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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