# MCQ control (root locus - State space)

Quiz 1 MCQ control

The gain at the breakaway point for the unity feedback system where G(s)H(s)=(K(s2+2))((s+3)(s+4))(K(s2+2))((s+3)(s+4)) is

• a. 17.8
• b. 1.78
• c. 27.8
• d. 0.178

The gain at the breakaway point for the unity feedback system where G(s)H(s)=

المسأله دي عاوز k

For G(s)H(s)=Ks(s+2)(s+3)Ks(s+2)(s+3) the coordinates of valid breakaway/in point is

• a. -0.785
• b. 2.55
• c. -2.55
• d. 0.785

For G(s)H(s)=Ks(s+2)(s+3)Ks(s+2)(s+3) the coordinates of valid breakaway/in point is

• a. -0.785
• b. 2.55
• c. -2.55
• d. 0.785

The range of K for closed-loop stability, with unity feedback, G(s)=$$\frac{(K(s+2))}{(s(s-1)(s+3))}$$ is

• a. 1<k<100
•  b. There is no value of K that will stabilize this system
•  c. 0<K<100
•  d. -100<K<100

The break in point for the unity feedback system where G(s)H(s)=(K(s+2)(s+1))((s−2)(s−1))(K(s+2)(s+1))((s−2)(s−1)) is at

• a. 0.141
• b. -14.1
• c. -1.41
• d. -141

midterm MCQ control

The breakaway point for G(s)H(s)=(K(s+3)(s+5))((s+1)(s−7))(K(s+3)(s+5))((s+1)(s−7)) is at

• a. -4
• b. -6
• c. 0.6
• d. 3.78

The gain at the breakaway point for the unity feedback system where G(s)H(s)=(K(s+2)(s+1))((s−2)(s−1))(K(s+2)(s+1))((s−2)(s−1)) is

• a. 30
• b. 0.30
• c. 0.03
• d. 3.0

Consider a point S = -2 + j3 in the s-plane. Then for a system with the open loop transfer function G(s)H(S) = K(s+3)(s+4)(s+1)(s+2)K(s+3)(s+4)(s+1)(s+2)?

• a. S is on root locus with k = 29
• b. none of the above
• c. S is on root locus with k = 2.9
• d. S is not on root locus

how many poles of the following function are in the right half-plane, in the left half-plane, and on the jw-axis: T(s)=(s2+4s−3)(s4+4s3+8s2+20s+15)(s2+4s−3)(s4+4s3+8s2+20s+15)

• a. 2rhp, 2lhp
• b. 2jw, 2lhp
• c. 1rhp, 3lhp
• d. 3rhp, 1jw

quiz 2 MCQ control

3. State space analysis is applicable for non-linear systems and for multiple input and output systems.

• a) True
• b) False

Explanation: State space analysis is the technique that used state variables and state model for the analysis and is applicable for non-linear systems and for multiple input and output systems.

The transfer function for the state representation of the continuous time LTI system:

dq(t)/dt=Aq(t)+Bx(t)

Y(t)=Cq(t)+Dx(t)

is given by:

• a)C(sI-A)-1B+D
• b)B(sI-A)-1B+D
• c)C(sI-A)-1B+A
• d)D(sI-A)-1B+C

Explanation: Transfer function which is ratio of Laplace output to the Laplace input when the initial conditions are zero and is calculated by using both the equations.

6. Which among the following constitute the state model of a system in addition to state equations?

• a) Input equations
• b) Output equations
• c) State trajectory
• d) State vector

Explanation: Output Equations constitute the state model of a system in addition to state equations and for the complete state model mainly input model, output model and state models are required.

Consider the network shown in fig. this system represented in state space representation The system state variables are

• a. iL , ic
• b. Vc, iL
• c. None of these
• d. iR1, IR2

Conventional control theory is applicable to ______ systems

• a. Time varying
• b. Non-linear
• c. MIMO
• d. SISO
Consider the network shown in fig. the state equation for the circuit is
a.

1. Which among the following is a unique model of a system?
• a) Transfer function
• b) State variable
• c) Block diagram
• d) Signal flow graphs
Explanation: Transfer Function is defined as the ratio of the Laplace output to the Laplace input with the zero initial conditions and is a unique model of the system.

the transfer function y(s)/u(s) of a system described by the state equations x∙(t) = -2x(t)+2u(t) y(t) = 0.5x(t) is
• a.
• b.
• c.
• d.

Which among the following plays a crucial role in determining the state of dynamic system?
• a) State variables
• b) State vector
• c) State space
• d) State scalar
Explanation: State Variables are the integral part of the state variable analysis and plays a crucial role in determining the state of dynamic system.

State variable analysis has several advantages overall transfer function as:

• a) It is applicable for linear and non-linear and variant and time-invariant system
• b) Analysis of MIMO system
• c) It takes initial conditions of the system into account
• d) All of the mentioned
Explanation: State variable analysis has several advantages overall transfer function as it is applicable for linear and non-linear and variant and time-invariant system, analysis of MIMO system, it takes initial conditions of the system into account.

https://instrumentationtools.com/state-variable-analysis-part-ii/