Model Reference Adaptive Control System Research Articles

Event‐triggered model reference adaptive control system design for SISO plants using meta‐learning‐based physics‐informed neural networks without labeled data and transfer learning

SummaryThis paper examines the controllability of a novel Lyapunov‐based model reference adaptive control (MRAC) system designed with a meta‐learning‐based physics‐informed neural network (MLPINN) for linear and nonlinear single‐input and single‐output (SISO) plants without labeled data (MLPINN‐MRAC system). It is devised with the benefits of several techniques: the integration of the identification process in a training mode into an online control mode (straightforward design); no labeled data generation for online identification by a physics‐informed neural network; the prevention of degradation in tracking performance by meta‐learning, as the system triggers a meta‐learning process only when an error threshold detects the deterioration (high efficiency and the reduction of computation cost); quick adaptation to new inputs and an updated control input for each sub‐time span by transfer learning. It is worth noting that the frequency of the meta‐learning event detection significantly affects the step response stability of the nonlinear plant. To achieve a better quality of the stabilization, more frequent event detection is necessary for both beginning and end intervals in control. Sixteen triggering events are enough to shape the acceptable step response of the nonlinear plant, and 44 triggering events achieve the plant's desired step response with its minor modeling error. While, as for the linear plant, a single triggering event is sufficient to attain its tolerable step response and modeling error, implying that intensive event detection is not critical in the identification. It is obvious that the MLPINN‐MRAC system functions well and is more beneficial and efficient for the nonlinear plant.

Quadrotor Trajectory Tracking Using Model Reference Adaptive Control, Neural Network-Based Parameter Uncertainty Compensator, and Different Plant Parameterizations

A quadrotor trajectory tracking problem is addressed via the design of a model reference adaptive control (MRAC) system. As for real-world applications, the entire quadrotor dynamics is typically unknown. To take that into account, we consider a plant model, which contains uncertain nonlinear terms resulting from aerodynamic friction, blade flapping, and the fact that the mass and inertia moments of the quadrotor may change from their nominal values. Unlike many known studies, the explicit equations of the parameter uncertainty for the position control loop are derived in two different ways using the differential flatness approach: the control signals are (i) used and (ii) not used in the parametric uncertainty parameterization. After analysis, the neural network (NN) is chosen for both cases as a compensator of such uncertainty, and the set of NN input signals is justified for each of them. Unlike many known MRAC systems with NN for quadrotors, in this study, we use the kxx+krr baseline controller, which follows from the control system derivation, with both time-invariant (parameterization (i)) and adjustable (parameterization (ii)) parameters instead of an arbitrarily chosen non-tunable PI/PD/PID-like one. Adaptive laws are derived to adjust the parameters of NN uncertainty compensator for both parameterizations. As a result, the position controller ensures the asymptotic stability of the tracking error for both cases under the assumption of perfect attitude loop tracking, which is ensured in the system previously developed by the authors. The results of the numerical experiments support the theoretical conclusions and provide a comparison of the effectiveness of the derived parameterizations. They also allow us to make conclusions on the necessity of the baseline controller adjustment.

Research on the Control Problem of Autonomous Underwater Vehicles Based on Strongly Coupled Radial Basis Function Conditions

This paper addresses tracking control problems for autonomous underwater vehicle (AUV) systems with coupled nonlinear functions. For the first time, the radial basis function (RBF) is applied to the model reference adaptive control system, and the vehicle horizontal plane model is proposed. When the AUV movement is affected by the driving force, ocean resistance, and the force generated by the water current, the expected output of the AUV’s system is difficult to meet the expectations, making the AUV trajectory tracking problems challenging. There are two main options for finding suitable controllers for AUVs. The first is making the AUV model achieve better stability using a more complex controller. The second is the simpler controller structure, which can ensure faster system feedback. The RBF and model reference adaptive control (MEAC) system are combined to increase the number of hidden layers, increasing the AUV tracking stability. Because the embedded computing module of an AUV is a bit limited, 31 hidden layers are chosen to simplify the controller structures. A couple of Lyapunov functions are designed for the expected surge and sway velocities, and the vehicle tracking error gradually converges to (0,0). The controller design results are imported into the AUV actuator model by software, and after 0.64 s, the AUV tracking error is less than 1%. At last, the vehicle tracking experiments were carried out, showing that after 0.5 s, the AUV tracking error was less than 1%.

