Compensators · Control Systems · GATE ECE

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

Which of the following statement is incorrect?

The transfer function of a first-order controller is given as $${G_c}(s) = {{K\left( {s + a} \right)} \over {s + b}}$$

where k, a and b are positive real numbers. The condition for this controller to act as a phase lead compensator is

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

The pole-zero plot given below corresponds to a

The transfer function of a phase-lead compensator is given by $${G_c}(s) = {{1 + 3Ts} \over {1 + Ts}}$$

where T > 0. The maximum phase-shift provided by such a compesator is

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

The transfer function of a phase lead controller is $${\textstyle{{1 + 3Ts} \over {1 + Ts}}}.$$ The maximum value of phase provided by this controller is

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 lead compensator network includes a parallel combination of 'R' and 'C' in the feed-forward path. If the transfer function of the compensator is $${G_C}(s) = {{s + 2} \over {s + 4}}.$$ The value of RC is ____

The position control of a DC servo-motor is given in the figure. The values of the parameters are
K_t=1 N-m/A, R_a=$$1\Omega ,$$ L_a=0.1H,
J=5kg-m², B=1 N-m/(rad/sec) and K_b=1V/(rad/sec).
The steady-state position response (in radians) due to unit impulse disturbance torque T_d is ____.

The transfer function of a compensator is given as $${G_C}(s) = {{s + a} \over {s + b}}.$$

The phase of the above lead compensator is maximum at

The transfer function of a compensator is given as $${G_C}(s) = {{s + a} \over {s + b}}.$$

$${G_C}(s)$$ is a lead compensator if

A unity negative feedback closed loop system has a plant with the transfer function $$G(s) = {1 \over {{s^2} + 2s + 2}}$$ 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 sate error is

Group I gives two possible choices for the impedance Z in the diagram. The circuit elements in Z satisfy the condition $${R_2}{C_2} > {R_1}{C_{1.}}$$ The transfer $${\textstyle{{{V_0}} \over {{V_1}}}}$$ function represents a kind of controller. Match the impedances in Group I with the types of controllers in Group II. Group - I

Group - II
1. PID controller
2. Lead compensator
3. Lag compensator

A control system with a PD controller is shown in the figure. If the velocity error constant $${K_v} = 1000$$ and the damping ratio $$\zeta = 0.5,$$ then the values of $${K_P}$$ and $${K_D}$$ are

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

A double integrator plant, $$G(s) = {K \over {{s^2}}},H(s) = 1$$ 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 process with open-loop model $$G(s) = {{K{e^{ - s{\tau _d}}}} \over {\tau s + 1}},$$ is controlled by a PID controller. For this process

The transfer function of a simple RC network functioning as a controller is: $${G_c}(s) = {{s + {z_1}} \over {s + {p_1}}}$$

The condition for the RC network to act as a phase lead controller is:

A unity feedback system has the plant transfer function G_p(s)=$${1 \over {\left( {s + 1} \right)\left( {2s + 1} \right)}}$$
(a) Determine the frequency at which the plant has a phase lah of 90^o.
(b) An intergral controller with transfer function G_c(s)=$${k \over s}$$ , isplaced in the forwardpath the value of k such that the compensated system has an open loop gain margin of 2.5.
(c) Determine the steady state errors of the compensated system to unit-step and unit-ramp inputs.

For the feedback control system shown in the figure, the process transfer function is G_p(s) = $${1 \over {s(s + 1)}},$$ and the amplification factor of the Power amplifier is K$$ \ge $$0. The design specifications required for the system, time constant is 1 sec and a damping ratio of 0.707.
(a) Find the desired location of the closed loop poles.
(b) Write down the requiredcharacteristic equation for the system. Hense determine the PD controller transfer function G_p(s) when K = 1.
(c) Sketch the root-locus for the system.

A system with derivative control is shown in figure.
(a)Determine the transfer function and the characteristic equation of the system.

(b)Given that K > 0, find the range of '$$\tau $$' for which the system is unconditionally stable.