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A Positioning system drives a tester in electronic manufacturing processes. The system is made of a power amplifier, a motor field circuit, and a DC motor, as shown in the block diagram: u(t) v(t) i(t) K (1)e Amplifier Field circuit Motor The inputs and outputs of these variables are related by the following differential equations: de dr di 1) + e(t) = i(t) 2) dt + 5-i(t) = v(t) 3) v(t) = K•u(t) , Kis a constant a) Derive a state space equation for the open-loop system. (Define states, input, output and all the matrices). b) Is the system completely controllable (reachable) and observable? c) Find eigen values of the open-loop system.

A Positioning system drives a tester in electronic manufacturing processes. The system is made of a power amplifier, a motor field circuit, and a DC motor, as shown in the block diagram: u(t) v(t) i(t) K (1)e Amplifier Field circuit Motor The inputs and outputs of these variables are related by the following differential equations: de dr di 1) + e(t) = i(t) 2) dt + 5-i(t) = v(t) 3) v(t) = K•u(t) , Kis a constant a) Derive a state space equation for the open-loop system. (Define states, input, output and all the matrices). b) Is the system completely controllable (reachable) and observable? c) Find eigen values of the open-loop system.

Introductory Circuit Analysis (13th Edition)
Introductory Circuit Analysis (13th Edition)
13th Edition
ISBN:9780133923605
Author:Robert L. Boylestad
Publisher:Robert L. Boylestad
Chapter1: Introduction
Section: Chapter Questions
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A Positioning system drives a tester in electronic manufacturing processes. The system is made of a power amplifier, a motor field circuit, and a DC motor, as shown in the block diagram: u(t) v(t) i(t) K (1)e Amplifier Field circuit Motor The inputs and outputs of these variables are related by the following differential equations: de 1) dr + e(t) = i(t) di dt + 5-i(t) = v(t) 2) 3) v(t) = K•u(t) , Kis a constant a) Derive a state space equation for the open-loop system. (Define states, input, output and all the matrices). b) Is the system completely controllable (reachable) and observable? c) Find eigen values of the open-loop system. d) Design a closed-loop system with state feedback and with an input r(t) as command input to the closed-loop system. O(t) is to follow r(t). e) Choose specific state feedback gains and the power amplifier gain K, such that the systems response on e(t) to a step command r(t) = 1, t 2 0, has: 1) Zero steady state error 2) 2% settling time, T,s2 seconds 3) Overshoot s 4%
Transcribed Image Text:A Positioning system drives a tester in electronic manufacturing processes. The system is made of a power amplifier, a motor field circuit, and a DC motor, as shown in the block diagram: u(t) v(t) i(t) K (1)e Amplifier Field circuit Motor The inputs and outputs of these variables are related by the following differential equations: de 1) dr + e(t) = i(t) di dt + 5-i(t) = v(t) 2) 3) v(t) = K•u(t) , Kis a constant a) Derive a state space equation for the open-loop system. (Define states, input, output and all the matrices). b) Is the system completely controllable (reachable) and observable? c) Find eigen values of the open-loop system. d) Design a closed-loop system with state feedback and with an input r(t) as command input to the closed-loop system. O(t) is to follow r(t). e) Choose specific state feedback gains and the power amplifier gain K, such that the systems response on e(t) to a step command r(t) = 1, t 2 0, has: 1) Zero steady state error 2) 2% settling time, T,s2 seconds 3) Overshoot s 4%
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