Model reference adaptive system speed estimator based on type-1 and type-2 fuzzy logic sensorless control of electrical vehicle with electrical differential

Introduction. In this paper, a new approach for estimating the speed of in-wheel electric vehicles with two independent rear drives is presented. Currently, the variable-speed induction motor replaces the DC motor drive in a wide range of applications, including electric vehicles where quick dynamic response is required. This is now possible as a result of significant improvements in the dynamic performance of electrical drives brought about by technological advancements and development in the fields of power commutation devices, digital signal processing, and, more recently, intelligent control systems. The system’s reliability and robustness are improved, and the cost, size, and upkeep requirements of the induction motor drive are reduced through control strategies without a speed sensor. Successful uses of the induction motor without a sensor have been made for medium- and high-speed operations. However, low speed instability and instability under various charge perturbation conditions continue to be serious issues in this field of study and have not yet been effectively resolved. Some application such as traction drives and cranes are required to maintain the desired level of torque down to low speed levels with uncertain load torque disturbance conditions. Speed and torque control is more important particularly in motor-in-wheel traction drive train configuration where vehicle wheel rim is directly connected to the motor shaft to control the speed and torque. Novelty of the proposed work is to improve the dynamic performance of conventional controller used of model reference adaptive system speed observer using both type-1 and type-2 fuzzy logic controllers. Purpose. In proposed scheme, the performance of the engine is being controlled, fuzzy logic controller is controlling the estimate rotor speed, and results are then compared using type-1 and type-2. Method. For a two-wheeled motorized electric vehicle, a high-performance sensorless wheel motor drive based on both type-2 and type-1 fuzzy logic controllers of the model reference adaptive control system is developed. Results. Proved that, using fuzzy logic type-2 controller the sensorless speed control of the electrical differential of electric vehicle EV observer, much better results are achieved. Practical value. The main possibility of realizing reliable and efficient electric propulsion systems based on intelligent observers (type-2 fuzzy logic) is demonstrated. The research methodology has been designed to facilitate the future experimental implementation on a digital signal processor.

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.

Real Time Discrete Optimized Adaptive Control for Ionic Polymer Metal Composites

This paper describes a proposed method for optimizing the parameters of a Model Reference Adaptive Control (MRAC) system. The MRAC system uses a reference model to control a plant with unknown dynamics and continuously updates its parameters to improve control accuracy. The system requires an adjustment of parameter γ, which participates in the feedback of the system but cannot be adjusted in real time through trial and error. The proposed method uses optimization techniques to adjust the γ parameters in real time, specifically at the start of the control process, when the maximum deviation of the plant from the reference model is observed. The optimization technique varies the parameters and seeks the best solution to quickly reduce the error. Once the optimal solution is found, the optimization is turned off, allowing the MRAC to continue efficiently reducing the error. In the case of sudden changes in the error due to endogenous or exogenous factors, optimization is activated again to redefine the γ parameters. The magnitude of the change depends on the rate of error changes. The response of the IPMC was measured and compared against a reference signal using three different control techniques MRAC, Model Reference Adaptive Control (MRAC), MRAC-Taguchi, and MRAC-Taguchi-DCT, and the results show that the last penalizes frequencies beyond the fundamental frequency through the cost function, resulting in negligible harmonic distortion.

Coordinated control of stability and economy of distributed drive electric vehicle based on Lyapunov adaptive theory

In order to solve the problem of poor coordinated control between handling stability and economy of distributed drive electric vehicles, a model reference adaptive yaw moment controller based on Lyapunov stability theory and a quadratic programing wheel torque distribution controller considering energy loss of motors are proposed. A hierarchical control strategy is adopted. The upper controller is a model reference adaptive yaw moment controller based on Lyapunov stability theory. The adaptive control law is obtained by solving the Lyapunov function, and the stability of the model reference adaptive control system is proved. The upper controller provides additional yaw moment in real time according to the vehicle state, which can ensure the handling stability of the vehicle. The lower controller adopts the quadratic programing wheel torque distribution controller considering the energy loss of the motor to realize the real-time torque distribution to the wheel. Moreover, the weight distribution of stability and economy is dynamically coordinated based on the phase portrait. The double lane changing condition and fishhook steering condition are selected, and the simulation test of the proposed control method is carried out on the CarSim/Simulink joint simulation platform. The simulation results under the above two road conditions show that the vehicle has good handling stability when using Lyapunov adaptive control method. In addition, the coordinated decision control strategy can effectively reduce the load and energy loss of hub motor.

