Mikhailov's criterion states that a real Hurwitz polynomial) (s  of degree n satisfies the monotonic phase increase, that is to say the argument of) (jw  goes through n quadrants as w runs from zero to infinity. In this paper, we utilize the generalized Mikhailov criterion presented in [1] to give a solution to the problem of finding the stabilizing feedback gains for a given linear-time invariant plant having a P controller, a PI controller and a PID controller.

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This paper describes the design and implementation of various type of controllers, used in controlling the double integrator system with input saturation none linearity. Two different types of controllers for the double integrator system will be discussed, conventional or classical controllers and intelligent controllers. The double integrator plant, which is one of the most fundamental systems in control applications, is considered here. Some of applications of the double integrator plant are, satellite control system [1], [2], single-degree-of-freedom translational [4], single-axis spacecraft rotation, alpha joint of Space station, inverted pendulum system with an on-off actuator, and, conventional hard disk drive with a single voice-coil-motor (VCM) actuator. First, the design of different conventional controllers for the double integrator plant with saturation nonlinearity will be presented. Then, the design and implementation of two types of Fuzzy Logic Controller (FLC) will be presented. Finally, PID controller for the Double Integrator system that is tuned using genetic algorithms will be presented. It was found that PID controller for the double integrator system that is tuned using genetic algorithms is better than the other controller.