Model-free Adaptive Control Research Articles

Model-free adaptive predictive control with unscented Kalman filter for hovercraft speed and heading stabilization

This paper develops a novel unscented Kalman filter-model free adaptive predictive control (UKF-MFAPC) method for an underactuated hovercraft speed and heading stabilization under the influence of measurement noise. First, the proposed method is based on the compact form dynamic linearization (CFLD) technique, which involves an analysis of the tight format dynamic linearization method. This approach specifically addresses the unique non-real-time scalability of the heading control subsystem, rendering the CFDL method unsuitable. Through redefining the linear combination of lateral velocity and heading as output to fulfill all assumptions of CFDL methods, this scheme effectively mitigates the lateral velocity vibration problem of the hovercraft. Secondly, this controller introduces the measurement noise during the data collection process into the optimization function and combines the unscented Kalman filtering method with data-driven models, the influence of error suppression noise on the controller is suppressed, ensuring that the output can still be controlled within a certain range of expected values. This paper also delves into the convergence of tracking errors and examines the stability of bounded inputs and outputs. Finally, the noise suppression effect and stability of the UKF-MFAPC scheme are demonstrated through a comparative analysis of simulation results with proposed model-free methods.

Under-Actuated Motion Control of Haidou-1 ARV Using Data-Driven, Model-Free Adaptive Sliding Mode Control Method.

We propose a data-driven, model-free adaptive sliding mode control (MFASMC) approach to address the Haidou-1 ARV under-actuated motion control problem with uncertainties, including external disturbances and parameter perturbations. Firstly, we analyzed the two main difficulties in the motion control of Haidou-1 ARV. Secondly, in order to address these problems, a MFASMC control method was introduced. It is combined by a model-free adaptive control (MFAC) method and a sliding mode control (SMC) method. The main advantage of the MFAC method is that it relies only on the real-time measurement data of an ARV instead of any mathematical modeling information, and the SMC method guarantees the MFAC method's fast convergence and low overshooting. The proposed MFASMC control method can maneuver Haidou-1 ARV cruising at the desired forward speed, heading, and depth, even when the dynamic parameters of the ARV vary widely and external disturbances exist. It also addresses the problem of under-actuated motion control for the Haidou-1 ARV. Finally, the simulation results, including comparisons with a PID method and the MFAC method, demonstrate the effectiveness of our proposed method.

Quantized Iterative Learning Bipartite Containment Tracking Control for Unknown Nonlinear Multi-agent Systems

This paper proposes a quantized model-free adaptive iterative learning control (MFAILC) algorithm to solve the bipartite containment tracking problem of unknown nonlinear multi-agent systems, where the interactions between agents include cooperation and antagonistic interactions. To design the controller, the agent’s dynamics is transformed into the linear data model based on the dynamic linearization method, and then a quantized MFAILC algorithm is established based on the quantized values of the relative output measurements. The designed controller only depends on the input and output data of the agent. We prove that under the quantized MFAILC algorithm, the multi-agent systems can achieve the bipartite containment, that is, the output trajectories of followers converge to the convex hull formed by the leaders’ trajectories and the leaders’ symmetric trajectories. Finally, we provide simulations to illustrate the effectiveness of our theoretical results.

Resilience enhancement to loss of actuator effectiveness in a Model-Free Adaptive framework

Within the theoretical framework supporting the Model Free Adaptive Control approach, this paper investigates on the presence of possible loss of effectiveness affecting the actuator of a Single-Input Single-Output plant. In particular, stemming from a tracking controller proposed in a seminal paper and the related proofs, an identification algorithm is proposed for the estimation of the loss of effectiveness, with proved bounded estimation error, along with a condition for the detection of actuator faults. A fault-resilient tracking controller is finally proposed, based on the estimated loss of effectiveness, providing asymptotically vanishing tracking error. A comparative analysis by simulation on a benchmark system taken from the pertinent literature is also presented to validate the proposed development.