Adaptive Control of Second-Order Safety-Critical Multiagent Systems With Nonlinear Dynamics

In this article, we propose a distributed adaptive control architecture for leader-following consensus of uncertain multiagent systems with second-order nonlinear dynamics. A nonlinear reference model system captures an ideal behavior of the agents for the leader-following consensus problem. We design a modified nonlinear reference model system and propose a distributed model reference adaptive control architecture to suppress the effects of system uncertainties without a strict knowledge of their magnitude and rate upper bounds. Consequently, each agent evolves within a (possibly different) prescribed distance from the corresponding modified reference system trajectories. Based on an input-to-state stability analysis, it is shown that the trajectories of the modified reference model system can get arbitrarily close to the trajectories of the ideal reference model system. As a result, the trajectories of the agents evolve within a user-specified prescribed distance from their ideal system trajectories, satisfying the safety constraints. The key feature of the presented control architecture in this article is the elimination of the <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">ad hoc</i> tuning process for the adaptation rate that is conventionally required in model reference adaptive control systems to ensure safety. An illustrative numerical example finally demonstrates the efficacy of the proposed distributed adaptive control architecture.

Model reference adaptive control with adjustable gain for piezoelectric actuator

In this paper, a model reference adaptive control with adjustable gain is investigated to reduce the nonlinear hysteresis effect of piezoelectric actuator. Firstly, the unknown system dynamics of piezoelectric actuator are described based on Bouc-Wen model. By linearizing the nonlinear hysteresis effect, the corresponding reference model is designed to track the output error. Then, the stability and robustness of the model reference adaptive control system is ensured by the Lyapunov stability theorem. In addition, an iteration adjustment rule is proposed to improve the convergence rate of the tracking error. Finally, the simulation results of the proposed control are compared with the traditional PID control and other model reference adaptive control. The results demonstrate that the proposed method has a faster convergence speed and smaller error range.

Robust Adaptive Control Laws for a Winged Re-entry Vehicle

The flight control system for reusable launch vehicles has to work for an extensive flight envelope ranging from hypersonic to subsonic Mach numbers. Since the plant dynamics are highly nonlinear, time-varying, and coupled, classical controllers are designed for large stability margins about the linearised points. This limits the performance of the classical controller, and the design process is iterative and time-consuming. Hence adaptive controllers are designed to handle such complex systems using a standard quadratic Lyapunov function. The existing parameter update laws of the model reference adaptive control system are not robust to bounded disturbances and unmodelled dynamics. Hence this paper proposes modified controller parameter update laws using a rectangular projection operator and barrier Lyapunov function, ensuring robustness to structured and unstructured uncertainties. The rectangular projection-based control law provides that the controller parameters remain within the specified upper and lower limits, whereas the barrier Lyapunov-based controller maintains the trajectory also within the specified error limit. The effectiveness of the proposed update laws is demonstrated for the automatic landing phase of a reusable launch vehicle.

Fuzzy-Optimized model reference adaptive control of interacting and noninteracting processes based on MIT and Lyapunov rules

Various system parameter variations occur during operations in several existing process industries. These parameter variations result in process shifts, thus, requiring adequate control strategies to compensate for these alterations, which consequently maintain desired system response. A paradigm is the coupled tank systems; in such systems, the level and flow of liquid must be adequately controlled to maintain the reaction equilibrium as well as to avoid spillage or equipment damage. The model reference adaptive control (MRAC) is an adaptive control strategy that creates a control law, subject to an adaptation gain, which causes the system’s plant to continuously track a reference model until a zero tracking error is achieved. The Massachusetts Institute of Technology (MIT) and Lyapunov approaches were used to develop the adaptation mechanism, which is used to adjust the parameters in the control law. Conventionally, a fixed value is adopted as the adaptation gain; however, the adaption gain can also be determined heuristically. The fuzzy logic control was used to optimally determine the value of the adaptation gain, which thus results in the fuzzy-optimized MRAC (FOMRAC) system. Consequently, these schemes were comparatively analysed for the control of the flow and level of liquid in coupled two-tank systems, arranged in noninteracting and interacting fashions. Using MATLAB/Simulink, results depicted that the FOMRAC systems had faster settling times in comparison with the fixed adaptation gain MRAC systems. Overall, the FOMRAC system based on Lyapunov rule yielded the lowest performance indices values. In addition, the scheme completely eliminated the overshoot that resulted from the implementation of the other schemes for the control of the interacting process.

