Fixed order controller design via linear programming

Yip, King-Chi
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Aerospace Engineering
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Fixed order controllers, such as PD, PI and PID controllers, are the most commonly used in hardware implementations. Therefore, control engineers are often given the task to design fixed order controllers with time domain specifications as the system design requirements. To solve this problem, a systematic fixed order controller design process employing mathematical programming is developed in this thesis. The design process is based on fixed order pole assignment problem. Natural frequencies and minimum damping ratio are the design parameters of the developed controller design process. The design parameters are insightful since damping ratio and frequencies are closely related to time domain specifications. The interval polynomial search algorithm is formulated to maximize the interval characteristic polynomial within the design domain defined by the design parameters on the s-plane. The Edge Theorem is applied to ensure the performance and stability of the interval characteristic polynomial [3]. It is followed by solving the optimal controller, using the linear or non-linear programming with linear constraints technique. This proposed method ensures that the controller will attain the acceptable performance and stability even if the plant dynamic consists of some level of uncertainties. The advantage of this method is the freedom of the choices of design emphasis.

Aerospace engineering and engineering mechanics, Aerospace engineering