Adaptive collaborative speed control of PMDC motor using hyperbolic secant functions and particle swarm optimization

Abstract

This paper presents an adaptive collaborative speed controller for a permanent magnet direct-current (PMDC) motor. The proposed scheme beneficially combines the control efforts of a proportional-integral (PI) controller and a linear-quadratic regulator (LQR) via a weighted summing module. Initially, the weightages of the summing module are kept fixed. They are optimally tuned and tested via the particle swarm optimization algorithm. In order to synergize the controller combination, these weightages are adaptively modulated as well, using hyperbolic secant functions of the error dynamics of the motor's angular speed. The adaptive combination renders significant enhancement in the transient response, steady-state response, input-energy consumption, disturbance rejection, and variable load-torque handling capability of the motor. The adaptive-weighted controller is tested against the PI controller, the LQR, and a fixed-weighted collaborative controller via 'hardware-in-the-loop' experiments. The experimental results are presented to validate the robustness of the adaptive controller.

Improvement of the linear quadratic regulator control applied to a DC-DC boost converter driving a permanent magnet direct current motor

“…It allows the motor to run without disturbances and fluctuations in steady-state for different responses, the LQI controller is complemented by a Lyapunov-based model reference adaptation system (MRAS) that modulates the controller gains adaptively while maintaining the asymptotic stability of the controller [2]. An adaptive and collaborative speed controller used to control a permanent magnet direct current (PMDC) motor; this controller is designed by a proportionalintegral (PI) regulator and a linear-quadratic regulator (LQR), the adaptive combination of the two controllers brings an improvement on the transient and steady-state responses and the removal of the disturbances due to load-torque variations [3].…”

“…𝑠).𝐹 𝐵𝑜𝑜𝑠𝑡 (𝑠) 1+ 𝐹 𝑃𝐼 (𝑠).𝐹 𝐵𝑜𝑜𝑠𝑡 (𝑠) (34) By calculating the numerator and denominator of the closed-loop transfer function, then comparing the denominator with the third-order characteristic equation represented as (35). (𝑆 + 𝑎)3 = 𝑆 3 + 3𝑎𝑆 2 + 3𝑎 2 𝑆 + 𝑎3 (35)From the characteristic (35) and the denominator of the (34) we deduce the gains of the proportional integral corrector (PI), with: KP is the proportional gain and KI the integral gain. The LQR, LQR-PI and 𝐿𝑄𝑅 − 𝐾 𝑐𝑇𝑠+1control system is represented by Figure3.…”