A Consider the DC motor-driven wheeled mobile robot shown in Figure 6.82, in which the voltage applied to the DC motor is computed by a controller. Assume that \(v_{\mathrm{a}}=2.56 i-0.37 x+4.61 \dot{x}+0.37 x_{r}\), where \(x_{r}\) is a reference trajectory that the cart should follow. Build a block diagram of the feedback control system, in which the mobile robot is constructed using Simscape blocks and the controller is constructed using Simulink blocks. Find the displacement response \(x(t)\) of the mobile robot if a unit-step reference command signal is sent to the system.

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Top view 12rk x m Driving wheel VV Front view (a) (b) La 0000 FIGURE 6.82 Problem 12. (a) a DC motor-driven wheeled mobile robot and (b) the simplified drive system.