### Determining the System Type in Control TheoryTo define the type of a given control system, we must examine its components and feedback loop. Let's consider the following system:#### Controller and System:\[ C(s) = \frac{K(s + 1)}{s + 0.1} \]\[ G(s) = \frac{1}{s(s + 3)} \]where:- \( C(s) \) represents the transfer function of the controller.- \( G(s) \) represents the transfer function of the plant (system to be controlled).### Unit Feedback System:We assume a unit feedback for the system, meaning the feedback loop has a transfer function of 1.### Error Coefficients:For a control system, the position, velocity, and acceleration error coefficients are fundamental in determining the steady-state errors for different types of inputs (step, ramp, and parabolic).#### Position Error Coefficient (\( K_p \)):\[ K_p = \lim_{{s \to 0}} G(s) \cdot C(s) \]#### Velocity Error Coefficient (\( K_v \)):\[ K_v = \lim_{{s \to 0}} s \cdot G(s) \cdot C(s) \]#### Acceleration Error Coefficient (\( K_a \)):\[ K_a = \lim_{{s \to 0}} s^2 \cdot G(s) \cdot C(s) \]### Steady-State Errors:The steady-state error for different types of inputs are calculated as follows:#### For Step Input:\[ e_{ss} = \frac{1}{1 + K_p} \]#### For Ramp Input:\[ e_{ss} = \frac{1}{K_v} \]#### For Parabolic Input:\[ e_{ss} = \frac{1}{K_a} \]### Conclusion:Determine the system type by calculating these error coefficients and analyze the steady-state error for the given step, ramp, and parabolic inputs. This systematic approach allows us to understand the behavior and accuracy of the control system.

Given C(s)=K(S+1)/(S+0.1)G(s)=1/S(S+3)Unity feedback system we need to find position, Velocity,…

Define the system type. C(s) = K(s+1) s +0.1 G(s) = s(s+ 3) a unit feedback Determine the position-velocity-acceleration error coefficients in the control system. steady state error Find for step, ramp and parabola input. controller and serial to it

Define the system type. C(s) = K(s+1) s +0.1 G(s) = s(s+ 3) a unit feedback Determine the position-velocity-acceleration error coefficients in the control system. steady state error Find for step, ramp and parabola input. controller and serial to it

Introductory Circuit Analysis (13th Edition)

13th Edition

ISBN:9780133923605

Author:Robert L. Boylestad

Publisher:Robert L. Boylestad

Chapter1: Introduction

Section: Chapter Questions

Problem 1P: Visit your local library (at school or home) and describe the extent to which it provides literature...

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