Iterative Learning Tracking Control for Nonlinear Systems Based on Data Driven Control

This paper introduces a novel methodology for tracking control of general nonlinear systems. Unlike traditional methods, which rely on linearization or nonlinear cancellation. This article starts from the iterative domain and utilizes the concept of iterative learning control to improve the control performance of the system. It employs a data-driven approach for model-free adaptive control, addressing the challenges posed by strong system nonlinearity, difficulties in control, and even modeling issues caused by disturbances and other factors. It enables precise trajectory tracking without the need for complex computations, making it suitable for real-time control applications. The effectiveness of the methodology is demonstrated through examples.

An online model-free adaptive learning control solution for robotic arms

This paper focuses on the online control of a class of nonlinear dynamical systems, specifically robotic manipulators. Solutions utilizing Proportional–Integral–Derivative (PID) control schemes are employed to control the joints of robotic manipulators. However, the existing control strategies utilize fixed gains, which do not fully account for the inherent nonlinearity of the dynamical structure or the dynamics of reference-tracking error. Additionally, the individual joint’s dynamic performance is optimized independently from the performance of other joints. This work introduces an adaptive integral Reinforcement Learning algorithm to control a four-DoF robotic arm in real time. This is done using a model-free Value Iteration process implemented in a continuous-time mode. The solution does not assume any knowledge of the dynamics of the robot arm and does not require any initial admissible control strategy to proceed with the adaptive learning solution. The self-learning algorithm provides adaptable strategies to control the turntable, forearm, bicep, and wrist joints of the robotic arm. The performance of the adaptive learning solution is compared with those of Proportional–Integral–Derivative and high-order model-free adaptive control schemes to highlight its effectiveness.

On the Performance of the Model-Free Adaptive Control For A Novel Moving-Mass Controlled Flying Robot

In this paper, the performance of Model-Free Adaptive Control (MFAC) has been investigated on a novel and specific moving-mass controlled (MMC) flying robot system. The novel one-degree-of-freedom (1 DOF) MMC flying robot test bed presented in this paper has highly nonlinear and slow dynamics with a variable center of gravity (CoG) and moment of inertia. This makes the control of this system a challenging problem. One of the solutions to this challenge is the use of data-driven control methods, in particular, MFAC. This controller uses a data-driven model to control the system using only input and output (I/O) data. This paper compares this data-driven controller with proportional-integral-derivative (PID) control, and Linear Quadratic Regulator (LQR) as two model-free and model-based controllers which are widely used controllers in industry. The results of the comparison show that in the various scenarios applied, MFAC has a clear superiority over the PID and LQR, and its adaptive structure gives more freedom of action in the implementation of different scenarios and the presented noise. The results are obtained using the Integral Time Absolute Error (ITAE) criteria and the mean maximum error has also been compared in a Monte Carlo analysis. For a more detailed study, the amount of control energy consumption was also compared, which showed a clear superiority of the MFAC. Also, the robustness of the controller was demonstrated by introducing uncertainty in the plant parameters and by running 100 Monte Carlo simulations with random initial conditions. Finally, despite the PID controller, the MFAC followed the desired scenarios well and compared to LQR consumed less energy. The results demonstrate that the MFAC outperformed the PID and LQR controllers in the presence of random initial conditions and noise in terms of mean maximum error (70.4%)\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$(70.4\\%)$$\\end{document}, mean ITAE (91%)\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$(91\\%)$$\\end{document}, and energy consumption (46%)\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$(46\\%)$$\\end{document}.

An Adaptive Control Scheme Based on Non-Interference Nonlinearity Approximation for a Class of Nonlinear Cascaded Systems and Its Application to Flexible Joint Manipulators.

Control design for the nonlinear cascaded system is challenging due to its complicated system dynamics and system uncertainty, both of which can be considered some kind of system nonlinearity. In this paper, we propose a novel nonlinearity approximation scheme with a simplified structure, where the system nonlinearity is approximated by a steady component and an alternating component using only local tracking errors. The nonlinearity of each subsystem is estimated independently. On this basis, a model-free adaptive control for a class of nonlinear cascaded systems is proposed. A squared-error correction procedure is introduced to regulate the weight coefficients of the approximation components, which makes the whole adaptive system stable even with the unmodeled uncertainties. The effectiveness of the proposed controller is validated on a flexible joint system through numerical simulations and experiments. Simulation and experimental results show that the proposed controller can achieve better control performance than the radial basis function network control. Due to its simplicity and robustness, this method is suitable for engineering applications.

