Two independent feedback control systems are needed to

Chapter , Problem 12.27

(choose chapter or problem)

Two independent feedback control systems are needed to position the pen of a flatbed x-y plotter. Consider only the control system for the x axis. An optical encoder provides feedback of the pen’s location. Assume that the dynamics of the motor and pen assembly are described by the following plant transfer function.

                                      \(G_{p} (s) =\frac{X(s)}{V(s)} =\frac{0.005}{s(0.1s + 1)(0.001s + 1)}\)

where x is the pen location in meters and v is the motor voltage. Design a compensator to achieve zero steady-state error for a step input and a 2% settling time of no more than 1 s, with an overshoot of no more than 4%.