Consider the below closed-loop block diagram of a second-order internal feedback process with an integrator block to produce Y(s). This process is being controlled by a proportional-derivative (PD) controller with proportional gain Kc and derivative gain Kp. The controller is in parallel form, as shown in the block diagram. We would like to analyze the stability of this system to determine the set of controller values that will result in closed-loop stability. 2.1. R(s) Kc+ KDS 1 (s+2)(s+3) IS Y(s) Perform block diagram algebra to arrive at the standard feedback loop control structure as depicted below. Clearly identify the transfer function G(s) based on the values given in the diagram above. R(s) KC + KDS G(s) Y(s) .2. 3. The "characteristic polynomial" is obtained by setting the denominator D(s) of the closed-loop transfer function equal to zero. Determine the characteristic polynomial for this system. Note that Kc and KD are Y(s) R(s) unknown parameters at this point. Regardless of what you arrived at in part (2.2), assume that the characteristic polynomial is: s3+4s² + (7+KD)s + Kc = 0 Determine the conditions for Kc and K, that are guaranteed to result in a stable closed-loop response this system is controlled via a PD feedback controller.
Consider the below closed-loop block diagram of a second-order internal feedback process with an integrator block to produce Y(s). This process is being controlled by a proportional-derivative (PD) controller with proportional gain Kc and derivative gain Kp. The controller is in parallel form, as shown in the block diagram. We would like to analyze the stability of this system to determine the set of controller values that will result in closed-loop stability. 2.1. R(s) Kc+ KDS 1 (s+2)(s+3) IS Y(s) Perform block diagram algebra to arrive at the standard feedback loop control structure as depicted below. Clearly identify the transfer function G(s) based on the values given in the diagram above. R(s) KC + KDS G(s) Y(s) .2. 3. The "characteristic polynomial" is obtained by setting the denominator D(s) of the closed-loop transfer function equal to zero. Determine the characteristic polynomial for this system. Note that Kc and KD are Y(s) R(s) unknown parameters at this point. Regardless of what you arrived at in part (2.2), assume that the characteristic polynomial is: s3+4s² + (7+KD)s + Kc = 0 Determine the conditions for Kc and K, that are guaranteed to result in a stable closed-loop response this system is controlled via a PD feedback controller.
Electricity for Refrigeration, Heating, and Air Conditioning (MindTap Course List)
10th Edition
ISBN:9781337399128
Author:Russell E. Smith
Publisher:Russell E. Smith
Chapter11: Thermostats, Pressure Switches, And Other Electric Control Devices
Section: Chapter Questions
Problem 23RQ
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Transcribed Image Text:Consider the below closed-loop block diagram of a second-order internal feedback process with an integrator block
to produce Y(s). This process is being controlled by a proportional-derivative (PD) controller with proportional gain
Kc and derivative gain Kp. The controller is in parallel form, as shown in the block diagram. We would like to analyze
the stability of this system to determine the set of controller values that will result in closed-loop stability.
2.1.
R(s)
Kc+ KDS
1
(s+2)(s+3)
IS
Y(s)
Perform block diagram algebra to arrive at the standard feedback loop control structure as depicted below.
Clearly identify the transfer function G(s) based on the values given in the diagram above.
R(s)
KC + KDS
G(s)
Y(s)
.2.
3.
The "characteristic polynomial" is obtained by setting the denominator D(s) of the closed-loop transfer
function equal to zero. Determine the characteristic polynomial for this system. Note that Kc and KD are
Y(s)
R(s)
unknown parameters at this point.
Regardless of what you arrived at in part (2.2), assume that the characteristic polynomial is:
s3+4s² + (7+KD)s + Kc = 0
Determine the conditions for Kc and K, that are guaranteed to result in a stable closed-loop response
this system is controlled via a PD feedback controller.
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