Model Reference Adaptive Control Research Articles

Model reference adaptive disturbance rejection control using partial-state feedback

In this paper, we propose a partial-state feedback model reference adaptive control strategy for uncertain linear time-invariant systems with unmatched disturbances. The new control design is based on parametrization and observer technique. The control structure and output matching of nominal partial-state feedback disturbance rejection are presented. The adaptive partial-state feedback disturbance rejection scheme guarantees closed-loop system stability and asymptotic output tracking. A simulation example indicates the effectiveness of the presented adaptive partial-state feedback control design.

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.

Model reference adaptive control for nonlinear time‐varying hybrid dynamical systems

SummaryThis paper presents the first model reference adaptive control system for nonlinear, time‐varying, hybrid dynamical plants affected by matched and parametric uncertainties, whose resetting events are unknown functions of time and the plant's state. In addition to a control law and an adaptive law, which resemble those of the classical model reference adaptive control framework for continuous‐time dynamical systems, the proposed framework allows imposing instantaneous variations in the reference model's trajectory to rapidly steer the trajectory tracking error to zero, while retaining the closed‐loop system's ability to follow a user‐defined signal. These results are enabled by the first extension of the classical LaSalle–Yoshizawa theorem to time‐varying hybrid dynamical systems, which is presented in this paper as well. A numerical simulation shows the key features of the proposed adaptive control system and highlights its ability to reduce both the control effort and the trajectory tracking error over a classical model reference adaptive control system applied to the same problem.

Tackling Modeling and Kinematic Inconsistencies by Fixed Point Iteration-Based Adaptive Control

The Fixed Point Iteration-based Adaptive Control design methodology is an alternative to the Lyapunov function-based technology. It contains higher-order feedback terms than the standard resolved acceleration rate control. This design approach strictly separates the kinematic and dynamic issues. At first, a purely kinematic prescription is formulated for driving the components of the tracking error to zero. Then an available approximate dynamic model is used to calculate the approximated necessary control forces. Before exerting on the controlled system, these forces are adaptively deformed in order to precisely obtain the prescribed kinematic behavior. The necessary deformation is iteratively found by the use of a contractive map that results in a sequence that converges to the unique fixed point of this map. In the case of underactuated systems, when the relative order of the control task also increases, the highest-order time-derivative depends on the lower-order ones according to the dynamic model of the system. This makes it impossible to realize the arbitrarily constructed kinematic design. In the paper, a resolution to this discrepancy is proposed. The method is demonstrated using two non-linear paradigms, a three-degree-of-freedom robot arm, and a two-degree-of-freedom system, i.e., two coupled non-linear springs. The operation of the method was investigated via simulations made by the use of Julia language and simple sequential programs. It was found that the suggested solution could be considered as a new variant of the fixed point iteration-based model reference adaptive control that is applicable for underactuated systems even if the relative order of the task is increased.

A hybrid robust model reference adaptive controller and proportional integral controller without reference model for partially modeled systems

SummaryThis work presents the discrete‐time stability analysis of a hybrid robust model reference adaptive controller and proportional‐integral controller (MRAC‐PI) controller using Lyapunov criterion. The control structure merges the classical PI controller with a robust model reference adaptive control, resulting in an adaptive and robust control strategy, where the gains unite both control techniques in a unique structure and it does not require the design of a reference model, being able to track straightforwardly the reference signal. The adaptive gains are updated continuously by a modified gradient algorithm regarding control action, regulation error, and the system output. The stability analysis provides the controller design constraints, while also demonstrate the tendency of regulation error to a residual set, and proves the boundedness of all closed‐loop signals. Furthermore, as the controller is robust to unmodeled dynamics, it is feasible to control partially modeled systems. Simulation results in a real‐world engineering application are presented to corroborate the robustness of this controller and show its fast response in the face of critical exogenous system perturbations.