Multivariable Model Reference Adaptive Control of an Industrial Power Boiler Using Recurrent RBFN

In industrial steam systems, the process requires a specific pressure, and the maximum permissible operating pressure is different. If the inlet steam pressure to the steam consuming equipment exceeds the operating pressure, it may cause hazards. Therefore, the more precise control of the boiler pressure is important. Since we are dealing with a nonlinear, time-varying, and multivariable system, the control method must be designed to handle this system well. Most of the methods proposed so far are either not physically feasible or the system has considered very simple. Therefore, in this paper, while modeling the boiler and its pressure relations more precisely, we will introduce a recurrent type-2 fuzzy RBFN-based model reference adaptive control system with various uncertainties so that the uncertainty and inaccuracy of the model can be compensated. The experimental results prove the efficiency of the proposed method in boiler control.

Speed sensorless control of a bearingless induction motor based on fuzzy PI fractional MRAS scheme

ABSTRACT To handle the suspended rotor speed self-identification problem of a bearingless induction motor (BL-IM), a sensorless control strategy based on fuzzy PI fractional model reference adaptive system (MRAS) is proposed. First, based on the flux linkage error, fractional MRAS adaptive law is designed to accelerate the response speed of the controlled object, and Lyapunov theorem is used to prove the stability of the adaptive law. Then, the fuzzy control rules in the fuzzy PI controller are used to adjust PI parameters of adaptive law online in real time. Finally, the speed under no-load operation, abrupt speed change and abrupt change of load is estimated and sensorless control is realized. The simulation and experimental results show that the proposed fuzzy PI fractional MRAS control system of the BL-IM can not only effectively realize self-identification of speed under no-load, speed change and abrupt change of load, but also have good suspension characteristics of the motor suspended rotor, realizing high reliability and low costs of BL-IM.

Adaptive control systems with unstructured uncertainty and unmodelled dynamics: a relaxed stability condition

As it is well-known, system uncertainties and unmodeled dynamics can deteriorate stability properties of model reference adaptive control systems. Motivated by this standpoint, we first analyse stability conditions of model reference adaptive control architectures in the presence of unstructured system uncertainties and unmodeled dynamics. We then synthesise adaptive robustifying terms to relax the aforementioned stability condition, which presents our main contribution. Specifically, these terms in the feedback loop guarantee overall system stability even in the presence of significant system uncertainties when unmodeled dynamics satisfy a condition. We further demonstrate our theoretical findings in an experiment involving an inverted pendulum on a cart (modeled dynamics) coupled with another cart through a spring (unmodeled dynamics).

Implementation of Stir-Speed Adopted Controllers Onto a Batch Bioreactor for Improved Fermentation

Quality, quantity, and economy of the fermentation product depend on the transient response and the steady-state of the fermentation process. Due to its simple construction, an industrial batch bioreactor cannot be equipped with a closed-loop control system that applies adding or removing substances during fermentation. This theoretical and practical study displays how fermentation can be controlled, in this case by altering the rotational speed of a stirrer system of such a bioreactor. A numerical analysis was employed to set up a mathematical model that describes the impact of the stirrer speed on the fermentation. The model consists of linear and non-linear parts. To determine their parameters, a least square identification and a particle swarm optimization method were utilized. The model was fitted and tested experimentally in a laboratory on the operating batch bioreactor. The design and synthesis of a conventional linear control system and an advanced model reference adaptive control system, which is also convenient for control of non-linear controlled plants, were carried out based on the determined mathematical model. Both control concepts were first implemented into the dSpace 1103 control system, convenient for faster development and prototyping. Finally, they were realized with the Siemens SIMATIC S7 programmable logic controller, which was ideal for industrial environment operation. During the operation of the bioreactor, the control systems were tested along with the acquisition of measured data involving CO2 concentration of a fermentation product. The findings of successfully applying linear and adaptive controllers of the milk fermentation in the batch bioreactor are analyzed and presented.

New Adaptive Control Strategy for a Wind Turbine Permanent Magnet Synchronous Generator (PMSG)

