Design of Linear Quadratic Regulator (LQR) Controller for Sepic Converter /

Abstract

DC-DC converters are extensively used in nearly all electrical and electronics products. Their purpose is to step up or step down the input voltage to an acceptable level for the device to be operated on it. Most of the electrical devices need constant input voltage for proper operation and any type of ripples or variations in the voltage can cause ill operation of the device. Control system is designed for the DC-DC converter to keep the output voltage constant regardless of the disturbances in input voltage, operating environment, or load. The performance of the controller depends upon the type of the controller and its design. Although, some of the controllers are very simple to design and can be implemented in hardware with ease, but they fail to meet the performance criterion in applications where large errors in output voltage cannot be tolerated. So, in those applications robust controllers are used. In this work, a Linear Quadratic Regulator (LQR) controller has been designed for Sepic Converter. Sepic Converter is a DC-DC converter which can step up or step down its input DC voltage. The significance of this converter over other converters is that it does not invert its input voltage, its ripple factor is very low, and it has continuous input current. It is used for the correction of power factor in industry and tracking Maximum Power Point (MPPT) in renewable energy harvesting. For the design of the controller, first a linearized model of Sepic converter is obtained. This is done by applying a linearization technique to average state space equations of Sepic converter. In LQR control, states are weighted by the designer in accordance with the results designer wants to achieve e.g., if the designer wants to set the overshoot or settling time for some value, he can set the weighting of the states accordingly in the 𝑄𝑙 Matrix. In this thesis, the steady state energies of the inductors and capacitors are used to calculate weighting for each state. To check controller performance, the controller response is analyzed for abrupt variations in input voltage, sudden variations in reference voltage and load. The results were analyzed, and the performance of the controller was found to be robust for all these sudden disturbances.