自动控制理论-第三章.pptVIP

Error Signal Analysis Consider Sensitivity of Control Systems to Parameter variations The closed-loop transfer function: An open-loop system’s sensitivity is 1. A closed-loop system’s sensitivity is reduced by the loop gain Gc(s) G(s) , and allows G(s) to be less accurate. The Cost of Feedback Increase the number of components and complexity in the system. Loss of gain. Possibility of instability. The transient response is the response that disappears with time.——General Solution The steady-state response is the response that exits for a long time following an input signal initiation.——Special Solution 积分环节的增加使系统动态特性变差，因此，不能为消除稳态误差而随意增加系统型别。 3.5 Performance Indices A system is considered an optimum control system when the system parameters are adjusted so that the index reaches an extremum, commonly a minimum value. Table 3.2 The Optimum Coefficients of T(s) Based on the ITAE Criterion for Step Input DC motor DC motor 3.4 The steady state error of feedback control system Steady-state error is defined as the difference between the input and output of a system in the limit as time goes to infinity (i.e. when the response has reached the steady state). The steady-state error will depend on the type of input (step, ramp, etc) as well as the system type (0, I, or II). How to calculating steady-state errors The steady-state error for non-unity feedback systems The error constants of Kp, Kv, Ka The constant G(0) is denoted by Kp, which is called position error constant, and is given by: The constant sG(0) is denoted by Kv , which is called velocity error constant, and is given by: The constant s2G(0) is denoted by Ka , which is called acceleration error constant, and given by: G(s) : open-loop transfer function The steady state error with different test signals Unit Step Input (R(s) = 1/s): Unit Ramp Input (R(s) = 1/s2): Unit Parabolic Input (R(s) = 1/s3): System type and steady-state error Type 0 systems Step