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.
Delmar's Standard Textbook Of Electricity
7th Edition
ISBN:9781337900348
Author:Stephen L. Herman
Publisher:Stephen L. Herman
Chapter24: Resistive-inductive-capacitive Parallel Circuits
Section: Chapter Questions
Problem 1RQ: An AC circuit contains a 24 resistor, a 15.9-mH inductor, and a 13.3F capacitor connected in...
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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%](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F25ba2389-39eb-4ed1-aa8c-95543d75ad1a%2Fe73b1ee7-371e-4c8c-8baf-ae7203acb16d%2F8oib4c3_processed.jpeg&w=3840&q=75)
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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