DC motor control using model reference adaptive control

Despite having higher maintenance costs than AC motors, DC motors had been widely employed in the industry due to their outstanding speed control capabilities. This employment increased due to the DC output of some renewable sources recently. This article introduces the speed control of DC motors using model reference adaptive control (MRAC). This control is achieved through regulating the armature voltage at different load changes. A comparison between the proposed adaptive controller and optimized PI controller using the elephant herding optimization (EHO) is presented. The PI controller parameters were optimality adjusted to minimize the integral absolute error, minimum overshoot, and minimum settling time. Computer simulations show that the suggested MRAC is preferable to a traditional optimized PI controller. In addition, the proposed controller is effective in regulating the DC motor over a broad range of operating speeds.

DC motor control using model reference adaptive control

Despite having higher maintenance costs than AC motors, DC motors had been widely employed in the industry due to their outstanding speed control capabilities. This employment increased due to the DC output of some renewable sources recently. This article introduces the speed control of DC motors using model reference adaptive control (MRAC). This control is achieved through regulating the armature voltage at different load changes. A comparison between the proposed adaptive controller and optimized PI controller using the elephant herding optimization (EHO) is presented. The PI controller parameters were optimality adjusted to minimize the integral absolute error, minimum overshoot, and minimum settling time. Computer simulations show that the suggested MRAC is preferable to a traditional optimized PI controller. In addition, the proposed controller is effective in regulating the DC motor over a broad range of operating speeds.

Adaptive Two-Degrees-of-Freedom Current Control for Solenoids: Theoretical Investigation and Practical Application

In this article, an adaptive two-degrees-of-freedom current control algorithm for solenoids is presented comprising an adaptive pole placement controller in combination with a regularized least-squares parameter estimation law. An additional adaptive feedforward controller takes advantage of the estimated plant parameters to further enhance the tracking performance. The stability of the overall closed-loop system is rigorously proven. The proposed solution differs from existing approaches by the adaptive feedforward controller and the way the parameter estimation is performed. The control concept is applied with the same controller parametrization to three solenoids from different applications, with substantially differing parameters. The experimental results show high tracking performance and fast parameter convergence even with poor initial estimates and despite the nonlinear dependence of the inductance on the current and position. The experimental results are also compared to two benchmark control design paradigms known from the literature, i.e. a second-order sliding mode controller and a nonlinear model reference adaptive control solution, which are both outperformed by the proposed controller.

Adaptive nonlinear controllers based approach to improve the frequency control of multi islanded interconnected microgrids

Islanded microgrids (MGs) are now widely used to electrify rural areas at a lesser cost and with greater efficiency. To maintain system balance and guarantee stability when exposed to various disturbances, MGs should be equipped with efficient controllers. Traditional controllers (like the PI controller) are linear and offer the best performance at a certain operating point, but the performance may degrade when the operating situation changes. To mitigate the drawbacks of fixed parameters controller, the paper suggested a fuzzy PI controller-based model reference adaptive control (FPI-MRAC) optimized by an advanced meta-heuristic optimization technique coronavirus herd immunity optimizer (CHIO) for enhancing the dynamic performance of several interconnected MGs. The proposed controller is non-linear adaptive controller that can improve the system performance over a wide range of operating conditions. The effectiveness of FPI-MRAC is assessed by subjecting the system to various disturbances, such as generation variation, load change, changing in uncertain system parameters and occurrence short circuit faults. Additionally, it investigated how quick reaction supercapacitors can improve the dynamic performance of the system. The acquired results show that, for all applied scenarios, the FPI-MRAC offers a much superior dynamic response than PI controller. Using super-capacitors also improves the system frequency when there are disruptions.

