1. Physical Setup
A common actuator in control systems is the DC motor. It directly provides rotary motion and. coupled with wheels or drums and cables, can provide transitional motion The electric circuit of the armature and the free body diagram of the rotor are shown in the following figure:
For this project, we will assume the following values for the physical parameters. • moment of inertia of the rotor (1) = 3.2284E-6 kgent21s"2 • damping ratio of the mechanic, l system (b)= 3.5077E-6 Nms • electromotive force constant (K=KeKt) = XXXXXXXXXXNm/Amp • electric resistance (R)= 4 ohm • electric inductance (L) = 2.75E-6 H • input (V): Source Voltage • output (theta): position of shaft • The rotor and shaft are assumed to be rigid
2. System Equations
The motor torque, T, is related to the armature current, i, by a constant factor K,. The back tint e. is related to the rotational velocity by the following equations:
I-
e —
State Space Model These equations can also be represented in state-space form. If we choose motor position. motor speed. and armature current as our state variables. we can write the equations as follows-d = 00 K0IJ XXXXXXXXXXV 1 tit t 0 -KIL -JUL i 1IL 8 .1.=11 0 0] 8
3. Design specifications
R
Controller
AB. Plant
We will want to be able to position the motor very precisely. thus the steady-state error of the motor position should be zero. We will also want the steady-state error due to a step disturbance input D. to be zero as well The other performance requirement is that the motor reaches its final position very quickly In this case we want it to have a settling time of 4Onts We also want to have an overshoot smaller than 16% Thus if we simulate the reference input (R) by a unit step input. then the motor position output should satisfy • Settling unit less than 0 04 second • Overshoot less than 16°0 • Zero steady-state atm to a step input • Zeto steady-state coot due to a step disturbance
4. Project objectives Design a controller using the state-space method to meet the above specifications Your project report should contain the detailed justification of the type 'structure of controller. all the design steps. plots. the results, conclusions. and references No hand-written reports will be accepted