1. Consider a mass-spring-damper system (i.e., the plant) described by the following second-order differential equation ÿ+3y+y=u (1) where y represents the position displacement of the mass. Our goal is to design a controller so that y can track a reference position r. The tracking error signal is then e(t) = r − y(t). (a) Let there be a PID controller •t u(t) = Kpe(t) + Ki S e(T)dT + Kɖė(t). (2) Derive the closed-loop system equation in forms of ODE. (b) Draw the block diagram of the whole system using transfer function for the blocks of plant and controller. Compute the closed-loop transfer function from the block diagram.
1. Consider a mass-spring-damper system (i.e., the plant) described by the following second-order differential equation ÿ+3y+y=u (1) where y represents the position displacement of the mass. Our goal is to design a controller so that y can track a reference position r. The tracking error signal is then e(t) = r − y(t). (a) Let there be a PID controller •t u(t) = Kpe(t) + Ki S e(T)dT + Kɖė(t). (2) Derive the closed-loop system equation in forms of ODE. (b) Draw the block diagram of the whole system using transfer function for the blocks of plant and controller. Compute the closed-loop transfer function from the block diagram.
Power System Analysis and Design (MindTap Course List)
6th Edition
ISBN:9781305632134
Author:J. Duncan Glover, Thomas Overbye, Mulukutla S. Sarma
Publisher:J. Duncan Glover, Thomas Overbye, Mulukutla S. Sarma
Chapter11: Transient Stability
Section: Chapter Questions
Problem 11.17P
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Hi there, I need help with this control systems question. Thank you.
![1. Consider a mass-spring-damper system (i.e., the plant) described by the following second-order
differential equation
ÿ+3y+y=u
(1)
where y represents the position displacement of the mass. Our goal is to design a controller so that
y can track a reference position r. The tracking error signal is then e(t) = r − y(t).
(a) Let there be a PID controller
•t
u(t) = Kpe(t) + Ki
S
e(T)dT + Kɖė(t).
(2)
Derive the closed-loop system equation in forms of ODE.
(b) Draw the block diagram of the whole system using transfer function for the blocks of plant
and controller. Compute the closed-loop transfer function from the block diagram.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F2b33a8c0-f1ae-4a2f-8b6f-1af4247b3f3d%2Fe268704b-08b0-4073-a64e-9520c4e043e5%2F8gljdw_processed.png&w=3840&q=75)
Transcribed Image Text:1. Consider a mass-spring-damper system (i.e., the plant) described by the following second-order
differential equation
ÿ+3y+y=u
(1)
where y represents the position displacement of the mass. Our goal is to design a controller so that
y can track a reference position r. The tracking error signal is then e(t) = r − y(t).
(a) Let there be a PID controller
•t
u(t) = Kpe(t) + Ki
S
e(T)dT + Kɖė(t).
(2)
Derive the closed-loop system equation in forms of ODE.
(b) Draw the block diagram of the whole system using transfer function for the blocks of plant
and controller. Compute the closed-loop transfer function from the block diagram.
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