Use of a motor to control the position of a certain load

Chapter , Problem 11.23

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Use of a motor to control the position of a certain load having inertia, damping, and elasticity gives the following plant transfer function. See Figure P11.23.

                                   \(G_p(s)=\frac{\Theta(s)}{V(s)}=\frac{0.5}{\left(s^2+s+1\right)(s+0.5)}\)

a. Use the ultimate cycle method to compute the controller gains for P, PI, and PID control.

b. Plot and compare the unit-step responses for the three designs obtained in (a). If the PID response is unsatisfactory, tune the gains to improve the performance.

                                                       

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