CLASSICAL CONTROL - TRANSFER FUNCTION MODEL

CLASSICAL CONTROL - TRANSFER FUNCTION MODEL

Classical Control - Transfer FUNCTION MODEL

1. Classical control is a branch of control engineering that deals with the behavior of dynamical systems with inputs, and how their behavior is modified by feedback, using the Laplace transform as a basic tool to model such systems.

2. In classical control systems, knowledge of the plant is in the form of a set of algebraic and differential equations, which analytically relate inputs and outputs.  

3. The system analysis is carried out in the time domain using differential equations in the complex-s domain with Laplace transform or in the frequency domain by transforming from the complex-s domain.

4. All systems are assumed to be second-order and single variable, and higher-order system responses and multivariable effects are ignored

5. The classical control theory and methods (such AS ROOT locus) are based on a simple input-OUTPUT DESCRIPTION of the plant, usually expressed as A TRANSFER function.

6. These methods do not HAVE ANY knowledge of the interior structure of THE PLANT, and limit us to single-input single-OUTPUT (SISO) systems, and allows only limited control of the closed-loop behavior when feedback control is used

7. Transfer function models describe the relationship between the inputs and outputs of a system using a ratio of polynomials. The order of the Transfer Function model is equal to the order of the denominator polynomial.

8. The roots of the denominator polynomial are referred to as the poles of the Transfer Function model. The roots of the numerator polynomial are referred to as the zeros of the model. The parameters of a transfer function model are its poles, zeros, and transport delays.

LIMITATIONS/DRAWBACKS

1. Transfer function defined only under zero initial condition

2. Applicable only to the linear time-invariant system. (Due to the assumptions such as linearity, time-invariance, etc.)

3. It Is restricted to single input single output as this becomes highly cumbersome for use in the multi-input multi-output system.

4. It reveals only the system output for a given input and provides no information regarding the internal states of the system

5. It does not provide an optimal design