The block diagram below shows a feedback controller for a skyscraper elevator’s vertical position. (a) Determine the closed-loop transfer function of the system, HCL(s) = Y(s)/R(s). (b) Assume that all initial conditions are zero. From HCL(s) in part (a), derive the equation of motion of the system. (c) Define the state variables of the system as phase variables and substitute them into the equation of motion in part (b). (d) Define the control input vector as u(t) = r(t). Rewrite the equation of motion in part (b) instate-space form, xdot = Ax+Bu. (e) Define 2 outputs: the elevator position and the elevator velocity. Write the output equation in state-space form, y = Cx + Du.
The block diagram below shows a feedback controller for a skyscraper elevator’s vertical position.
(a) Determine the closed-loop transfer function of the system, HCL(s) = Y(s)/R(s).
(b) Assume that all initial conditions are zero. From HCL(s) in part (a), derive the equation of motion of the system.
(c) Define the state variables of the system as phase variables and substitute them into the equation of motion in part (b).
(d) Define the control input
(e) Define 2 outputs: the elevator position and the elevator velocity. Write the output equation in state-space form, y = Cx + Du.
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