Unit 1&2Lecture 1
UNIT - 1 & UNIT - 2
State Variable Analysis & Design
State Variable Analysis or State Space Analysis :-
The state variable approach is a powerful tool/technique for the analysis and design of control system.
The state space analysis is a modern approach and also easier for analysis using digital computers. It's gives the total internal state of the system considering all initial conditions.
Why do we need state space analysis?
The conventional approach used to study the behavior of linear time invariant control systems, uses time domain or frequency domain methods. When performance specifications are given for single input, single output linear time invariant systems, then system can be designed by using Root locus. When time domain specifications are given, Root locus technique is employed in designing the system. If frequency domain specifications are given, frequency response plots like Bode plots are used in designing the system.
In conventional methods, the systems are modelled using Transfer Function approach, which is the ratio of Laplace transform of output to input, neglecting all the initial conditions.
The drawbacks in the transfer function model and analysis are,
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Unit 1&2Lecture 1
- Transfer function is defined under zero initial conditions.
- transfer function is applicable to linear time invariant systems.
- It is restricted to single input and single output systems.
- Does not provides information regarding the internal state of the system.
- The classical methods like Root locus, Bode plot etc. are basically trial and error procedures which fail to dive the optimal solution required
State variables analysis can be applied for any type of systems like,
Linear system
Non- linear system
Time invariant system
Time varying system
Multiple input and multiple output system. the analysis can be carried with initial conditions.
Advantages of state variable analysis
- Convenient tool for MIMO systems
- Uniform platform for representing time-invariant systems, time-varying systems, linear systems as well as nonlinear systems
- Can describe the dynamics in almost all systems (mechanical systems, electrical systems, biological systems, economic systems, social systems etc.
- It can be performed with initial conditions.
- Variables used to represent system can be any variables in the system.
- Using this analysis the internal states of the system at any time instant can be predicted.
- As the method involves matrix algebra, can be conveniently adopted for digital computers.
Classical Control (Linear) / Modern Control (Linear)
/ Developed in 1920- / / Developed in 1950-
1950 / 1980
/ Frequency domain / / Time domain analysis
analysis & Design(Transfer / and design(Differential
function based) / equation based)
/ Based on SISO / / Based on MIMO
models / models
/ Deals with input and / / Deals with input,
output variables / output and state variables
/ Well-developed / / Not well-developed
robustness concepts / robustness concepts
(gain/phase margins)
/ No /
Controllability/Observabilit / Controllability/Observabilit
y inference / y can be inferred
/ No optimality / / Optimality issues can
concerns / be incorporated
/ Well-developed / / Fairly well-developed
concepts and very much in / and slowly gaining
use in industry / popularity in industry
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