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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 *(1) = – 36 -12 FIGURE DP11.6 and y(t) = x1(t). 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.. (a) 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.

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 *(1) = – 36 -12 FIGURE DP11.6 and y(t) = x1(t). 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.. (a) 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.

Principles of Heat Transfer (Activate Learning with these NEW titles from Engineering!)
Principles of Heat Transfer (Activate Learning with these NEW titles from Engineering!)
8th Edition
ISBN:9781305387102
Author:Kreith, Frank; Manglik, Raj M.
Publisher:Kreith, Frank; Manglik, Raj M.
Chapter11: Heat Transfer By Radiation
Section: Chapter Questions
Problem 11.12P
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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 =
Transcribed Image 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 =
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