Desing of Controllable/Observable Control Systems

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, 12 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.