Modern Control Theory Previous
Question With Solution
AKU Modern Control Theory 2017
1. Answer any seven
questions of the following: 2x7=14
(a) What are the
drawbacks in transfer function model analysis?
(b) What is state and
state variable?
(c) What is the need for
state observer?
(d) Explain Eigen
vector.
(e) What is pole
placement by state feedback?
(f) Explain backlash.
(g) Write any two
properties of eigenvalues.
(h) What is a dominant
pole?
(i) What are phase
variables?
(j) What is state
observer?
SOLUTION
(a.) What are the
drawbacks in transfer function model analysis?
Ans.- (i)Transfer
function is defined under zero initial conditions.
(ii)Transfer function is applicable to linear time invariant
systems.
(iii)Transfer function analysis is restricted to SISO
systems.
(IV)It does not provides information regarding the internal state
of the system.
(b.) What is State and
state variable?
Ans.- *The state is the
condition of a system at any time instant, t.
*A set of variable which describes the state of the system at any
time instant are called state variables.
(c.) What is the need
for state observer?
Ans.- In certain systems
the state variables may not be available for measurement and feedback. In such
situations we need to estimate the un measurable state variables from the
knowledge of input and output. Hence a state observer is employed which estimates
the state variables from the input and output of the system. The estimated
state variable can be used for feedback to design the system by pole placement.
Ans.- Eigenvectors- The
eigenvectors Xi of a square matrix A is the vector that
satisfies
AXi= λi Xi
Where λi is one of the eigenvalues of A
(e) What is pole placement by state feedback?
Ans.-The pole placement by state feedback is a control system design technique ,in which the state variables are used for feedback to achieve the desired closed loop poles.
(f) Explain backlash.
Ans.-Backlash in engineering sometimes called lash or play is a clearance or lost motion in a mechanism caused by gaps between the parts.
(g) Write any two properties of eigenvalues.
Ans.- (i) A matrix and its transpose have the same eigen values.
(ii)The product of the eigen values (counting multiplicities) of the matrix equals the determinant of the matrix
(h) What is a dominant pole?
Ans.-Dominant(or insignificant) poles.The slowest pole of a system (those closest to the imaginary axis in the s-plane) give rise to the longest lasting terms in the transient response of the system. If a pole or set of poles are very slow compound to others in the transfer function, then is called as dominant pole.
(i) What are phase variables?
Ans.-The phase variables are defined as those particular state variables which are obtained from one of the system variable and its derivatives. Usually the variable used is the system output and the remaining state variables and then derivatives.
(j) What is state observer?
Ans.-A device (or a computer program) that estimates or observes the state variables is called state observer
(e) What is pole placement by state feedback?
Ans.-The pole placement by state feedback is a control system design technique ,in which the state variables are used for feedback to achieve the desired closed loop poles.
(f) Explain backlash.
Ans.-Backlash in engineering sometimes called lash or play is a clearance or lost motion in a mechanism caused by gaps between the parts.
(g) Write any two properties of eigenvalues.
Ans.- (i) A matrix and its transpose have the same eigen values.
(ii)The product of the eigen values (counting multiplicities) of the matrix equals the determinant of the matrix
(h) What is a dominant pole?
Ans.-Dominant(or insignificant) poles.The slowest pole of a system (those closest to the imaginary axis in the s-plane) give rise to the longest lasting terms in the transient response of the system. If a pole or set of poles are very slow compound to others in the transfer function, then is called as dominant pole.
(i) What are phase variables?
Ans.-The phase variables are defined as those particular state variables which are obtained from one of the system variable and its derivatives. Usually the variable used is the system output and the remaining state variables and then derivatives.
(j) What is state observer?
Ans.-A device (or a computer program) that estimates or observes the state variables is called state observer