北京理工大学810自动控制原理考研课件4.pptVIP

* * 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 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: * 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 Input Ramp Input Parabolic Input Steady State Error Formula 1/(1+Kp) 1/Kv 1/Ka Static Error Constant Kp = constant Kv= 0 Ka = 0 Error 1/(1+ Kp) infinity infinity For n=0, it will be called type 0 system. * For n=1, it will be called type 1 system. Type 1 systems Step Input Ramp Input Parabolic Input Steady State Error Formula 1/(1+ Kp) 1/Kv 1/Ka Static Error Constant Kp = infinity Kv = constant Ka = 0 Error 0 1/Kv infinity * For n=2, it will be called type 2 system. Type 2 systems Step Input Ramp Input Parabolic Input Steady State Error Formula 1/(1+ Kp) 1/Kv 1/ Ka Static Error Constant Kp = infinity Kv = infinity Ka = constant Error 0 0 1/ Ka * System Type Constants Steady state error ess(∞) Kp Kv Ka R(s)=1/s R(s)=1/s2 R(s)=1/s3 Type 0 Type 1 Type 2 Kp 0 0 ∞ Kv 0 ∞ ∞ Ka 1/(1+Kp) ∞ ∞ 0 1/Kv ∞ 0 0 1/Ka Steady state error with different input for different sys