Pitch Angle Control of an Airplane Using Fractional Order Direct Model Reference Adaptive Controllers

This paper deals with the longitudinal movement control of an airplane (pitch angle) using fractional order adaptive controllers (FOACs). It shows the improvements achieved in the plane’s behavior, in terms of the minimization of a given performance index. At the same time, less control effort is needed to accomplish the control objectives compared with the classic integer order adaptive controllers (IOACs). In this study, fractional order direct model reference adaptive control (FO-DMRAC) is implemented at the simulation level, and exhibits a better performance compared with the classic integer order (IO) version of the DMRAC (IO-DMRAC). It is also shown that the proposed control strategy for FO-DMRAC reduces the resultant system control structure down to a relative degree 2 system, for which the control implementation is simpler and avoids oscillations during the transient period. Moreover, it is interesting to note that this is the first time that an FOAC with fractional adaptive laws is applied to the longitudinal control of an airplane. A suitable model for the longitudinal movement of the airplane related to the pitch angle θ as the output variable with the lifter angle (δe) as the control variable, is first analyzed and discussed to obtain a reliable mathematical model of the plane. All of the other input variables acting on the plane are considered as perturbations. For certain operating conditions defined by the flight conditions, an FO-DMRAC is designed, simulated, and analyzed. Furthermore, a comparison with the implementation of the classical adaptive general direct control (relative degree ≥ 2) is presented. The boundedness and convergence of all of the signals are theoretically proven based on the new Lemma 3, assuring the boundedness of all internal signals ω(t).

Leader‐following consensus of a class of heterogeneous uncertain multi‐agent systems with a distributed model reference adaptive control law

SummaryThis paper considers the leader‐following consensus problem of a multi‐agent system whose agents have heterogeneous uncertain dynamics in homogeneous state dimensions. Each agent utilizes a distributed model reference adaptive control (MRAC) law to deal with uncertainties. The nominal part of the MRAC is a distributed static state feedback control law. The reference model is the leader‐following consensus problem of reference agents with homogeneous linear time‐invariant dynamics. This problem becomes an N‐player graphical differential game under a given cost function. The reference agents utilize distributed static state feedback controllers that constitute a Nash equilibrium solution to the graphical differential game. This paper provides the conditions for the distributed MRAC to guarantee that each agent asymptotically tracks the corresponding reference agent; consequently, the multi‐agent system solves the leader‐following consensus problem as the reference model does. These conditions yield a straightforward design method for the MRAC. A numerical example demonstrates an application of the proposed approach to a multi‐robot system with nonlinear dynamics.

Novel Lyapunov-based rapid and ripple-free MPPT using a robust model reference adaptive controller for solar PV system

The technological, economic, and environmental benefits of photovoltaic (PV) systems have led to their widespread adoption in recent years as a source of electricity generation. However, precisely identifying a PV system's maximum power point (MPP) under normal and shaded weather conditions is crucial to conserving the maximum generated power. One of the biggest concerns with a PV system is the existence of partial shading, which produces multiple peaks in the P–V characteristic curve. In these circumstances, classical maximum power point tracking (MPPT) approaches are prone to getting stuck on local peaks and failing to follow the global maximum power point (GMPP). To overcome such obstacles, a new Lyapunov-based Robust Model Reference Adaptive Controller (LRMRAC) is designed and implemented to reach GMPP rapidly and ripple-free. The proposed controller also achieves MPP accurately under slow, abrupt and rapid changes in radiation, temperature and load profile. Simulation and OPAL-RT real-time simulators in various scenarios are performed to verify the superiority of the proposed approach over the other state-of-the-art methods, i.e., ANFIS, INC, VSPO, and P&O. MPP and GMPP are accomplished in less than 3.8 ms and 10 ms, respectively. Based on the results presented, the LRMRAC controller appears to be a promising technique for MPPT in a PV system.

