Model Reference Adaptive Control Design Research Articles

Model Reference Adaptive PID Controller Design and Analysis of the Impact of Controller Parameters on System Behavior: DC Motor Position Control

Oransal-integral-türev (PID) kontrol yöntemi, basit mimarisi, kolay tasarım ve otomatik kazanç ayarlama gibi çekici özellikleri nedeniyle endüstride yaygın olarak uygulanmaktadır. Bununla birlikte, PID denetleyicisiyle başarılı bir endüstriyel uygulama yapabilmek için genellikle denetleyicinin önceden manuel olarak yeniden ayarlanması gerekmektedir. Bu sorunu çözmek için çalışma kapsamında, düşük maliyetli STM32F4 uygulama geliştirme kiti ve Waijung blok seti kullanılarak uyarlamalı kontrol yöntemlerinden biri olan Model Referans Uyarlamalı PID Denetleyici (MRUPIDD) tasarımı gerçekleştirilmiştir. Uyarlanabilir PID denetleyicisi, sistem parametreleri zamanla değişse bile istenen kontrol performansını sağlamak için parametre ayarlama mekanizmasına sahiptir. Parametre ayarlama mekanizması ve denetleyici tasarımı için Massachusetts Teknoloji Enstitüsü (Massachusetts Institute of Technology-MIT) kuralı kullanılmıştır. Çalışma kapsamında tasarlanan denetleyicinin DC motor üzerinde konum kontrol uygulaması gerçekleştirilmiş ve PID denetleyicisi ile karşılaştırılarak hata maliyetleri hesaplanmıştır. Uyarlama kazanç parametrelerinin sistem davranışına etkisinin incelenmesi için ise farklı gama kazanç değerleri sisteme uygulanmış ve kararlılığı bozan durumlar incelenmiştir.

Design and implementation of a new adaptive MPPT controller for solar PV systems

This research provides an adaptive control design in a photovoltaic system (PV) for maximum power point tracking (MPPT). In the PV system, MPPT strategies are used to deliver the maximum available power to the load under solar radiation and atmospheric temperature changes. This article presents a new adaptive control framework to enhance the performance of MPPT, which will minimize the complexity in system control and efficiently manage uncertainties and disruptions in the environment and PV system. Here, the MPPT algorithm is decoupled with model reference adaptive control (MRAC) techniques, and the system gains MPPT with overall system stability. The simulation and design of the new MRAC for MPPT based on a boost converter are addressed here. Moreover, a mathematical model is formulated and an efficient MRAC is designed for MPPT. To validate the robustness of the controller, MATLAB/Simulink is utilized to compare with the state-of-the-art approach, which is incremental conductance (INC) and perturb & observe (P&O) under various operating conditions based on the convergence time, tracking efficiency, PV current & voltage ripple, overall efficiency, and error rates. The proposed controller’s average tracking efficiency is 99.77% and 99.69% under diverse temperature and radiation conditions, respectively. In addition, it takes only 3.6 msec to capture MPP, which is around ten times faster than INC and twelve times faster than the P&O approach. When compared to INC and P&O, the MPP error rates in the MRAC-MPPT scheme are significantly lower. The simulation outcomes indicate that the presented controller exhibits excellent tracking under varying circumstances like solar radiation and temperature.

Composite model-reference adaptive control with least-squares estimator

This work presents a new design of a composite model-reference adaptive control (MRAC) with a least-squares parameter estimator. The objective of the design is to preserve the remarkable transient adaptation characteristic obtained by a modified MRAC algorithm recently introduced and, at the same time, enjoy the superior parameter convergence performance of a least-squares estimator. The algorithm employs two different estimators for the same controller parameter, one updated by a gradient law driven by the tracking error and the other updated by a least-squares algorithm driven by a prediction error. In this way, the performance of each one is kept unchanged. The existence of a Lyapunov function assures the global uniform stability of the proposed composite adaptive scheme and simulation results confirm and illustrate its properties.

Fractional order output-feedback tube-MRAC design for a class of fractional order transfer functions with unknown parameters

In this paper, we address a class of fractional order systems defined by transfer function with unknown parameters and present a novel fractional order tube model reference adaptive control (FOTMRAC) design for their control despite the fact that the only available signals are the input and output of the system. This is the main difference with preceding authors' recent study, where the states of the system where available. Based on the output feedback, this strategy is a generalisation of the tube model reference adaptive control (TMRAC) to fractional order systems. The basic idea is to replace the single reference trajectory well known in reference model control theory by a set of admissible trajectories called tube reference. Also, an optimisation problem is resolved online in order to update the correction control signal minimising a control cost criterion. The asymptotic stability is proved using the Lyapunov extension theorem. Simulation results illustrate and confirm the effectiveness of the proposed control design.

Model-free continuation of periodic orbits in certain nonlinear systems using continuous-time adaptive control

This paper generalizes recent results by the authors on noninvasive model-reference adaptive control designs for control-based continuation of periodic orbits in periodically excited linear systems with matched uncertainties to a larger class of periodically excited nonlinear systems with matched uncertainties and known structure. A candidate adaptive feedback design is also proposed in the case of scalar problems with unmodeled nonlinearities. In the former case, rigorous analysis shows guaranteed performance bounds for the associated prediction and estimation errors. Together with an assumption of persistent excitation, there follows asymptotic convergence to periodic responses determined uniquely by an a priori unknown periodic reference input and independent of initial conditions, as required by the control-based continuation paradigm. In particular, when the reference input equals the sought periodic response, the steady-state control input vanishes. Identical conclusions follow for the case of scalar dynamics with unmodeled nonlinearities, albeit with slow rates of convergence. Numerical simulations validate the theoretical predictions for individual parameter values. Integration with the software package coco demonstrates successful continuation along families of stable and unstable periodic orbits with a minimum of parameter tuning. The results expand the envelope of known noninvasive feedback strategies for use in experimental model validation and engineering design.

Robust Adaptive Control of Knee Exoskeleton-Assistant System Based on Nonlinear Disturbance Observer

This study presents a control design of an angular position for the exoskeleton knee assistance system based on a model reference adaptive control (MRAC) strategy. Three schemes of the MRAC design have been proposed: the classical MRAC, MRAC with an adaptive disturbance observer, and MRAC with a nonlinear observer. The stability analysis for each scheme has been conducted and developed based on the Lyapunov theorem to prove the uniform ultimate bound of tracking and estimation errors. In addition, the adaptive laws have been developed for the proposed schemes according to the stability analysis. The effectiveness of the proposed state and output feedback controllers has been verified via computer simulation. The results based on numerical simulation have shown that the MRAC with a nonlinear observer could give better robustness characteristics and better performance in terms of tracking and estimation errors as compared to the other controllers.

Yaw-Rate-Tracking-Based Automated Vehicle Path Following: An MRAC Methodology With a Closed-Loop Reference Model

Abstract Concerning automated vehicles, various path-following controllers have been designed by the model reference adaptive control (MRAC) approach. Through appropriate Lyapunov redesigns, asymptotical stability and signal boundedness are ensured for the path-tracking control loops. However, transient behaviors of the closed-loop responses are seldom considered in the context of MRAC synthesis. To bridge the foregoing gap, a closed-loop-reference-model-based MRAC, which yields an improved transient performance compared with a traditional MRAC, is exploited to synthesize a vehicular path-following control law. Besides, an infinitely differentiable projection operator is complemented to the control parameters’ adaptation schemes for estimation speed-up and robustness enhancement. Hardware-in-the-loop experiments are used to evaluate the proposed method and to demonstrate its improvement over some conventional MRAC designs.

