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Desing of Controllable/Observable Control Systems

Desing of Controllable/Observable Control Systems

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##### Date

2015-04-27

##### Authors

Hassan ibraheem, ibraheem

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##### Publisher

University of Khartoum

##### Abstract

The controllable/ observable control systems are designed using the
state equation model. In project we are interested in controlling the
system with control signal u (t), which is a function of several measure of
state variables. The basic ingredients of a control system can be described
by objectives of control, control system components and results or
outputs. In more technical term, the objectives can be identified with
inputs, or actuating signals, u, and outputs or the controlled variables, y.
An important first step in the design of controllable/ observable
control systems is the mathematical modeling of the controlled process.
In general, given a controlled process, the set of variables that identify the
dynamic characteristics of the process should first be defined. Therefore,
the key words to the design linear controllable/ observable control
systems are assumptions, identification, linearization and modeling.
The studies of design of controllable/ observable control systems
rely to a great extent on the use of applied mathematics. One of the major
purposes of the studies is to develop a set of analytical tools, so that the
designer can arrive at reasonable predicable and reliable designs without
depending completely on the drudgery of experimentation or extensive
computer simulation. MATLAB has been used for solving differential
equations
In the modern control theory, it is often desirable to use matrix
notation to simply complex mathematical expressions. The matrix
notation usually makes the equations much easier to handle and
manipulate.
Because of their simplicity and versatility, block diagrams are often
used to model all types of systems. A block diagram can be used simply
to describe the composition and interconnection of system. It can be used,
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together with transfer function, to describe the cause-and-effect
relationships through the system.
The signal-flow graph (SFG) may be regarded as a simplified
version of a block diagram. The (SFG) for the cause and effect
representation of linear systems, that are modeled by algebraic equations.
A SFG may be defined as a graphical means of portraying the inputoutput
relationships between the variables of a set of linear algebraic
equations
The states diagram an extension of the SFG to portray the state
equations, and differential equations. The significance of the state
diagram is that it forms a close relationship among the state equations,
and transfer functions.
In contrast to the transfer function approach to the design of
controllable/ observable linear control systems, the state variable method
is regarded as modern, since it is the underlying force for optimal control.
Transfer functions are defined only for linear time-invariant systems. The
relationship between the conventional transfer function approach and
state variable approach is established
So that, the analyst will be able to investigate a system problem with
various alternative methods.
Finally, the designs of controllable/ observable linear systems are
defined and their applications investigated.

##### Description

112 Pages