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Module 9 : Robot Dynamics & controls

Lecture 32 : General procedure for dynamics equation forming and introduction to control

Mathamatical Modelling of physical system:

We must keep in mind that deriving reasonable mathematical models is the most important part of the entire analysis of control systems.Mathamatical representation of given system may assume any one of the form among the following.

Differential Equation form:

It represents differential equations governing system dynamics. Such differential equations may be obtained by using physical laws governing a particular system e.g. Newton's laws for mechanical systems and Kirchoff's laws for electrical systems.

Transfer Function:

The model is derived from linear time invariant differential equation using the Laplace Transform. Though transfer function can be used only for linear systems, it yield more intuitive information than the differential equation. In this the input, output & system are distinct & separate parts.

With this we are in position to see the effect of changing system parameters on the system response.

The transfer function is also useful in modeling the interconnection of subsystems by forming block diagram but with a mathematical function inside each block.

Transfer function is obtained by using Laplace transforms of differential equations (linear systems).

State-Space Representation:

This can be used for that systems that can not be described by linear differential equations.

State space methods are used to model systems for simulation on digital computer.

This representation turns an n^th order differential equation into n simultaneous first order differential equation.

Issues in Design and Analysis of control system:

Major objectives of Control system analysis & Design:-

Producing desired transient response.

Reducing steady state error.

Achieving stability.

Consider a example of block sliding on frictionless floor.

We want to move block from AA to BB'. i.e Move to BB' is our command.