Cascade control algorithm for slip rate in a brake-by-wire system based on direct drive valve

To achieve a rapid response and precise control of braking hydraulic pressure, a brake-by-wire electro-hydraulic braking system based on a direct drive valve was designed. This system employs an electromagnetic linear actuator to drive the valve core directly, achieving swift adjustment of brake wheel cylinder hydraulic pressure. Given the strong coupling and non-linearity of the electromagnetic linear actuator, solely using a single-loop controller to control the slip rate can easily lead to weakened system performance. Hence, we proposed a cascade control algorithm for the brake-by-wire system, with an outer loop for slip rate control and an inner loop for direct drive valve position. The outer loop adopted a fuzzy PID control, while the inner loop adopted a model-free adaptive sliding mode control. By combining model-free adaptive control with a novel discrete exponential approach, we addressed the system’s non-linearity and unknown disturbances. A braking system test platform was constructed to verify the superior hydraulic tracking performance of this brake-by-wire system and to perform slip rate control performance analysis under different road conditions. Results demonstrated that compared to the fuzzy PID-MFAC algorithm, the proposed fuzzy PID-MFASMC control enhanced car slip rate control precision, and reduced both braking time and distance.

A model-free adaptive predictive path-tracking controller with PID terms for tractors

An efficient tractor path-tracking method can increase the operational accuracy, improve land utilisation, and more efficiently provide services for autonomous tractors and precision agriculture. In this study, a model-free adaptive predictive control-proportional-integral-derivative (MFAPC-PID) method was devised. Based on preview theory, a tracking system based on course deviation angle was designed. After the tracking system was linearised, an MFAPC tracking system was developed, and its inherent defects were analysed. Referring to the control structure of an incremental PID algorithm, the MFAPC was considered as an adaptive integral item, and the MFAPC-PID controller was obtained by adding adaptive proportional and differential terms. To verify the proposed controller, collaborative simulation and hardware-in-the-loop tests were performed. The controller was simulated and tested under different paths, road surfaces, and tractor models. Compared with other methods, the MFAPC-PID path-tracking method exhibits superior comprehensive performance, adaptability, universality, and robustness. Moreover, the MFAPC-PID method is insensitive to external interference and model changes of controlled objects.

Modeling and analysis of vehicle stability region based on Lyapunov and coordinated control

The timely intervention of the assisted driving system is the key to improving the handling stability and roll stability of the vehicle, and the vehicle stability region serves as the core basis for determining the intervention timing of the assisted driving system. With the aim of modeling and analyzing the vehicle stability region, a three-degree-of-freedom (3-DOF) vehicle dynamics model including yaw, roll, and lateral motions, as well as a nonlinear Magic Formula tire model are established in this paper. Based on this, a simplified but improved cubic tire model is developed to accurately fit the tire lateral force of Magic Formula tire model within a larger range of slip angles. Subsequently, using the Lyapunov method, the roll stability region and the yaw stability region are respectively constructed, and the accuracy verification and robustness analysis of the established stability region are conducted in the Matlab/Simulink environment. Finally, a model-free adaptive control method is employed to keep the vehicle state within the stability region, without tracking specific vehicle state objectives. The study in this paper can provide theoretical support for stability boundary determination, formulation of intervention timing for assisted driving stability control, and coordination control of vehicle stability and anti-rollover with local compatibility or even conflicts.

