Comprehensive tuning of Frequency shifted IMC-PID controller for boost converter using Harris Hawk optimization

Abstract The proportional integral derivative (PID) controller has been widely adopted in different applications because of its easy implementation compared to other existing control techniques. In most of the cases, PID controller’s tuning has been focussed on three main parameters: proportional gain <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:mfenced close=")" open="(" separators=""> <mml:mrow> <mml:msub> <mml:mrow> <mml:mi>K</mml:mi> </mml:mrow> <mml:mrow> <mml:mi>P</mml:mi> </mml:mrow> </mml:msub> </mml:mrow> </mml:mfenced> </mml:math> , integral gain <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:mfenced close=")" open="(" separators=""> <mml:mrow> <mml:msub> <mml:mrow> <mml:mi>K</mml:mi> </mml:mrow> <mml:mrow> <mml:mi>I</mml:mi> </mml:mrow> </mml:msub> </mml:mrow> </mml:mfenced> </mml:math> , derivative gain <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:mfenced close=")" open="(" separators=""> <mml:mrow> <mml:msub> <mml:mrow> <mml:mi>K</mml:mi> </mml:mrow> <mml:mrow> <mml:mi>D</mml:mi> </mml:mrow> </mml:msub> </mml:mrow> </mml:mfenced> </mml:math> . Other than the classical approaches, the internal model control (IMC) approach is an established approach to design a PID controller. In the IMC framework, the controller’s performance, viz., stability, robustness and transient response, depends upon the selection of an adequate IMC filter and proper tuning of filter constants. In this work a frequency shifted internal model control (FSIMC) approach is opted to design PID controller for a non-minimum phase (NMP) plant specifically the boost converter. Here, the PID controller is considered as a second order four-parameter modelled controller considering the derivative filter time constant <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:mfenced close=")" open="(" separators=""> <mml:mrow> <mml:msub> <mml:mrow> <mml:mi>T</mml:mi> </mml:mrow> <mml:mrow> <mml:mi>f</mml:mi> </mml:mrow> </mml:msub> </mml:mrow> </mml:mfenced> </mml:math> as an essential parameter other than its three gains <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:msub> <mml:mrow> <mml:mi>K</mml:mi> </mml:mrow> <mml:mrow> <mml:mi>P</mml:mi> </mml:mrow> </mml:msub> </mml:math> , <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:msub> <mml:mrow> <mml:mi>K</mml:mi> </mml:mrow> <mml:mrow> <mml:mi>I</mml:mi> </mml:mrow> </mml:msub> </mml:math> and <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:msub> <mml:mrow> <mml:mi>K</mml:mi> </mml:mrow> <mml:mrow> <mml:mi>D</mml:mi> </mml:mrow> </mml:msub> </mml:math> . In this work, optimal tuning of the three gains <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:msub> <mml:mrow> <mml:mi>K</mml:mi> </mml:mrow> <mml:mrow> <mml:mi>P</mml:mi> </mml:mrow> </mml:msub> </mml:math> , <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:msub> <mml:mrow> <mml:mi>K</mml:mi> </mml:mrow> <mml:mrow> <mml:mi>I</mml:mi> </mml:mrow> </mml:msub> </mml:math> and <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:msub> <mml:mrow> <mml:mi>K</mml:mi> </mml:mrow> <mml:mrow> <mml:mi>D</mml:mi> </mml:mrow> </mml:msub> </mml:math> of FSIMC-PID controller is achieved by two variables: (i) IMC filter constant ( <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:mi>λ</mml:mi> </mml:math> ) and (ii) frequency shifting parameter ( <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:mi>ψ</mml:mi> </mml:math> ). The derivative filter time constant <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:msub> <mml:mrow> <mml:mi>T</mml:mi> </mml:mrow> <mml:mrow> <mml:mi>f</mml:mi> </mml:mrow> </mml:msub> </mml:math> which is the fourth parameter of PID controller is optimized independently. A comprehensive optimal tuning of the FSIMC-PID controller which includes four parameters is achieved using the Harris-Hawk Optimization (HHO) algorithm. The optimized controller’s performance is evaluated in comparison to a conventional PID controller. Simulations study is performed on MATLAB Simulink platform to evaluate the servo and regulatory performance of the proposed controller based on transient response and performance indices including integral absolute error ( IAE ), integral square error ( ISE ), integral time absolute error ( ITAE ) and integral time square error ( ITSE ). Stability of the proposed FSIMC-PID controller is verified based upon the frequency response parameters and Routh-Herwitz (R-H)