Performance enhancement of multivariable model reference optimal adaptive motor speed controller using error-dependent hyperbolic gain functions

Abstract

The main contribution of this paper is to formulate a robust-adaptive and stable state-space speed control strategy for DC motors. The linear-quadratic-integral (LQI) controller is utilized as the baseline controller for optimal speed-regulation, accurate reference-tracking and elimination of steady-state fluctuations in the motor's response. To reject the influence of modelling errors, the LQI controller is augmented with a Lyapunov-based model reference adaptation system (MRAS) that adaptively modulates the controller gains while maintaining the asymptotic stability of the controller. To further enhance the system's robustness against parametric uncertainties, the adaptation gains of MRAS online gain-adjustment law are dynamically adjusted, after every sampling interval, using smooth hyperbolic functions of motor's speed-error. This modification significantly improves the system's response-speed and damping against oscillations, while ensuring its stability under all operating conditions. It dynamically re-configures the control-input trajectory to enhance the system's immunity against the detrimental effects of random faults occurring in practical motorized systems such as bounded impulsive-disturbances, modelling errors, and abrupt load-torque variations. The efficacy of the proposed control strategy is validated by conducting credible hardware-in-the-loop experiments on QNET 2.0 DC Motor Board. The experimental results successfully validate the superior tracking accuracy and disturbance-rejection capability of the proposed control strategy as compared to other controller variants benchmarked in this article.

Indirect Adaptive State-Feedback Control of Rotary Inverted Pendulum Using Self-Mutating Hyperbolic-Functions for Online Cost Variation

“…Two different nonlinear-type adaptive weight-scaling mechanisms are synthesized in the following sub-sections by employing Secant-Hyperbolic-Functions (SHFs). The SHFs are utilized owing to their symmetry, bounded nature, and smoothness [18], [30]. The proposed adaptation mechanism is simply based on a set of algebraic equations that does not entail recursive computational burden on the embedded processor.…”

“…These attributes help in achieving good position-regulation accuracy, across a broad range of conditions, which is normally unattainable via linear compensators [16], [17]. The model-reference-adaptivesystem minimizes the error between the outputs of the actual system and a reference model in order to modify the critical control parameters [18]. However, accurate identification of the reference model is a difficult task due to the complex dynamics of higher-order systems [19].…”

Self-tuning state-feedback control of a rotary pendulum system using adjustable degree-of-stability design

“…The zero-mean Gaussian function is avoided because it computes the square of the input variable to establish even-symmetry, after every sampling instant, which inevitably increases the command execution time. Hence, in this work, the online reconfiguration of β is done by means of a Hyperbolic-Secant-Function (HSF) that is driven by the real-time variation in the state-error variables [19,33]. The HSF waveform is shown in Figure 2.…”

“…The model-reference adaptive systems track the output of a reference model to reconfigure the behaviour of the operational controller [18]. However, identifying the adaptation-rates for the Lyapunov gain-adjustment law is a cumbersome task [19]. The gain-scheduling technique dynamically modifies the controller-parameters by commuting between a predefined set of distinct linear controllers, each designed to address a specific operating condition, which is usually selected via a state-error dependent look-up table(s) [20].…”

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

“…Extensive research has been done to synthesize robust adaptive controllers for under-actuated mechatronic systems [ 35 , 36 ]. The Model-Reference-Adaptive-Controllers utilizes the Lyapunov theory to track a reference control model which leads to the online dynamic adjustment of the critical controller parameters [ 37 , 38 ]. However, identifying an accurate reference model for the tracking purpose is a difficult task [ 39 ].…”