Q2The position of an elevator h(s) is controlled by means of lifting cables. A feedbackcontrol system is used to control the force applied by the cables to the elevator. Thetransfer function of the plant is,1Gp(s) =ControllerElevatorhr(s)h(s)E(s)G.(s)GP(s)A unit step input is provided. If only proportional control is used, show that theposition of the elevator oscillates about the reference value of 1. Find the period(a)of this oscillation.(b)Show that the addition of derivative action to the system can ensure a non-oscillatory response. Find a relation between the derivative and proportionalgains that ensures the response is non-oscillatory.(c)When the proportional and derivative gains are set to Kp = 9 and Kd = 6,respectively, find the damping ratio and natural frequency of the system. Derivethe time-domain response of the elevator for a unit step input and confirm thatit is not oscillatory.

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he position of an elevator h(s) is controlled by means of lifting cables ontrol system is used to control the force applied by the cables to the ransfer function of the plant is, 1 Gp(s) = s2 Controller Elevator hr(s) E(s) h(s) G(s) Gp(s) (E A unit step input is provided. If only proportional control is used, position of the elevator oscillates about the reference value of 1. F of this oscillation.

he position of an elevator h(s) is controlled by means of lifting cables ontrol system is used to control the force applied by the cables to the ransfer function of the plant is, 1 Gp(s) = s2 Controller Elevator hr(s) E(s) h(s) G(s) Gp(s) (E A unit step input is provided. If only proportional control is used, position of the elevator oscillates about the reference value of 1. F of this oscillation.

Elements Of Electromagnetics

7th Edition

ISBN:9780190698614

Author:Sadiku, Matthew N. O.

Publisher:Sadiku, Matthew N. O.

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Fluid Kinematics

The branch of science that deals with objects which are either in motion or stationary are studied under the branch of classical mechanics. Fluid mechanics is a subcategory of classical mechanics that deals with the behavior of fluids at rest (fluid statics) or in motion (posing some velocity). In fluid kinematics, studies focus on the associated motion of fluid particles or groups of particles, and its associated parameters like displacements, velocity, and acceleration without concerning about the forces that caused the motion. All the laws of classical mechanics are applied in the study of fluid kinematics.

Question

Q2
The position of an elevator h(s) is controlled by means of lifting cables. A feedback
control system is used to control the force applied by the cables to the elevator. The
transfer function of the plant is,
1
Gp(s) =
Controller
Elevator
hr(s)
h(s)
E(s)
G.(s)
GP(s)
A unit step input is provided. If only proportional control is used, show that the
position of the elevator oscillates about the reference value of 1. Find the period
(a)
of this oscillation.
(b)
Show that the addition of derivative action to the system can ensure a non-
oscillatory response. Find a relation between the derivative and proportional
gains that ensures the response is non-oscillatory.
(c)
When the proportional and derivative gains are set to Kp = 9 and Kd = 6,
respectively, find the damping ratio and natural frequency of the system. Derive
the time-domain response of the elevator for a unit step input and confirm that
it is not oscillatory.

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