This paper presents a discrete-time Robust Adaptive Super-Twisting Sliding Mode controller and its stability analysis by means of Lyapunov stability theory. The control law is composed by two ...different control structures: a Robust Model Reference Adaptive Controller (RMRAC) and an Adaptive Super-Twisting Sliding Mode (STSM) Controller. The main advantage of the control structure is its robust performance and high adaptability in face of unmodelled dynamics, presenting a fast reference tracking without chattering, since it uses a second-order Sliding Mode action into adaptive control structure. The stability and robustness analysis of the control structure are presented in discrete time, considering the overall plant, that is, in presence of matched and unmatched dynamics. In addition, the control structure performance is corroborated with simulation results, considering a non-minimum phase unstable plant. Moreover, the presented results are compared with an adaptive first-order SM control-based RMRAC, which can be clearly seen that proposed controller has better performance, mainly by means of chattering mitigation.
This paper designs a simple model reference adaptive control based speed controller (MRAC-SC) for a surface-mounted permanent magnet synchronous motor drive. The proposed adaptive scheme is designed ...to track a reference model that ensures the desired exponential decay of a controlled speed error trajectory. Also, the proposed MRAC method includes an adaptive compensating control term and a stabilizing feedback control term. The former is proposed to compensate for uncertain model parameters (i.e., inertia, friction, and load torque) and the latter is constructed to asymptotically stabilize the error dynamics. The asymptotic stability of the closed loop is guaranteed with both control terms using the Lyapunov approach. The comparative studies between the proposed MRAC-SC, the nonadaptive model reference speed controller, and the conventional proportional-integral SC are performed to justify a fast transient response, a good tracking possibility, and robustness against the parameter uncertainties of the proposed MRAC technique.
The accuracy of the motion control for robotic mechanisms will have an effect on their overall performance. Under the condition where the robotic end-effector carries different loads, the motions for ...each joint of robotic mechanisms change depending on different payload masses. Conventional control systems possess the potential issue that they cannot compensate the load variation effect. Adaptive control, especially the model reference adaptive control (MRAC), has therefore been put forward to handle the above issue. Adaptive control is generally divided into three categories, model reference, self-tuning and gain-scheduled. In this study, the authors only focus on the model-reference approach. To the best of the authors’ knowledge, very few recent research articles can be found in the area of MRAC especially for robotic mechanisms since robotic system is a highly nonlinear system, and it is difficult to guarantee the stability of MRAC in such system. This study presents a review and discussion on the MRAC of robotic mechanisms and some issues of MRAC for robotic mechanisms are also demonstrated. This study can provide a guideline for upcoming research in the field of MRAC for robotic mechanisms.
This article presents an innovative control architecture for tilt-rotor quadcopters with H-configuration transporting unknown, sling payloads. This control architecture leverages on a thorough ...analysis of the aircraft's equation of motion, which reveals gyroscopic effects that were not fully characterized and were disregarded while synthesizing control algorithms in prior publications. Furthermore, the proposed control architecture employs barrier Lyapunov functions and a novel robust model reference adaptive control law to guarantee a priori user-defined constraints on both the trajectory tracking error and the control input, despite poor information on the aircraft's inertial properties and the presence of unknown, unsteady payloads. Flight tests involving a quadcopter pulling an unmodeled cart by means of a thin rope of unknown length, which is slack at the beginning of the mission, verify the effectiveness of the theoretical results.
Grid-connected converters are uncertain time-varying systems, whose controllers must deal with the relevant inductive content and high harmonic distortion of the sampled voltages. Adaptive ...controllers are feasible control strategies for these applications, because their gains are continuously adjusted in response to system perturbations, and they are also robust to unmodeled dynamics and exogenous disturbances. However, adaptive controllers are not necessarily capable of rejecting all harmonic components on grids with high harmonic distortion. Therefore, this work presents a Robust Model Reference Adaptive Control-based with an adaptive super-twisting sliding mode, which is improved with a harmonic compensation strategy in which additional control actions to deal with the harmonic contents of the <inline-formula><tex-math notation="LaTeX">5^{th}</tex-math></inline-formula>, <inline-formula><tex-math notation="LaTeX">7^{th}</tex-math></inline-formula>, <inline-formula><tex-math notation="LaTeX">11^{th}</tex-math></inline-formula>, and <inline-formula><tex-math notation="LaTeX">13^{th}</tex-math></inline-formula> of the fundamental component of the electrical grid are incorporated into the control structure. Experimental results are provided of a 7.5 kW converter connected to a distorted and unbalanced grid with an LCL filter, where the developed control structure presents a total harmonic distortion (THD) of 2%, while the controller without harmonic compensation obtains a 2.5% THD.
