Controller design by goal programming with optimization of dynamic error performance indices

• Grant number: 25/02079-0
• Support Opportunities: Scholarships in Brazil - Scientific Initiation
• Start date: April 01, 2025
• End date: January 31, 2026
• Field of knowledge: Engineering - Electrical Engineering - Industrial Electronics, Electronic Systems and Controls
• Principal Investigator: Alfredo Del Sole Lordelo
• Grantee: Renato Luchini Malatesta Junior
• Host Institution: Centro de Engenharia, Modelagem e Ciências Sociais Aplicadas (CECS). Universidade Federal do ABC (UFABC). Ministério da Educação (Brasil). Santo André , SP, Brazil

Abstract

This Scientific Initiation Research Project addresses the design of dynamic controllers for linear and time-invariant systems, monovariable and described by transfer functions, by pole placement based on goal programming with optimization of the dynamic error performance indices. The objective of the project is to minimize the total deviation of the closed-loop characteristic polynomial associated with the dominant pair of complex conjugate poles. The optimal solution of the goal programming problem results in the parameters of the dynamic controller transfer function and the tuning gain. The determination of the dominant pair of complex conjugate poles is based on the formulation of a convex and nonlinear optimization problem, whose solution results in the optimal damping factor and the optimal undamped natural frequency for linear and time-invariant, second-order systems in standard form, asymptotically stable and underdamped, that minimize the dynamic error performance indices ISE (Integral Square-Error) or ITSE (Integral-of-Time-multiplied Square-Error). This convex and nonlinear optimization problem considers as variables the damping factor and the undamped natural frequency associated with the constraints for the transient response performance indices, such as the peak time, the settling time and the maximum overshoot. The performance analysis will be based on the results obtained by computer simulation and by experimental implementation in an embedded microcomputer in the angular position control of the direct current electric motor.