Dynamics Of A Field Controlled DC Motor Assignment

where x1 is the armature current, sy is the speed, u is the field current, and 6, to 0, are positive constants. It is desired to design a state feedback controller such that the output y asymptotically tracks a time-varying reference signal r(t), where both r(t) and H) are continuous and bounded for all t?0. Assume that the domain of operation is restricted to x1>o3/2o1

1. Show that the system is input-output linearizable and has relative degree one.
2. Show that it is minimum phase.
3. Using feedback linearization, design a state feedback control to achieve the desired tracking.
4. Using computer simulation, study the performance of the system when ris the output of a first-order filter 1/(ra+ 1) driven by a step command w. The time constant r can be chosen to adjust the rate of change of r. In the simulation, take the initial conditions as z,(0) = 0/0, and 32(0) 0 and use the following numerical data: o1=60, o2=0.5, o3=40, o4=6, and o5=4.10⁴ Let the step command we change from 0 to 100 at t=1. Also, add saturation at the input of the plant such that the control signal is limited to ±0.05.
   1. 1. Adjust r and the feedback controller parameters to achieve a settling time of 0.5.
      2. Adjust and the feedback controller parameters to achieve a settling time of 0.1.
      3. Go back to the values used in part (1) and study the performance of the system when the rotor Inertia changes by 50%.
      4. Can you adjust the feedback controller parameters to improve its robust- ness to the parameter perturbations described in the previous part?

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