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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.

Introductory Circuit Analysis (13th Edition)
Introductory Circuit Analysis (13th Edition)
13th Edition
ISBN:9780133923605
Author:Robert L. Boylestad
Publisher:Robert L. Boylestad
Chapter1: Introduction
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Problem 1P: Visit your local library (at school or home) and describe the extent to which it provides literature...
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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.
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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