16-04-2012, 02:37 PM
A State-Space Controller for DC Motor Position Control
Example_DC_Motor_State_Space_position_Controller.pdf (Size: 703.68 KB / Downloads: 123)
For this example, we will assume the following values for the physical parameters. These values were derived by experiment from an actual motor in Carnegie Mellon's undergraduate controls lab.
Designing the full-state feedback controller
Since all of the state variables in our problem are very easy to measure (simply add an ammeter for current, a tachometer for speed, and a potentiometer for position), we can design a full-state feedback controller for the system without worrying about having to add an observer. The schematic for a full-state feedback system is:
Disturbance Response
In order to get the disturbance response, we must provide the proper input to the system. Physically, a disturbance is a torque which acts on the inertia of the motor. A torque acts as an additive term in the second state equation (which gets divided by J, as do all the other terms in this equation). We can simulate this simply by modifying our closed loop input matrix, B, to have a 1/J in the second row. Add the following line to your m-file and re-run.
Adding Integral Action
We know that if we put an extra integrator in series with the plant it can remove steady-state error to an input. If the integrator comes before the injection of the disturbance, it will cancel the disturbance in steady state. This changes our control structure so it now resembles the following: