Linear Control System

At high frequency, the asymptotic slope of the Bode magnitude plot for the transfer function G(s) = 100/[s(1+0.2s)(1+0.02s)]

1. −30 dB/decade
2. +60 dB/decade
3. −60 dB/decade
4. +20 dB/decade

The characteristic equation of a system is s³ + 5s² + 8s + K = 0 for marginal stability, the value of K is

1. 8
2. 20
3. 40
4. 50

For the transfer function G(s) = 1/(s+1) the magnitude at ω = 1 rad/s is

1. 0 dB
2. −3 dB
3. −6 dB
4. −10 dB

For a system with an open-loop transfer function G(s)H(s) = K/[s(s+2)(s+4)] the number of asymptotes in the root locus is

1. 1
2. 2
3. 3
4. 4

The root locus technique graphically shows the movement of

1. Zeros only
2. Closed-loop poles with varying gain
3. Poles only
4. Open-loop zeros with varying damping

A system is completely controllable if

1. The rank of the controllability matrix is less than the system order
2. Determinant of the system matrix is zero
3. The rank of the controllability matrix equals the system order
4. All eigenvalues are positive

For a unity feedback system with an open-loop transfer function G(s) = 20/[s(s+4)] the velocity error constant, K_v

1. 2
2. 4
3. 5
4. 20

For a minimum phase system, all zeros lie in

1. Right half plane
2. Left half plane
3. Imaginary axis only
4. Origin only

Which of the following devices converts shaft angular position into an electrical signal used for error detection in servo systems?

1. Tacho generator
2. Synchro
3. Stepper motor
4. Magnetic amplifier

The steady-state error for a Type-1 system subjected to unit step input is

1. Infinite
2. Unity
3. Zero
4. Depends on damping ratio

The open-loop transfer function of a control system is given below: G(s)H(s) = 30/[s(1+0.5s)(1+0.08s)]. Draw the Bode plot and determine: P.M., G.M., and comment on the closed-loop stability of the system.

Find C/R, C/D, and the total output for the system whose block diagram is shown below

The open-loop transfer function of a control system is given below: G(s)H(s) = K/[s(s+6)(s²+4s+13)]. Sketch the root locus and find the range of K for the system to be stable.

Determine the sensitivity of the overall transfer function at ω = 1 rad/sec w.r.t.
(i) Forward path transfer function (ii) Feedback path transfer function

Obtain the time response of the system given below: ẋ = Ax, where A = [0 1; −2 0]; x(0) = [1; 1] and y = [1 −1] [x₁; x₂].

For the given translational mechanical system, find the Force–Voltage (F-V) analogy.

Check the controllability of the system defined by the state matrix A = [0 1 0; 0 0 1; −6 −11 −6], B = [1; 0; 1], C = [10 5 1].

The open-loop transfer function of a control system is given below: G(s) = K/[s(1+0.2s)]. Design a suitable compensator such that the system will have K_v = 10 and P.M. = 50°.

Find the transfer function C/R

Using Nyquist stability criteria, examine the closed-loop stability of a control system whose open-loop transfer function is given below: G(s)H(s) = K/[s(1+sT)].

The open-loop transfer function of a control system is given by G(s) = K/[s(1+sT₁)(1+sT₂)]. Apply Routh-Hurwitz criteria to determine the values of K in terms of T₁ & T₂ for the system to be stable.

A second-order system is represented by a transfer function given below θ_o(s)/T(s) = 1/(Js²+fs+k), where θ_o the proportional output and T is the input torque. A step input of 10 Nm is applied to the system, and the test results are given below: M_p = 6 %, t_p = 1sec, and steady state output is 0.5 rad. Determine the values of J, f & k.

Absolute, conditional, and marginal stability with suitable examples

Nyquist stability criterion

P, PI, and PID controllers.

Concepts of controllability and observability