A Novel Implicit Adaptive Pole-Placement PID Controller

A. Zayed, M. El-Fandi (Libya), A. Hussain (UK), and A. El-Fllah (Libya)


Adaptive control design, pole placement, minimumvariance control, water bath system.


In this paper, a new computationally efficient multivariable self-tuning controller with a proportional plus integral plus derivative (PID) is derived. The algorithm features a combination of the self-tuning property, in which the controller parameters tuned automatically on-line, and also the structure of multivariable PID controller, making it more favorable for use in industry. In addition the proposed controller has the ability to place the closed loop poles at their desired positions. It is an implicit algorithm in the sense that the controller step is trivial and avoids solving simultaneous equations ( as is the case in the most of the adaptive pole placement controllers which involve solving a Diophantine equations at each sampling step). Moreover, the multivariable controller is obtained as a left matrix fraction and so can be immediately implemented. It tracks set-point changes with the desired speed of response, penalises excessive control action, and can be applied to non-minimum phase systems. Additionally, at steady state, the controller has the ability to regulate the constant load disturbance to zero. Example simulation results using simulated plant model demonstrate the effectiveness of the proposed controller.

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