On key properties of the Lion's and Kreisselmeier's adaptation algorithms

SummaryThe article revises properties of two identification/adaptation algorithms proposed by Lion and Kreisselmeier more than 40 years ago to accelerate parametric convergence under regressor persistency of excitation (PE) condition. First, motivated by the paper we demonstrate that these algorithms can provide asymptotic (not exponential) parametric convergence under a simple condition which is weaker than the requirement of PE. Second, it is shown that for some special choice of adaptation gain the algorithms can provide finite time parametric convergence if the regressor satisfies the interval excitation (IE) condition that is even weaker than the condition of asymptotic convergence. Third, it is shown that for some certain structural requirements these algorithms can generate the high‐order time derivatives of the adjustable parameters. This property can be used for solution of a wide range of problems of adaptive control including, in particular, model reference adaptive control and modular backstepping design with high‐order tuners.

Adaptive controller design for uncertain singular systems with actuator failure

In this paper, the problem of model reference adaptive controller design with actuator failure is solved for a series of uncertain singular systems. The research on partial actuator failure is relatively mature and it is necessary to solve the problem of how to guarantee the system performance when the actuator fails completely. For this reason, we treat the system with actuator failure as a switching system with two subsystems and then solve the stability analysis problem of the error switching system. The emphasis is to design the adaptive controller by some sufficient linear matrices inequalities (LMIs) conditions and obtain the global stability criterion of the error switching system through the resident time method. Finally, the proposed method is applied to HiMAT aircraft to illustrate the feasibility and effectiveness of this kind of problem.

Partial-state feedback multivariable MRAC and reduced-order designs

This paper develops a new model reference adaptive control (MRAC) framework using partial-state feedback for solving a multivariable adaptive output tracking problem. The developed MRAC scheme has full capability to deal with plant uncertainties for output tracking and has desired flexibility to combine the advantages of full-state feedback MRAC and output feedback MRAC. With such a new control scheme, the plant-model matching condition is achievable as with an output or state feedback MRAC design. A stable adaptive control scheme is developed based on LDS decomposition of the plant high-frequency gain matrix, which guarantees closed-loop stability and asymptotic output tracking. The proposed partial-state feedback MRAC scheme not only expands the existing family of MRAC, but also provides new features to the adaptive control system, including additional design flexibility and feedback capacity. Based on its additional design flexibility, a minimal-order MRAC scheme is also presented, which reduces the control adaptation complexity and relaxes the feedback information requirement, compared to the existing MRAC schemes. New results are presented for plant-model matching, error model, adaptive law and stability analysis. A simulation study of a linearized aircraft model is conducted to demonstrate the effectiveness and new features of the proposed MRAC control scheme.

Efficient Fractional Order Reference Model of Adaptive Controller Design for Multi-input Multi-output Thermal System

The diverse control techniques have been combined with fractional calculus to enhance the control system performance. This paper presents an efficient fractional-order model reference adaptive controller (FOMRAC) design, which aims to demonstrate the solution for temperature reference tracking and cross-coupling rejection in the multi-input multi-output thermal system as well as cognizing of power consumption saving constraints. The mathematical modeling, nonlinear dynamic characteristic details, and system identification of the thermal system are described while the fractional-order controller combined with a model reference adaptive control (FOMRAC) based on MIT rule is developed so that to create the nonlinear adaptive mechanism which enables the excellent performance to control the multi-input multi-output thermal system. Likewise, a decoupling compensator is constructed to remunerate the effect of the cross-coupling interaction. The validation of the proposed control scheme is performed through the Matlab simulation and the experiment on the multi-input multi-output thermal system. The results illustrated the FOMRAC technique in which the controller's adjustable parameters can provide efficiency stability and performance to minimize the settling time and percent overshoot of the control system response. Besides, the analysis of the power consumption in the control system is addressed to reinforce the useful ability of the proposed method compared with the integral-order model reference adaptive controller (IOMRAC) and the traditional PID controller. The results revealed that the proposed FOMRAC technique exhibited much better than other methods because of the effective optimization of adaptive gain mechanism and fractional-order operators.

