MODERN CONTROL THEORY [MCT]

               MODERN CONTROL THEORY           

Modern Control Theory

1. Modern control theory is carried out strictly in the complex-s or the frequency domain and can deal with multi-input and multi-output (MIMO) systems. This overcomes the limitations of classical control theory in more sophisticated design problems, such as fighter aircraft control.

2. In modern design, a system is represented as a set of the first order differential equations defined using state variables.

3. Nonlinear, Multivariable, adaptive, and robust control theories come under this division.

4. Rudolf E Kalman and Aleksandr Lyapunov are well-known among the people who has shaped modern control theory (MCT)?

MCT- STATE SPACE MODEL

Modern control theory solves many of the limitations by using a much “richer” description of the plant dynamics. The so-called state-space description provide the dynamics as a set of  coupled first-order differential equations in a set  of internal variables are known as state variables,  together with a set of algebraic equations that  combine the state variables into physical output variables.

STATE-SPACE MODEL

1. Uses matrices and vectors to represent the system parameters and variables

2. In control engineering, a state-space representation is a mathematical model of a physical system as a set of input, output, and State variables related by first-order differential equations. To abstract from the number of inputs, outputs and states, the variables are expressed as vectors.

Advantages of State Space Model

1. Additional information as states, other than input and output is available

2. Uniform platform for representing time-invariant systems, time-varying systems, linear systems as well as nonlinear systems

3. It is possible to optimize the systems and use them for optimal design.

4. It is possible to include initial conditions.

5. without truncation of system dynamics

6. Systematic analysis and synthesis of higher-order systems

7. Convenient tool for MIMO systems

8. Can describe the dynamics in almost all systems (mechanical  systems, electrical systems, biological systems, economic  systems, social systems, etc.)

9. Transfer function representations are valid only for linear time-invariant (LTI) systems

Disadvantages of State Space Model

1. Complex techniques

2. Many computations are required