现代控制工程-第十章.pptVIP

4-5 The steady-state error of control systems 3.Steady-state errors and error constants to typical inputs Type number Type number Type number Type number Example 4.8 the diagram of the control system is given as: Please determine the steady-state error when H(s)=1 and H(s)=0.5. Solution: The OL transfer function is: When H(s)=1 The steady-state error will be When H(s)=0.5, when H(s)=1, if the steady-state error is 0.2, what is the k ? 4. Some comments (1) The final value theorem may fail when the inputs are as etc., we can use the theorem. When the inputs are sinusoidal, we can not use it. (4) unlike the stability and other property, the steady-state error is closely related with the inputs. 5. Steady-state error under disturbance let the input is R(s)=0，the system is only excited by the disturbance N(s) , and the system error will be: The error is right the negative of the response to the disturbance, it is relative to the OL transfer function G(s)=G1(s)G2(s)H(s), the input N(s), and what is more, it is also relative to the location of the working point of disturbance. The problem lies on the “Feedback Loop” in figure (b). Proportional components can not feedback and then eliminate the accumulated error in the output. If we insert an integrator before the working point of the disturbance, replacing with PI controller , then we can eliminate this steady error. 6. Disturbance compensation If the disturbance is measurable, we can improve the system accuracy by disturbance compensation in theory. The response to the disturbance is: This means that we can totally eliminate the error caused by the disturbance, but in fact, the compensator is not really realizable. Example 4.10 Disturbance compensation The output is: Mathematically, we can choose