Let  be the transfer function of a second-order system. A controller  is connected to the system  in the configuration shown below.

Consider the following statements.

(i) There exists no controller of the form , where  is a positive real number, such that the closed loop system is stable.

(ii) There exists at least one controller of the form , where  and  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  cascaded with a compensator , where K and  are positive real constants.

In order for the closed-loop system to have poles at , the value of  must be ________.

A unity feedback system that uses proportional. integral (PI) control is shown in the figure.

The stability of the overall system is controlled by tuning the PI control parameters  and . The maximum value of  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 can be the pole-zero configuration of a phase-lag controller (lag compensator)?

Which of the following statements is incorrect?

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 , the value of RC is ________.

For the following feedback system. 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 first-order controller is given as . Where K, a and b are positive real numbers. The condition for this controller to act as a phase lead compensator is

The transfer function of a compensator is given as

 is a lead compensator if

The transfer function of a compensator is given as

The phase of the above lead compensator is maximum at

A unity negative feedback closed loop system has a plant with the transfer function  and a controller  in the feed forward path. For a unit step 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 condition . The transfer 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

The open-loop transfer function of a plant is given as  . If the plant is operated in a unity feedback configuration, then the lead compensator that can stabilize this control system is

The transfer function of a phase lead controller is. The maximum value of phase provided by this controller is

Which one of the following polar diagrams corresponds to a lag network?

A double integrator plant, ,  is to be compensated to achieve the damping ratio , and an un-damped natural frequency, . Which one of the following compensator  will be suitable?

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

A unity feedback system has the plant transfer function

(a) Determine the frequency at which the plant has a phase lag of 90º

(b) An integral controller with transfer function  is placed in the feed-forward path of the feedback system. Find 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 Figure, the process transfer function is , and the simplification factor of the power amplifier is . The design specifications required for the system are a time constant of 1 sec and a damping ratio of 0.707.

(a) Find the desired locations of the closed loop poles.

(b) Write down the required characteristic equation for the system. Hence determine the PD controller transfer function  when K=1.

(c) Sketch the root-locus for the system.

Tachometer feedback in a DC position control system enhances stability. ( True=1, False=0)

A process with open-loop model  is controlled by a PID controller. For this process