To study closed loop position constrol using a DC motor and PID controller.
The motor has the model considered in the previous example. It is constrolled by a PID controller which has the position error as input. Note that the motor transfer function constains an integration so that there will be no steady state error to a step reference input with the PID controller in the proportional mode. On the other hand a non zero value for the disturbance input W will cause a steady state error.
There are two inputs, the reference input, S, and the disturbance input, W.
Check that there is a position error with the controller in the P mode when W is not zero. You may wish to calculate this for specific parameters and compare with the simulation results. Include an integral term in the controller to show that with finite W there is now no position error. By examining the controller output signal, note that to avoid pure differentiation of the step input and therefore a very high value of controller output at t = 0+ a non zero value of τ is required.
|J||3.2284E-6||J = 3.2284.10–6||[kg.m2]||moment of inertia of the rotor|
|B||3.5077E-6||B = 3.5077.10–6||[N.m.s/rad]||damping ratio of the mechanical system|
|K||0.0274||K = 0.0274||[Nm/Amp]||electromotive force constant|
|R||4||R = 4||[Ω]||electric resistance|
|L||2.75E-6||L = 2.75.10–6||[H]||electric inductance|
|P||17||P = 17|
|I||600||I = 600|
|D||.15||D = 0.15|
|tau||0.0015||tau = 0.0015|
|S||1||S = 1||desired position of shaft|
|W||0||W = 0||disturbance|
May 20, 2012