Adaptive optimal control of under-actuated robotic systems using a self-regulating nonlinear weight-adjustment scheme: Formulation and experimental verification

This paper formulates an innovative model-free self-organizing weight adaptation that strengthens the robustness of a Linear Quadratic Regulator (LQR) for inverted pendulum-like mechatronic systems against perturbations and parametric uncertainties. The proposed control procedure is devised by using an online adaptation law to dynamically adjust the state weighting factors of LQR's quadratic performance index via pre-calibrated state-error-dependent hyperbolic secant functions (HSFs). The updated state-weighting factors re-compute the optimal control problem to modify the state-compensator gains online. The novelty of the proposed article lies in adaptively adjusting the variation rates of the said HSFs via an auxiliary model-free online self-regulation law that uses dissipative and anti-dissipative terms to flexibly re-calibrate the nonlinear function's waveforms as the state errors vary. This augmentation increases the controller's design flexibility and enhances the system's disturbance rejection capacity while economizing control energy expenditure under every operating condition. The proposed self-organizing LQR is analyzed via customized hardware-in-loop (HIL) experiments conducted on the Quanser's single-link rotational inverted pendulum. As compared to the fixed-gain LQR, the proposed SR-EM-STC delivers an improvement of 52.2%, 16.4%, 55.2%, and 42.7% in the pendulum's position regulation behavior, control energy expenditure, transient recovery duration, and peak overshoot, respectively. The experimental outcomes validate the superior robustness of the proposed scheme against exogenous disturbances

Nonlinear Robust Disturbance Attenuation Control Design for Static Var Compensator in Power System

The problem of designing an adaptive backstepping controller for nonlinear static var compensator (SVC) system is addressed adopting two perspectives. First, instead of artificially assuming an upper bound or inequality scaling, the minimax theory is used to treat the external unknown disturbances. The system is insensitive to effects of large disturbances due to taking into account the worst case disturbance. Second, a parameter projection mechanism is introduced in adaptive control to force the parameter estimate within a prior specified interval. The proposed controller handles the nonlinear parameterization without compromising control smoothness and at the same time the parameter estimate speed is improved and the robustness of system is strengthened. Considering the short-circuit ground fault and mechanical power perturbation, a simulation study is carried out. The results show the effectiveness of the proposed control method

On the centrality of disturbance rejection in automatic control

In this paper, it is shown that the problem of automatic control is, in essence, that of disturbance rejection, with the notion of disturbance generalized to symbolize the uncertainties, both internal and external to the plant. A novel, unifying concept of disturbance rejector is proposed to compliment the traditional notion of controller. The new controller-rejector pair is shown to be a powerful organizing principle in the realm of automatic control, leading to a Copernican moment where the model-centric design philosophy is replaced by the one that is control-centric in the following sense: the controller is designed for a canonical model and is fixed; the difference between the plant and the canonical model is deemed as disturbance and rejected

Advances In Internal Model Principle Control Theory

In this thesis, two advanced implementations of the internal model principle (IMP) are presented. The first is the identification of exponentially damped sinusoidal (EDS) signals with unknown parameters which are widely used to model audio signals. This application is developed in discrete time as a signal processing problem. An IMP based adaptive algorithm is developed for estimating two EDS parameters, the damping factor and frequency. The stability and convergence of this adaptive algorithm is analyzed based on a discrete time two time scale averaging theory. Simulation results demonstrate the identification performance of the proposed algorithm and verify its stability. The second advanced implementation of the IMP control theory is the rejection of disturbances consisting of both predictable and unpredictable components. An IMP controller is used for rejecting predictable disturbances. But the phase lag introduced by the IMP controller limits the rejection capability of the wideband disturbance controller, which is used for attenuating unpredictable disturbance, such as white noise. A combination of open and closed-loop control strategy is presented. In the closed-loop mode, both controllers are active. Once the tracking error is insignificant, the input to the IMP controller is disconnected while its output control action is maintained. In the open loop mode, the wideband disturbance controller is made more aggressive for attenuating white noise. Depending on the level of the tracking error, the input to the IMP controller is connected intermittently. Thus the system switches between open and closed-loop modes. A state feedback controller is designed as the wideband disturbance controller in this application. Two types of predictable disturbances are considered, constant and periodic. For a constant disturbance, an integral controller, the simplest IMP controller, is used. For a periodic disturbance with unknown frequencies, adaptive IMP controllers are used to estimate the frequencies before cancelling the disturbances. An extended multiple Lyapunov functions (MLF) theorem is developed for the stability analysis of this intermittent control strategy. Simulation results justify the optimal rejection performance of this switched control by comparing with two other traditional controllers

Robust controller design for input-delayed systems using predictive feedback and an uncertainty estimator

[EN] This paper deals with the problem of stabilizing a class of input-delayed systems with (possibly) nonlinear uncertainties by using explicit delay compensation. It is well known that plain predictive schemes lack robustness with respect to uncertain model parameters. In this work, an uncertainty estimator is derived for input-delay systems and combined with a modified state predictor, which uses current available information of the estimated uncertainties. Furthermore, based on Lyapunov-Krasovskii functionals, a computable criterion to check robust stability of the closed-loop is developed and cast into a minimization problem constrained to an LMI. Additionally, for a given input delay, an iterative-LMI algorithm is proposed to design stabilizing tuning parameters. 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広島大学(Hiroshima University)博士(学術)Doctor of Philosophydoctora