DP11.6 A coupled-drive apparatus is shown in Figure DP11.6. The coupled drives consist of two pulleys connected via an elastic belt, which is tensioned by a third pulley mounted on springs providing...

Extracted text: DP11.6 A coupled-drive apparatus is shown in Figure DP11.6. The coupled drives consist of two pulleys connected via an elastic belt, which is tensioned by a third pulley mounted on springs providing an un- derdamped dynamic mode. One of the main pulleys, pulley A, is driven by an electric DC motor. Both pul- leys A and B are fitted with tachometers that generate measurable voltages proportional to the rate of rota- tion of the pulley. When a voltage is applied to the DC motor, pulley A will accelerate at a rate governed by the total inertia experienced by the system. Pulley B, at the other end of the elastic belt, will also acceler- ate owing to the applied voltage or torque, but with a lagging effect caused by the elasticity of the belt. Integration of the velocity signals measured at each pulley will provide an angular position estimate for the pulley [23]. The second-order model of a coupled-drive is Spring Tensioning pulley Elastic belt 1 Pulley A Pulley B x(t) -36 -12 FIGURE DP11.6 and y(t) = x1(t). (a) Design a state variable feedback controller that will yield a step response with deadbeat response and a settling time (with a 2% criterion) of Ts ... 0.5 s. (b) (b) Design an observer for the system by placing the observer poles appropriately in the left half-plane. (c) (c) Draw the block diagram of the system including the compensator with the observer and state feedback. Write the Matlab code that used on pole placement on the system (d) (e) [0 0]T. (d) Simulate the response to an initial state at x102 = [1 0]T and xn102 =