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Design of a Robust Hi/H2/MOC LMI-based Iterative Multivariable PID for Speed and Voltage Control of a Sample Power System

This paper presents the design steps and carries a comparative study between three Linear Matrix Inequality (LMI)-based iterative multivariable Proportional-Integral-Derivative (PID) controllers; PID design using H∞-norm, named Hi, PID design using H2-norm, named H2, of the system transfer function, PID design with Maximum Output Control (MOC), named Max, and the classical LMI-based robust output feedback controller using H∞-norm, named ROB. Multivariable PID is considered here because of its wide use in the industry, simple structure and easy implementation. It is also preferred in plants of higher order that cannot be reduced and thus require a controller of higher order such as is the case for the classical robust H∞ output feedback controller whose order is the same as that of the plant. LMI technique is selected because it allows easy inclusion of divers system constraint requirements that should be fulfilled by the controller, and thus make its design very efficient. The duty of each of the controllers is to drive a single-generator connected to a large power system via a transformer and a transmission line. The generator is equipped with its speed/power (governor) and voltage (exciter) control-loops that are lumped in one block. The errors in the terminal voltage and in the output active power, with respect to their respective references, represent the controller inputs and the generator-exciter voltage and governor-valve position represent the controller outputs. A comparative study is carried out using the named controllers (Hi, H2, Max, ROB). Divers tests are applied, namely, step-change and tracking in the references of the controlled variables, and variation in some plant parameters, to demonstrate the controllers effectiveness. Encouraging results are obtained that motivate for further investigations.