An experimental comparison of different hierarchical self-tuning regulatory control procedures for under-actuated mechatronic systems

Abstract

This paper presents an experimental comparison of four different hierarchical self-tuning regulatory control procedures in enhancing the robustness of the under-actuated systems against bounded exogenous disturbances. The proposed hierarchical control procedure augments the ubiquitous Linear-Quadratic-Regulator (LQR) with an online reconfiguration block that acts as a superior regulator to dynamically adjust the critical weighting-factors of LQR’s quadratic-performance-index (QPI). The Algebraic-Riccati-Equation (ARE) uses these updated weighting-factors to re-compute the optimal control problem, after every sampling interval, to deliver time-varying state-feedback gains. This article experimentally compares four state-of-the-art rule-based online adaptation mechanisms that dynamically restructure the constituent blocks of the ARE. The proposed hierarchical control procedures are synthesized by self-adjusting the (i) controller’s degree-of-stability, (ii) the control-weighting-factor of QPI, (iii) the state-weighting-factors of QPI as a function of “state-error-phases”, and (iv) the state-weighting-factors of QPI as a function of “state-error-magnitudes”. Each adaptation mechanism is formulated via pre-calibrated hyperbolic scaling functions that are driven by state-error-variations. The implications of each mechanism on the controller’s behaviour are analyzed in real-time by conducting credible hardware-in-the-loop experiments on the QNET Rotary-Pendulum setup. The rotary pendulum is chosen as the benchmark platform owing to its under-actuated configuration and kinematic instability. The experimental outcomes indicate that the latter self-adaptive controller demonstrates superior adaptability and disturbances-rejection capability throughout the operating regime.

A robust variable-structure LQI controller for under-actuated systems via flexible online adaptation of performance-index weights

“…The Linear-Quadratic-Regulator (LQR) is a state-space controller that minimizes a quadratic performance index of the system's state-variations and control-input to deliver the optimal control decisions [10]. Despite its benefits, the LQR is incapable to address identification errors, model variations, and environmental indeterminacies [11,12]. The LQR can be retrofitted with auxiliary integral controllers to improve its robustness against uncertainties and load disturbances [13].…”

“…The aforementioned drawbacks of the LQR, and its variant(s), can be addressed by augmenting it with auxiliary online adaptation systems [12]. The dynamic adjustment of statecompensator gains offers a pragmatic approach to redesign the control law (after every sampling interval) to reject the transient disturbances in minimum time and attenuate the ensuing position-regulation fluctuations with minimal control energy expenditure while maintaining the controller's stability throughout the operating regime [15].…”

Fractional investigation of time-dependent mass pendulum

“…In many engineering areas more advanced pendulum configurations take place such as rotary or inverted pendulums where you have several, multi-variable equations of motion. 1,2 Then, there is always a need to develop methods in modelling and controlling such complex systems. In article, 1 flexible online adaptation strategies for the performance-index weights are presented to constitute a variable structure Linear-Quadratic-Integral controller for an under-actuated rotary pendulum system.…”

“…1,2 Then, there is always a need to develop methods in modelling and controlling such complex systems. In article, 1 flexible online adaptation strategies for the performance-index weights are presented to constitute a variable structure Linear-Quadratic-Integral controller for an under-actuated rotary pendulum system. Simple pendulum-bob is one of the most important examples in classical mechanics.…”

Global Asymptotic Stability of Nonlinear Strict Feedback System via Backstepping Control Approach

“…Two of the more efective techniques are feedback linearization, also known as nonlinear dynamic inversion (NDI), and linear quadratic (LQ) control [24]. Te suggested control (linear-quadratic-integral (LQI)) method aims to increase the adaptability of the controller by enabling fexible manipulation of the control rigidity, which helps in successfully discarding the bounded exogenous disturbances yet preserving the system's closed-loop stability and reducing the entire control energy expenditure [25].…”