Wind energy conversion systems have become a key technology to harvest wind energy worldwide. In permanent magnet synchronous generator-based wind turbine systems, the rotor position is needed for variable speed control and it uses an encoder or a speed sensor. However, these sensors lead to some obstacles, such as additional weight and cost, increased noise, complexity and reliability issues. For these reasons, the development of new sensorless control methods has become critically important for wind turbine generators. This paper aims to develop a new sensorless and adaptive control method for a surface-mounted permanent magnet synchronous generator. The proposed method includes a new model reference adaptive system, which is used to estimate the rotor position and speed as an observer. Adaptive control is implemented in the pulse-width modulated current source converter. In the conventional model reference adaptive system, the proportional-integral controller is used in the adaptation mechanism. Moreover, the proportional-integral controller is generally tuned by the trial and error method, which is tedious and inaccurate. In contrast, the proposed method is based on model predictive control which eliminates the use of speed and position sensors and also improves the performance of model reference adaptive control systems. In this paper, the proposed predictive controller is modelled in MATLAB/SIMULINK and validated experimentally on a 6-kW wind turbine generator. Test results prove the effectiveness of the control strategy in terms of energy efficiency and dynamical adaptation to the wind turbine operational conditions. The experimental results also show that the control method has good dynamic response to parameter variations and external disturbances. Therefore, the developed technique will help increase the uptake of permanent magnet synchronous generators and model predictive control methods in the wind power industry.

A Generalization for Model Reference Adaptive Control and Robust Model Reference Adaptive Control Adaptive Laws for a Class of Nonlinear Uncertain Systems with Application to Control of Wing Rock Phenomenon

Lyapunov's direct method is a primary tool for designing Model Reference Adaptive Control (MRAC) and robust MRAC schemes. In general, Lyapunov function candidates contain two categories of quadratic terms. The first category includes the system tracking error quadratic terms or, in some cases, consist of the system state quadratic terms. The second consists of the parameter estimation error quadratic terms. To design MRAC and Robust MRAC systems, researchers have used a limited variety for choosing quadratic terms. In this study, we consider a general form for the tracking error quadratic terms. We consider a strictly increasing function that belongs to the class of c1, which is a function of state tracking error quadratic terms. It yields a general structure for stable adaptive laws for updating controller parameters. For the MRAC scheme, the global asymptotic stability of the closed-loop system and stability and uniform bounded tracking of robust MRAC schemes are guaranteed. To evaluate the performance of the designed controllers, we consider the single DOF wing rock dynamics.

A New ${\rm{\delta }}$-MRAS Method for Motor Speed Estimation

This letter introduces a new method to estimate the motor speed based on the Model Reference Adaptive System (MRAS) technique. The novelty of the proposed MRAS control structure relies on using the motor input impedance angle as a reference state variable to estimate the motor speed. In this context, the reference angle is obtained from measuring the angle between the motor terminal voltage and current vectors using a double-structure Phase Locked Loop (PLL). The tunable angle is instantaneously calculated using the per-phase motor equivalent circuit. Having the impedance angle as the only candidate for the proposed scheme inherently decouples the reference and the adaptive models. This decoupling resulted in obtaining a superior performance at low, high, and zero speeds. The simplicity of the reference and the adaptive schemes ease the analysis, design, and implementation. The introduced speed estimation concept is validated under different scenarios of operating conditions.

Research on Electro-hydraulic Servo System of Air Rudder on Model Reference Adaptive Control

An adaptive control system with good following characteristics is designed for the electro-hydraulic servo system which are strongly coupled and seriously nonlinear. The model of position servo system on air rudder is discussed with the uncertain system equivalent to the one with parametric variable double input and single output to establish a Popov-MRAC (Model Reference Adaptive Control) system. The simulation results show that the Popov MRAC system has good following characteristics, precision and robustness.

A new model reference adaptive control with the disturbance observer‐based adaptation law for the Nonlinear Servomechanisms: SISO and MIMO Systems

AbstractA disturbance observer (DOB) is proposed to replace the external disturbance adaptation law in model reference adaptive control (MRAC) to perform robust tracking control performance for nonlinear servomechanisms. Lyapunov stable theory is implemented to combine the DOB with MRAC to simultaneously converge the estimated states and tracking errors toward null. Then, the disturbance observer‐based MRAC (DOBMRAC) is proposed and realized. The single‐input single‐output (SISO) mass‐spring‐damper system and multi‐input multi‐output (MIMO) two‐link manipulator robot system are both demonstrated as the control examples. However, in comparisons of tracking control performance between MRAC and DOBMRAC, it is found that the proposed controller reveals better robust tracking control performance for SISO and MIMO servomechanisms with unknown time‐varying disturbances. The contributions of this paper are: i) the proposed DOBMRAC is successfully implemented in both the SISO and MIMO systems; ii) the proposed controller performs better tracking control performance than MRAC for unknown time‐varying disturbances; iii) the DOBMRAC cannot only perform robust tracking control performance, but also shows disturbance estimation ability well; and iv) the proposed control methodology can also be widely applied to other MRAC systems with unknown time‐varying disturbance.