Data‐driven model‐free predictive control for microstage with coupling and hysteresis nonlinearities

SummaryThe precision motion control problem is investigated in this paper for microstages with cross‐axial coupling and hysteresis. Cross‐axis coupling generally results in stress‐stiffening effects, thereby causing time‐varying dynamics in the microstages. Additionally, when a microstage is driven by piezoelectric actuators (PEAs), the hysteresis effect of the actuator itself must also be considered. Modeling the microstages becomes complicated when both nonlinear characteristics, coupling and hysteresis, coexist. To address this challenge without the need for modeling, a novel data‐driven model‐free predictive control scheme called first‐order tensor‐vector product polynomial approximation based model‐free predictive control (TPPA ‐MFPC is proposed. TPPA ‐MFPC solely relies on the sampling input/output (I/O) data of the systems. The main concept behind TPPA ‐MFPC is to derive a linear approximation model using the I/O data collected during operation. This linear approximation model then serves as a nominal model in a predictive controller, enabling the control of the microstages. Finally, the effectiveness of the proposed TPPA ‐MFPC scheme and the performance improvement over existing model‐free schemes, for example, proportion integration differentiation control (PID), model‐free adaptive control (MFAC), model‐free adaptive predictive control (MFAPC), data‐dependent LMI (DDLMI), and data‐enabled predictive control (DeePC) are demonstrated in the simulation examples with a 2‐degree of freedom (DOF) multileaf spring‐based microstage driven by PEA.

Model-Free Adaptive State Feedback Control for a Class of Nonlinear Systems

This paper investigates state feedback control for a class of discrete-time multiple input and multiple output nonlinear systems from the perspective of model-free adaptive control and state observation. The design of a dynamic state feedback control can be efficiently carried out using dynamic linearization and state observation. The stability of the proposed method is guaranteed by theoretical analysis. Numerical simulation tests and experimentation on a continuous stirred tank reactor are carried out to validate the effectiveness of the proposed approach. <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">Note to Practitioners</i> —The growth in the scale of factories and the complexity of associated production processes increases the complexity and time involved in associated mathematical modelling. Data driven approaches to control remove the need to model processes. To the best of the authors’ knowledge, existing approaches to model-free adaptive control (MFAC) of general systems are all based on an input-output control paradigm. These methods thus cannot guarantee the stability of the system state. The purpose of this study is to develop a novel Model-Free Adaptive Control (MFAC) approach to achieve control of the system state. In this paper, the assumptions required to achieve model-free adaptive control by state feedback are presented mathematically. A controller design and the associated stability proof are then presented. Numerical simulation and experimentation is conducted to validate the effectiveness of the proposed approach. In future research, state feedback data control in the presence of random disturbances will be investigated.

Robust model-free adaptive iterative learning control for an autonomous bus trajectory tracking system.

A robust model-free adaptive iterative learning control (R-MFAILC) algorithm is proposed in this work to address the issue of laterally controlling an autonomous bus. First, according to the periodic repetitive working characteristics of autonomous buses, a novel dynamic linearized method used in the iterative domain is utilized, and a time-varying data model with a pseudo gradient (PG) is given. Then, the R-MFAILC controller is designed with a proposed adaptive attenuation factor. The proposed algorithm's advantage lies in the R-MFAILC controller, which solely utilizes the input and output data of the regulated entity. Moreover, the R-MFAILC controller has strong robustness and can handle the nonlinear measurement disturbances of the system. In simulations based on the Truck-Sim simulation platform, the effectiveness of the proposed algorithm is verified. A rigorous mathematical analysis is employed to demonstrate the stability and convergence of the proposed algorithm.

Model-free adaptive optimal control for fast and safe start-up of pumped storage hydropower units

Pumped storage unit (PSU) is a special kind of hydropower unit, that undertakes the task of power generation, and performs the function of energy storage. Due to its unique advantages, pumped storage power stations have been extensively developed in China in recent years and play an important role that is difficult to be performed by other energy sources. Although many studies have been carried out on the control of PSUs, most of the control algorithms are based on object models, which results in the control performance depending on the model accuracy to a large extent, limiting the practical application of these algorithms. For this reason, a preliminary application of model-free adaptive control in PSUs is investigated in this paper. Firstly, a refined nonlinear model of PSU is established, secondly, the model-free adaptive controller of PSU and its parameter optimization strategy are designed, and finally, verification is carried out by simulation studies for four different start-up conditions, and a comprehensive comparison is made with control strategies such as proportional-integral-derivative (PID), fractional-order PID, and nonlinear generalized predictive control. The results show that the proposed method has significant improvement in both speed and head control performance compared with other methods, with the regulation time being on average at least 5.53 s faster and the overshoot being on average at least 2.85 % lower. It proves the effectiveness and superiority of the method. In addition, the proposed method reduces energy consumption in the regulation process, and the computational cost meets the real-time control requirements, which has a wide range of application prospects.