Robust model reference adaptive control for transient performance enhancement

SUMMARYTo circumvent the potentially poor transient response induced by nonlinear uncertain dynamics in the adaptive control system, this article proposes a new model reference adaptive control design scheme to improve its transient control response. We first construct a compensator to online extract the undesired dynamics in the online learning, which is incorporated into the reference model and control simultaneously. Then, an error feedback term is incorporated into the reference model to speed up the convergence of both the compensator and tracking error. Moreover, a new leakage term containing the estimation error is constructed and then added in the adaptive law to guarantee the convergence of both the estimation error and tracking error. To further reveal the mechanisms behind these proposed methods, a new methodology to analyze the transient error bounds based on L2‐norm and Cauchy‐Schwartz inequality is also developed. Based on the analysis results, we find that the proposed methods can effectively reduce the bound of the tracking error and thus achieve an improved transient control performance without violating the system stability even with high‐gain adaptation. In addition, the frequency‐domain analysis is resorted to show the comparative responses of different adaptive laws, which indicate that the proposed adaptive law can maintain the stability margin even with a high‐gain learning rate. A numerical example is given to demonstrate improved control responses of these proposed schemes.

Lyapunov design of least-squares model-reference adaptive control

Abstract A Lyapunov design of a least-squares model-reference adaptive control (LS-MRAC) algorithm is presented. The plants considered are continuous with relative degree one. A Monopoli multiplier, originally proposed to extend the MRAC algorithm to the case of relative degree two, is introduced. As a result, fast convergence of the tracking error is achieved and, moreover, the Lyapunov analysis shows that a quadratic term depending on the parametric error belongs to L2, which improves the stability properties of the system. This is the key feature that allows a more powerful LS algorithm to be employed in the update law. The resulting LS-MRAC seems to be a missing algorithm in the literature. Simulation results illustrate the improvement in the transient behavior as well as in the parameter convergence attained with the proposed adaptive schemes.

A Partial-State Feedback Model Reference Adaptive Control Scheme

This paper develops a new partial-state feedback model reference adaptive control (MRAC) scheme, which has full capability to deal with plant uncertainties for output tracking and desired flexibility to combine the advantages of full-state feedback MRAC and output feedback MRAC. For partial-state feedback MRAC, plant-model matching is achievable as with full-state feedback control, while the controller structure enjoys less complexity as compared with an output feedback MRAC design. Adaptive partial-state feedback control designs are developed for relative-degree-one plants and for general plants. Both adaptive control designs ensure closed-loop system stability and asymptotic output tracking. New results are presented for plant-model matching, error model, adaptive law, and stability analysis. New features of partial-state feedback MRAC are addressed, including its design flexibility. Simulation studies are conducted whose results verify the effectiveness of partial-state feedback MRAC.

Generalized Model Reference Adaptive Control by Means of Global HOSM Differentiators

In this paper, we combine a global differentiator based on higher-order sliding modes (HOSM) and dynamic gains with classical model reference adaptive control (MRAC) schemes to solve the relevant and yet open problem of trajectory tracking via output feedback of uncertain plants with arbitrary relative degree in a simple-closed form for the control design. The gains of the differentiator are adapted through state-norm observers for the unmeasured state, whereas the control parametrization explores the input–output filters commonly used in the MRAC design. Global asymptotic stability and robust exact tracking are rigorously demonstrated. Simulations highlight the claimed properties as well as the remarkable simplicity of the proposed adaptive control system using robust exact differentiators when compared to more involved alternatives found in standard approaches. The theoretical results are also illustrated with an application to bilateral teleoperation.

Two MRAC Designs for the MEMS-Based AC Voltage Reference Source

This paper presents two well-known designs of model reference adaptive control (MRAC) based on state and output feedback, to control microelectromechanical system AC voltage reference source (MEMS AC VRS). The best performance of AC voltage reference is achieved when the movable plate of MEMS capacitor is located and stayed under the pull-in point. This study proposes two MRAC schemes to place the movable plate near the pull-in point in the presence of parameter uncertainties. Moreover, the asymptotic stability of the closed-loop system is guaranteed by the Lyapunov theory and Barbalat’s Lemma. Finally, simulation results verify the effectiveness of theoretical methods.