In this article, a robust nonlinear model reference adaptive control (MRAC) is proposed for disturbed linear systems, i.e., linear systems with parameter uncertainties, and external time-dependent ...perturbations or nonlinear unmodeled dynamics matched with the control input. The proposed nonlinear control law is composed of two nonlinear adaptive gains. Such adaptive gains allow the control to counteract the effects of some perturbations and nonlinear unmodeled dynamics ensuring asymptotic convergence of the tracking error to zero, and the boundedness of the adaptive gains. The nonlinear controller synthesis is given by a constructive method based on the solution of linear matrix inequalities. Besides, the simulation results show that, due to the nonlinearities, the rate of convergence of the proposed algorithm is faster than that provided by a classic MRAC.
This article describes an extension of the well-known model reference adaptive control (MRAC) approach. The extension relies on explicitly involving the tracking error in the feedback control law: it ...is shown that including this term along with its appropriate extra adaptive gain allows one to handle possibly unstable reference dynamics. Owing to its stabilizing nature, the proposed framework is referred to as model reference adaptive stabilizing control. Such an extension turns out to be particularly useful in leaderless consensus of heterogeneous uncertain agents, since the literature has discussed that leaderless adaptation may not avoid unstable closed-loop dynamics. In such consensus setting, the framework, referred to as model reference adaptive stabilizing consensus, generalizes the existing MRAC-based consensus schemes and can achieve consensus when state-of-the-art MRAC-based schemes may fail.
The existing non-cascaded control schemes for surface-mount permanent magnet synchronous motors (SPMSM) with stability guarantee inevitably depend on parameter information. To address this problem, ...we propose a multivariable model reference adaptive control (MRAC) scheme for SPMSM. And it does not require parameter information of the SPMSM but pole-pairs. The scheme consists of two parts: coordinate transformation and output feedback adaptive control. The coordinate transformation is presented to solve the undesirable effects of unmatched load torque. And the output feedback adaptive controller is used to guarantee the stability of the system. Furthermore, the stability proof of the overall system is given in detail. Finally, the effectiveness of the proposed scheme is verified by simulation and experiment.
The decentralized robust model reference adaptive control (MRAC) problem is studied for a class of large-scale systems with unknown plant parameters, unknown time-varying delayed interconnections, ...and unknown dead-zone inputs. Two robust adaptive control schemes are proposed for the cases of symmetric dead-zone input and asymmetric dead-zone input under the assumption of moderate time-delay nonlinearity and the matching conditions of the plant model and the reference model matrix, respectively. The control gain function is explicitly expressed, and its useful properties are established. The Lyapunov-Krasovskii functional with two integral functions is constructed. It is shown that all signals in the closed-loop system are bounded and the state tracking error converges exponentially to a tunable region. The effectiveness and feasibility of the proposed design approach is illustrated by a simulation example.
In this study, a distributed model reference adaptive control architecture is developed to achieve the cooperative tracking of uncertain dynamical multi-agent systems, where the reference model ...serves as a virtual leader for the group to track. Two adaptive laws, with one adjusting the coupling weights and the other adjusting the neural network weights, are designed based on the relative state information of neighbouring agents. The proposed controller guarantees that the state of each agent synchronizes to that of the reference model over any undirected connected communication graphs, and all signals in the closed-loop network are uniformly ultimately bounded. In contrast to the existing results, the developed controller can be implemented in a fully distributed manner by each agent without using any global information and the accurate model of each agent. An extension to asymptotic stability is further studied.
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