Problem 2 (Closed-loop performance of a robot arm, 25 pts)
A robotic arm actuated at the elbow is shown in Figure 1, along with its control system. Using the final value theorem, select the transfer function Gp(s) so that the steady-state error for a step input is zero. Using this filter, plot the output for a step input with K=1, 1.5, and 2.85. Record the rise time, settling time and overshoot for these three gains. We wish to limit the overshoot to less than 6% while achieving the shortest rise time as possible. Select the best gain K to achieve this. (Hint: you may use MATLAB tools from the control system diagram such as the 'step' command, and you can apply it to the system defined by transfer functions 'tf", 'series', and 'feedback' commands. Help 'control' for a complete list of control system toolbox commands).