Compensators And Controllers – GATE ECE Control SystemsPractice Questions & PYQs

Let $\mathrm{G}(\mathrm{s})=\frac{1}{10 \mathrm{~s}^{2}}$ be the transfer function of a secondorder system. A controller M(s) is connected to the system $\mathrm{G}(\mathrm{s})$ in the configuration shown below. Consider the following statements. (i) There exists no controller of the form $M(s)=\frac{K_{I}}{s}$ , where $K_{I}$ is a positive real number, such that the closed loop system is stable. (ii) There exists at least one controller of the form $\mathrm{M}(\mathrm{s})=\mathrm{K}_{\mathrm{P}}+\mathrm{s} \mathrm{K}_{\mathrm{D}}$ , where $\mathrm{K}_{\mathrm{P}}$ and $\mathrm{K}_{\mathrm{D}}$ are positive real numbers, such that the closed loop system is stable. Which one of the following options is correct?

A satellite attitude control system, as shown below, has a plant with transfer function $G(s)=\frac{1}{s^{2}}$ cascaded with a compensator $C(s)=\frac{K(s+\alpha)}{s+4}$ , where $K$ and $\alpha$ are positive real constants. In order for the closed-loop system to have poles at $-1 \pm j \sqrt{3}$ , the value of $\alpha$ must be ____

A unity feedback system that uses proportional-integral (\text{PI}$) control is shown \in the figure. The stability of the overall system is controlled by tuning the$\text{PI}$control parameters$K_{P}$and$K_{I}$. The maximum value of$K_{I}$ that can be chosen so as to keep the overall system stable or, in the worst case, marginally stable (rounded off to three decimal places) is ______

Which of the following statements is incorrect?

Which of the following can be pole-zero configuration of a phase-lag controller (lag compensator)?

A lead compensator network includes a parallel combination of R and C in the feed-forward path. If the transfer function of the compensator is $G(s)=\frac{s+2}{s+4}$ , the value of RC is ________.

The transfer function of a first-order controller is given as $G_{c}(s)=\frac{K(s+a)}{s+b}$ where K, a and b are positive real numbers. The condition for this controller to act as a phase lead compensator is

For the following feedback system $G(s)=\frac{1}{(s+1)(s+2)}$ . The 2% settling time of the step response is required to be less than 2 seconds. Which one of the following compensators C(s) achieves this ?

The transfer function of a compensator is given as $G_{c}(s)=\frac{s+a}{s+b}$ $G_{c}(S)$ is a lead compensator if

The transfer function of a compensator is given as $G_{c}(s)=\frac{s+a}{s+b}$ The phase of the above lead compensator is maximum at

A unity negative feedback closed loop system has a plant with the transfer function $G(s)=\frac{1}{s^{2}+2s+2}$ and a controller $G_{c}(s)$ in the feed forward path. For a unit set input, the transfer function of the controller that gives minimum steady state error is

The magnitude plot of a rational transfer function G(s) with real coefficients is shown below. Which of the following compensators has such a magnitude plot ?

Group I gives two possible choices for the impedance Z in the diagram. The circuit elements in Z satisfy the conditions $R_{2}C_{2} \gt R_{1}C_{1}$ . The transfer functions $\frac{V_{o}}{V_{i}}$ represents a kind of controller. Match the impedances in Group I with the type of controllers in Group II

A control system with PD controller is shown in the figure. If the velocity error constant $K_{V}$ =1000 and the damping ratio $\varsigma$ =0.5, then the value of $K_{P}$ and $K_{D}$ are

The open-loop transfer function of a plant is given as $G(s)=\frac{1}{s^{2}-1}$ . If the plant is operated in a unity feedback configuration, then the lead compensator that an stabilize this control system is

The transfer function of a phase lead compensator is given by $G_{c}(s)=\frac{1+3Ts}{1+Ts}$ where $T \gt 0$ The maximum phase shift provide by such a compensator is

A double integrator plant G(s) = K/ $s^{2}$ , H(s) = 1 is to be compensated to achieve the damping ratio $\zeta$ =0.5, and an undamped natural frequency, $\omega _{n}$ =5 rad/sec. Which one of the following compensator $G_{c}(s)$ will be suitable ?

A PD controller is used to compensate a system. Compared to the uncompensated system, the compensated system has