For a process , Gp(s)= (-2s+1)/(10s+2)(s+1) we use P controller to regulate the output. Assume Gv = 4 and Gm = e-1s . Determine the maximum Kc for which the output y'(t) is stable.
For a process , Gp(s)= (-2s+1)/(10s+2)(s+1)
we use P controller to regulate the output. Assume Gv = 4 and
Gm = e-1s . Determine the maximum Kc for which the output y'(t) is stable.
![**Transcription for Educational Website**
The given transfer function of a system can be expressed as:
\[ G_p(s) = \frac{-2s + 1}{(10s + 2)(s + 1)} \]
This function is composed of a numerator and a denominator:
- **Numerator**: \(-2s + 1\)
- This part indicates the zero of the system and reveals the impact of the frequency response at which the output tends to diminish or amplify.
- **Denominator**: \((10s + 2)(s + 1)\)
- This part indicates the poles of the system, which affect the stability and natural response of the system. The terms \(10s + 2\) and \(s + 1\) represent individual poles that contribute to the system's dynamics.
This transfer function is often used in control systems to analyze and design system behaviors in the frequency domain.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F4a76f768-a3a7-4f47-8ba0-be5f8bd27290%2Fefe15366-b02a-4c08-a2f7-46f497f7e190%2Fuyt7tnj_processed.png&w=3840&q=75)
Proportional controller (P-controller):
P-controller improves the steady-state performance. By using P-controller the error constant value increases which reduces the steady-state error produced by the system. It can reduce steady-state error but it cannot make it zero. P-controller also reduces the relative stability of the system.
Proportional derivative controller (PD-controller):
PD controller increases the value of zeta and reduces settling time and peak overshoot produced by the system.
It increases stability due to and is improved by the addition of zero. It is used to increase the stability of the system by adding zero. PD-controller improves the transient performance of the system.
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