Stability of Polynomial Characteristic Equation

Question 1

The term ____ refers to the
ideal situation where there are no physical limits on the input and output variables

Answer 1

unconstrained

Question 2

The term ____ refer to those forcing functions which do not
increase with time. Examples include a step or sinusoidal function. Ramp on the other hand is unbounded

Answer 2

bounded inputs

Question 3

The _____ determines the stability of a control system

Answer 3

closed loop characteristic
equation

Question 4

It states that a feedback control system is stable if and only if all roots of the characteristic equation are negative or have negative real parts. Otherwise, the system is said to be unstable.

Answer 4

General Stability Criterion

Question 5

Two commonly used methods
of stability analysis of control systems whose characteristic equations are polynomial in form.

Answer 5

Routh Stability Criterion / Array
Root Locus

Question 6

Routh (1905) developed an analytical technique in determining whether the roots of a polynomial have positive real parts

Answer 6

Routh Array

Question 7

A necessary and sufficient condition for all roots
of the characteristic equation to have negative real parts is
that all of the elements in the leftmost column of the Routh
array are positive.

Answer 7

Routh Stability Criterion

Question 8

In Routh Array all the coefficients are_____ than 0

Answer 8

greater

Question 9

A ____ is a visual representation
of how the roots of the characteristic equation changes with a certain control system parameter.

Answer 9

Root Locus Plot or Root Locus
Diagrams

Question 10

The point at which two root loci, emerging from two adjacent poles (or moving toward adjacent zeroes) on the real axis, intersect and then leave (or enter) the real axis is determined by the solution
of the equation

Answer 10

Breakaway Point

Question 11

There are q loci emerging from each qth order open loop pole at angles

Answer 11

Angle of Departure or Approach