIP

Review of last class: 1. Singularity points of the phase locus Example: (a graduate examination) G(s) 0 1 -1 Solution: The system is equivalent to the Fig.7.2.3.5. G(s) N(X) Graphical explanation is shown as Fig.7.2.3.6 Fig.7.2.3.6 Re Im Stability analysis: (1) (2) Exercise: for this example, if: 7.2.4 Attentions and development 1. Attentions (1) Using the describing function to analyze the nonlinear system, the Linear parts of the system must be provided with a good charact-eristic of the low-pass filter→so that the harmonics produced by the nonlinear element can be neglected. (2) Generally the describing function method can only be used for analyzing the stability and self-oscillation of the nonlinear systems, not the stead-state error and transient specifications. 2. development Modern analysis and design method of the nonlinear systems: Computer simulation and intelligent design. 7.3 Phase plane method It is a kind of graphic method to solve first and second order differen- tial equation, put forward by Poincare In 1885. Four items: What is the Phase plane？ How to plot the Phase plane ？ How to analyze the nonlinear systems by the Phase plane method. Attentions and development. 7.3.1 What is the Phase plane 7.3.1 What is the Phase plane Fig.7.3.1 Graphic expression Increasing t direction Phase plane graph Always to be clockwise 7.3.2. plotting method of the phase locus 1. Analytic method Example 7.3.1: 1. Analytic method m=1 x k=1 Stable position Solution: 7.3.2. plotting method of the phase locus Example 7.3.2: r =0 e y c - For the system: Plot the phase loci of the system: Solution: r The phase loci of the system is shown in following figure→self-oscillation. 2. Graphic method---isoclinal method 7.3.2. plotting method of the phase locus Example 7.3.3: solution －2 －1 －0.5 0 0.5 1 2 0.5 1 2 －0.5 －1 0 －2 0 The values are shown in following table for different We can plot the isoclinals like as fo