Consider the following statements regarding 'relative stability'

Relative stability can be determined

1. in terms of gain margin only

2. in terms of phase margin only

3. in terms of gain margin and phase margin and location of poles in s-plane

4. in relation to another identified system

This question was previously asked in

ESE Electronics 2017: Official Paper

Option 3 : 3 and 4

CT 1: Determinants and Matrices

2903

10 Questions
10 Marks
12 Mins

__Concept:__

The LTI system is said to be stable if it satisfies following two conditions

1. If the system is excited by bounded input the output must be bounded.

2. If the input to the system is zero, the output must be zero irrespective of the all initial conditions.

The stability is classified into the following ways:

**Absolute stability**: Here system is stable for **all values** of system parameters.Like 'k' from 0 to ∞

**Marginal / critical / limitedly stable system**:

If the system is stable for a certain **range** of system parameters like 'k' from 0 to 100

**Relative stability:**

It is applicable for closed-loop stable systems only.

By using this we can find the time constant, settling time, the time required to reach the steady-state.

For the relative stability, both Gain margin and Phase margin is required.

Below table shows the nature of the system with respect to stability by comparing Gain margin and Phase margin.

NOTE: This is valid for Minimum phase system only.

**Minimum phase system: **All poles and zeroes are present at the left side of s-plane.

Condition |
Stability of the closed-loop system |
Gain margin in dB |
Gain margin in linear |
Phase margin |

ω |
Stable |
Positive |
> 1 |
Positive |

ω |
Marginal stable |
0 |
= 1 |
o° |

ω |
Unstable |
Negative |
< 1 |
Negative |

Gain margin **indicates** how much system gain is increased to drive the system into the verge of stability

Phase margin indicates how much **additional** phase is added to drive the system into the verge of stability.

We can also determine the stability in terms of other identified system when we compare different systems.