A novel robust maximum power extraction framework for sustainable PV system using incremental conductance based MRAC technique

AbstractThis study proposes a maximum power point tracking (MPPT) approach with two components: an Incremental Conductance (INC) MPPT for reference voltage regulation and a Model Reference Adaptive Controller (MRAC) for adjusting the duty cycle of the DC‐DC converter switch. A robustness test is performed on the system considering real‐world situations that involve an abrupt change in atmospheric conditions with load uncertainties. The probabilistic load distribution analysis is accomplished through levels of uncertainty (i.e., Probabilistic DOWN and UP) to guarantee the operation of the proposed INC‐MRAC controller while generating unexpected disturbances in the system. Using MATLAB/Simulink, the performances of the novel INC‐MRAC MPPT are comparatively analyzed with PO, INC, VSSPO, and ANN under realistic case studies in seven states. After comparative analysis, it is evident that the proposed MPPT offers less tracking time, i.e., 3.8 ms, to track maximum power point (MPP) with negligible steady‐state oscillation and ripples. It is about 3, 7, 9, and 10 times faster than ANN, VSSPO, INC and PO, respectively. Moreover, the tracking efficiency of the proposed controller is up to 99.63% as well as overall efficiency of the system is more than 98%. The tracking power loss and error rate in finding MPP for the proposed controller is the lowest among all state‐of‐the‐art MPPT approaches. Finally, the effectiveness of the proposed INC‐MRAC approach is experimentally validated by employing a real‐time simulator OPAL‐RT (OP4510). The study helps in environmental protection and participation in sustainable development.

Distributed fault‐tolerant control for over‐actuated multi‐agent systems with uncertain perturbations using control allocation

AbstractThis paper proposes a distributed fault‐tolerant control for over‐actuated multi‐agent systems with uncertain perturbations and faults including partial loss of effectiveness or even complete failures. The entire distributed control law is divided into two parts that are the distributed observer and the decentralised controller with a hierarchical structure. The adaptive distributed observer estimates not only the leader's state, but also the leader's system matrix, which makes the whole distributed design more rigorous. For each over‐actuated subsystem, the control allocation based hierarchical control structure is used. The virtual control is developed based on adaptive optimal control approaches to cope with uncertain perturbations robustly. The model reference adaptive control is used to design the control allocator without the need for the fault detection and diagnosis module. The stability and robustness of the systems are rigorously demonstrated, and the feasibility and effectiveness of the control law are verified in simulations on the attitude dynamics system of spacecraft.

IMPROVED ADAPTIVE NONLINEAR CONTROL FOR VARIABLE SPEED WIND-TURBINE FED BY DIRECT MATRIX CONVERTER

This paper proposes a robust decoupling power algorithm based on a doubly fed induction generator (DFIG) for variable speed wind-turbine (WT). The DFIG rotor circuit is fed by the direct matrix converter (DMC), which presents several features such as no need to the dc-bus voltage, sinusoidal supply, rotor side waveforms, bidirectional power flow, and adjustable input power factor. The 18 bidirectional switches are controlled using the Venturini modulation technique. On the other hand, the DFIG stator circuit is connected directly to the grid. The nonlinear control strategy based on feedback linearization is applied to control the stator power (Ps and Qs) independently using the rotor quadrature and direct currents (irq and ird), which present the images of the previous stator powers. Some limitations appear in the power algorithm using the conventional pi controller, especially in power tracking, error, and quality. In this context, the model reference adaptive controller (MRAC) presents an alternative solution, a robust and efficient controller proposed instead of the pi controllers to control stator powers. Finally, the simulation results confirm that the proposed algorithm could work under hard conditions and demonstrate that the wind energy conversion system (WECS) provides enhanced dynamic responses in transient and steady states and good power quality delivered to the grid.

A Droop-Based Adaptive Power Management System for Energy Storage Integration to DC Grid Using a Modified Dual Active Bridge Converter

This article proposes an adaptive power management system (APMS) for energy storage integration to the dc grid using a modified dual active bridge (DAB) bi-directional dc–dc converter (BDC). The converter can achieve high voltage (HV) gain and zero voltage switching (ZVS) for a wide range of loading conditions with distributed voltage stress. An APMS is designed with a voltage droop control-based model reference adaptive control (MRAC). A reduced-order harmonic model of the converter is used for the APMS design. The proposed APMS does not require detailed knowledge of the system parameters and is also robust to uncertainty and multiple disturbances. The proposed converter and its control technique are verified in MATLAB/SIMULINK platform. An experimental laboratory prototype is also developed for 500 W rating, and the results are presented to validate the system’s efficacy by comparing it with conventional proportional-integral (PI) and sliding mode controllers.

