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Generally, the problem of a [[control system]] design consists of choosing a proper controller considering the system dynamics, which is to be controlled, and desired performance specifications. There are three main theory for a design procedure: Conventional Control Theory, Modern Control Theory and Algebraic Approach. The main difference among these theories is the design approach used to obtain the controller and the mathematical expressions used to represent the system.
Classical control methods, such as frequency response method and
Modern control methods, like pole-placement, [[optimal control]] (LQR) and H¥ , use [[state space (controls)|state-space representation]]. This representation, especially as the plant degree gets larger, involves complex calculations which require the use of a computer.
Algebraic methods like pole-placement direct method and CDM use polynomial expressions. In this representation, since the numerator and denominator of the transfer function are considered independently from each other, better results can be achieved against pole-zero cancellations. In this approach, the type and degree of the controller polynomials and characteristic polynomial of the closed-loop system are defined at the beginning. Considering the design specifications, coefficients of the polynomials are found later in the design procedure. In algebraic methods, CDM is the one which gives the most proper results with the easiest procedure. In CDM, design specifications are equivalent time constant (t ), stability indices (yi) and stability limits (yi*). These parameters have certain relations which will be explained later with the controller polynomials.<ref>S. Manabe (1994), ''A low cost inverted pendulum system for control system education'', The 3rd IFAC Symposium on advances in Control Education, Tokyo.</ref>
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