5. It is now desired to command test stand orientations using feedback control. Assume that we...

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5. It is now desired to command test stand orientations using feedback control. Assume that we have a sensor that measures the test stand orientation (s) with unity gain (i.e. it measures the test stand orientation exactly). Also assume that we have a proportional controller that takes the test stand orientation error as an input and produces the applied voltage to the DC motor. First, derive the closed-loop transfer function (s)/ (s). Next, find a proportional gain, k, such that the rise-time of the system is less than 0.26 sec, overshoot is less than 60%, and settling time is less than 5.5 sec. (Use the unmodified system). r?? Pref (t) e(t) Controller kp va(t) (t) Plant Figure 3: Control system schematic You can use MATLAB's feedback() function and stepinfo() function to determine the rise-time, overshoot, and settling time. Start with k = 1 and change the gain until the requirements are satisfied. Plot the resultant step response. 5. It is now desired to command test stand orientations using feedback control. Assume that we have a sensor that measures the test stand orientation (s) with unity gain (i.e. it measures the test stand orientation exactly). Also assume that we have a proportional controller that takes the test stand orientation error as an input and produces the applied voltage to the DC motor. First, derive the closed-loop transfer function (s)/ (s). Next, find a proportional gain, k, such that the rise-time of the system is less than 0.26 sec, overshoot is less than 60%, and settling time is less than 5.5 sec. (Use the unmodified system). r?? Pref (t) e(t) Controller kp va(t) (t) Plant Figure 3: Control system schematic You can use MATLAB's feedback() function and stepinfo() function to determine the rise-time, overshoot, and settling time. Start with k = 1 and change the gain until the requirements are satisfied. Plot the resultant step response.