Mixed therapy in cancer treatment for personalized drug administration using model reference adaptive control

The paper presents Model Reference Adaptive Control (MRAC) design strategy to determine personalized drug delivery protocol for mixed therapy with chemotherapy and immunotherapy in cancer treatment. We consider a nonlinear mathematical ODE set for cancer dynamics that includes tumor, natural killers, circulating lymphocytes and cytotoxic T-cells population together with the interaction of chemotherapy and immunotherapy. For researchers and physicians, the main challenge in mathematical models is the determination of the exact model parameters. In order to have a drug administration policy for a patient with unknown parameter set, we develop State Dependent Riccati Equations (SDRE) based MRAC design approach to determine the personalized drug delivery protocol for patients with unknown model parameters. First of all, we determine the optimal drug delivery scenario for a reference patient with known dynamics parameters using SDRE approach. Then for any patient with unknown parameters, the personalized mixed therapy protocol is determined based on the treatment regimen of the reference patient. In the proposed methodology, unknown patients are considered as a black-box simulator in the design and the mathematical model parameters of the patient are not essential for the design of drug administration protocol. In addition, the Bang-Bang and continuous drug delivery regimens could be obtained using proper adaptation gains in the presented MRAC methodology. The simulation results demonstrate the effectiveness of the proposed MRAC approach for prescribing a treatment regimen of chemo-immunotherapy.

Design of direct MRAC augmented with 2 DoF PIDD controller: An application to speed control of a servo plant

An adaptive control with reference model provides the solution for uncertainty in dynamics, transient performance characteristics of autonomous systems. The high frequency oscillation and poor settling time are the important challenges in adaptive control methodology. This article proposes the Model Reference Adaptive Control (MRAC) augmented with Proportional Integral Double Derivative (PIDD) controller for a solution of such kind of problems. This proposed multi-loop structure consists of two loops: a primary outer loop executes MRAC with two adjustment mechanism and a secondary inner loop act as a normal closed loop 2 DoF PIDD controller with plant dynamics. The function of 2 DoF PIDD controller is act as a filter for primary adaptive loop to control the high frequency oscillations and pulsating signals. This cascade or multi-loop structure will makes the secondary loop is more stable. The tuning of 2 DoF PIDD parameters again a challenging task due to the presence of extra two parameters and it was done by particle swarm optimization (PSO) algorithm. The effectiveness of the proposed methodology has been tested in servo plant model.

Model Reference Adaptive Control Design for Nonlinear Plants

In this paper, the basic theory of the model reference adaptive control design and issues of particular relevance to control nonlinear dynamic plants with a relative degree greater than or equal to one with unknown parameters are detailed. The studied analysis was motivated through its application to a robot manipulator with six degrees of freedom. After linearization using the input-output feedback linearization and decoupling algorithm, the nonlinear Multi-input Multi-output system was transformed into six independent single-input single-output linear subsystems each one has a relative degree equal to two, the obtained results in different simulations shows that the augmented reference model adaptive controller has been successfully implemented.

Fractional-order model reference adaptive control of a multi-source renewable energy system with coupled DC/DC converters power compensation

We propose a supervision strategy based on a fractional order model reference adaptive control (FO-MRAC) design for the control of electrical energy transfers in a multi-source renewable energy system. We consider a two sources system (photo-voltaic and lead-acid battery bank) with a specific zero voltage switch full-bridge isolated buck DC/DC power converter and the load which is supposed to be resistive. The global energy system involving coupled DC/DC converters on a DC bus is accurately modelized in the state space domain. Then, a fractional order MRAC control law is designed in order to stabilize the system’s current and voltage. We show by means of numerical simulation tests that the proposed FO-MRAC control is very efficient and robust even in presence of renewable sources fluctuations and load variations.