Reduced-Sensor-Based Multistage Model Reference Adaptive Control of PV-Fed PMSM Drive for Water Pump

Typically, photovoltaic (PV) array fed permanent magnet (PM) synchronous motor based water pumping system uses a current sensor to realize maximum power point tracking (MPPT) of PV array, and an encoder to obtain rotor speed. These sensors reduce reliability and increases cost of system. Besides, they are sensitive to both the temperature and electromagnetic noise. This necessitates the elimination of both the PV current sensor and encoder from the system. Thus, first, a multistage model reference adaptive control (MS-MRAC) for encoderless operation of system is presented in this article. The MS-MRAC is a three-stage structure wherein motor speed is estimated by first-stage, while resistance and PM flux linkages are estimated by the remaining two stages. Thus, the MS-MRAC is independent of motor parameters like resistance and PM flux linkages unlike conventional MRAC. Then, the motor speed as estimated by MS-MRAC is used to estimate PV array power, which along with PV voltage is used to realize MPPT, thereby eliminating PV current sensor. The effectiveness of presented control technique is shown through simulated results followed by their experimental validation under different operating scenarios.

Model reference adaptive control based on a novel scalar update law

AbstractThis paper puts forward a model reference adaptive control (MRAC) framework with a compensator based on a novel scalar update law for the dynamical systems with matched uncertainty. The scalar update law is given by an algebraic expression of basis functions and system errors. The main advantage of the proposed MRAC framework is that only a scalar function requires updating online such that the architecture is simple and the computational burden in the existing results can be relieved. Furthermore, the asymptotic stability of the system error dynamics is guaranteed by the proposed controller. Two numerical examples are given to demonstrate the effectiveness of the proposed MRAC framework.

Distributed fault‐tolerant control for high‐speed trains based on adaptive terminal sliding mode control

AbstractHere, a distributed multi‐body dynamics model of high‐speed train (HST) with actuator faults is established. Based on this detail model, a non‐singular terminal sliding mode control method is designed for HST distributed fault‐tolerant control, and the stability of the proposed controller is proved strictly. Considering the high uncertainty of the distributed dynamics model, a radial basis function neural network is introduced to approximate the system uncertainties. Then a universal fuzzy system is proposed to eliminate the chattering problem from sliding mode controller in train control, which further improves the comfort of the train. Finally, numerical simulations are carried out using data from CRH380B train, and model reference adaptive control (MRAC) and adaptive sliding mode control are also tested under the same condition for performance comparison. The results confirm the effectiveness of the proposed controller. Compared with existing MRAC, the root mean square of the speed and position tracking error are reduced by 23.4% and 52%, respectively.

Output feedback Model Reference Adaptive Control of nuclear reactor

This paper presents an output feedback Model Reference Adaptive Controller (MRAC) for controlling the total power of a nuclear reactor. It ensures set point tracking and estimation of unmeasurable states in the presence of unknown external disturbances and parametric uncertainties. A mathematical model of reactor core based on normalized point kinetic equations, with six groups of delayed neutron precursors, is considered along with reactivity feedbacks due to lumped fuel and coolant temperature. Parametric variations in thermal feedback coefficients are taken as uncertainties, reactivity disturbance is considered as a matched external disturbance and change in inlet coolant temperature is considered as an unmatched disturbance. The desired setpoints for reactor power control are generated by choosing a stable reference model based on LQR theory. An observer is designed based on the asymptotic properties of LQG/LTR for the estimation of unmeasurable states as well as external disturbances. Adaptive laws based on output error are developed to compensate for the effect of matched uncertainties and external disturbances. Further, a feedforward controller is augmented to the adaptive laws to compensate for unmatched disturbances. Overall stability and ultimate boundedness of the closed loop signals are analyzed with Lyapunov theory. Performance of the proposed controller is demonstrated through dynamic nonlinear simulations.