In the control system shown in the figure below- a referance signal rt-t2is applied at time t - 0- The control system employs a PID controller Cs-Kp-KId-KDs and the plants has a transfer function Ps-3s- If Kp-10 -KI-1 and KD-2- the steady state value of e is

E(s)R(s)=11+[(PID)(P)] =s^23[s^2+k_ps+k_I+K_Ds^2] ∴ Steady state value of E is nbsp; E(∞)=Lim_s→ 0 sE(s) =lim_s→ o s.s^23[s^2+K_ps+K_I+K_Ds^2]×2s^3 =23 ...

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Standard XII

Physics

Work Energy Theorem

In the contro...

Question

In the control system shown in the figure below, a referance signal $r (t) = t^{2}$ is applied at time t = 0. The control system employs a PID controller $C (s) = K_{p} + \frac{K_{I}}{d} + K_{D} s$ and the plants has a transfer function $P (s) = \frac{3}{s} .$ If $K_{p} = 10, K_{I} = 1 a n d K_{D} = 2$ , the steady state value of e is

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Solution

The correct option is B 2/3
$\frac{E (s)}{R (s)} = \frac{1}{1 + [(P I D) (P)]}$
$= \frac{s^{2}}{3 [s^{2} + k_{p} s + k_{I} + K_{D} s^{2}]}$
$∴$ Steady-state value of E is

$E (\infty) = L i m_{s \to 0} s E (s)$
$= l i m_{s \to o} s . \frac{s^{2}}{3 [s^{2} + K_{p} s + K_{I} + K_{D} s^{2}]} \times \frac{2}{s^{3}}$
$= \frac{2}{3}$

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In the control system shown in the figure below, a referance signal r(t)=t2is applied at time t = 0. The control system employs a PID controller C(s)=Kp+KId+KDs and the plants has a transfer function P(s)=3s. If Kp=10,KI=1 and KD=2, the steady state value of e is

The correct option is B 2/3E(s)R(s)=11+[(PID)(P)] =s23[s2+kps+kI+KDs2] ∴ Steady-state value of E is E(∞)=Lims→0 sE(s) =lims→o s.s23[s2+Kps+KI+KDs2]×2s3 =23