[CUSTOM SOLUTION] Classical Control System

Classical Control System Design Spring 2021Matlab ProjectCompensator Design & SimulationObjectiveYour term project will be to design and simulate PI compensators for a control system using Matlab/Simulink (using Octave is also accepted).System ModelFYI, a possible block diagram of a speed control scheme for a hybrid electric vehicle driven by a dc motor isWith typical values of the parameters, the system can represented in a simplified unity-feedback form as followswhere R(s) is the reference voltage, C(s) = KssV (s) is the output voltage of the speed sensor, and GSC(s) denotes a controller (to be designed).AssignmentTask 1. Proportional compensation Assume GSC(s) is a proportional (P) controller, i.e., GSC(s) = KP .(a) Find the closed-loop system transfer function and determine the range of KP > 0 for stability.(b) For the uncompensated closed-loop system (i.e., with KP = KP1 = 1):—Simulate and plot the system unit-step response c(t).—Determine (from the plot) the P.O., peak time Tp, rise time Tr, settling time Ts, and steady-state error estep(?) in % of the input—Find also eramp(?) =? —Plot the Bode diagrams and indicate the bandwidth, and the phase and gain margins.(c) Find KP = KP2 that yields a steady-state error estep(?) = 1%.

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