Novel integrated guidance and control design for a three-stage satellite carrier using model-free adaptive control

A model-free adaptive control is proposed for suboptimal guidance correction and control of a prototypical three-stage satellite carrier. For this sake, we consider a nominal guidance for the model of the system and design the adaptive control for a single-input multi-output system exposed to wind disturbance and measurement noise in the rates of inputs and outputs. Then, subsequent to the guidance correction, a differentiation model of the system is estimated and the control policy is realized under some profitable performance constraints to set the satellite in a desirable circular orbit. The simulation results readily reveal the efficiency of the proposed method and its robustness to uncertainties in the system.

Design of MFAC greenhouse temperature controller based on LESO with disturbance estimation and fuzzy controller with parameter tuning

The proper temperature is essential for the growth and development of greenhouse crops. Therefore, it is necessary to determine an appropriate greenhouse temperature automatic control strategy. In this paper, a model-free adaptive greenhouse temperature control strategy is proposed by combining a linear extended state observer and a fuzzy controller. Specifically, the linear extended state observer is introduced to estimate model approximation error generated by pseudo gradient estimation. The fuzzy controller is used to correct the system parameter ρ online. The simulation results show that when there is no disturbance, compared with the typical model-free adaptive scheme, the MAE and RMSE of the greenhouse temperature control scheme proposed in this paper are reduced by 57.55% and 5.40% respectively. In the presence of custom disturbances, the proposed control scheme still has a faster response speed, stronger robustness, and higher control accuracy. And the proposed method can reduce the frequent action of the actuator, thus effectively reducing the energy cost.

Research on improved partial format MFAC greenhouse temperature control method based on low energy consumption optimization

Temperature is critical to the growth of crops in agricultural greenhouses. Thus, designing a greenhouse temperature controller that maximizes energy savings while maintaining control accuracy is very important. This paper proposes an improved partial format model-free adaptive control method and designs a greenhouse temperature controller based on this method to balance control accuracy and energy consumption. Firstly, a limited energy consumption term is added to the control input cost function of the traditional partial format model-free adaptive control to penalize excessive control input. We derive an improved partial format model-free adaptive control input algorithm and design a greenhouse temperature controller using this algorithm. Then, the controller's sensitive parameters are selected using a Monte Carlo-based parameter sensitivity method. Finally, the whale optimization algorithm is used to optimize the sensitive parameters. The insensitive parameters are set according to experience. This paper, a theoretical study based on simulated experiments, proves the convergent tracking error of the proposed improved partial format model-free adaptive algorithm. Simulation results show that the improved controller minimizes energy consumption while ensuring control accuracy, reducing power consumption by 12.35 % compared to the traditional controller.

Intelligent control based on single-input interval type-2 fuzzy iPI and super twisting nonlinear sliding mode compensator for regulating PEMFC output voltage

The control of Proton Exchange Membrane Fuel Cell (PEMFC) is exceptionally challenging due to its complex nonlinearity, slow dynamics and load disturbance. In this paper, an Adaptive Model Free Control (AMFC) approach is introduced for regulating the PEMFC output voltage under load perturbation and measurement noise conditions. The proposed method consists of four sub-elements. Firstly, an Extended State Observer (ESO) based on a Single-Input Interval Type-2 Fuzzy intelligent PI (SI-IT-2-FLC-iPI) scheme is designed to enhance the performance of PEMFC. Secondly, a Nonlinear Sliding Mode Control-based Super Twisting Algorithm (NSMC-STA) is used as an auxiliary control approach to reduce the estimation error and ameliorate the system robustness. Thirdly, a Forgotten Recursive Least Square Error (FRLSE) is applied for adjusting the physical parameter of MFC and further ameliorating the control response. Finally, all these elements are merged together within what it is called Ultra Local Model (ULM).Through extensive simulation, the efficacy of the proposed regulator in accurately tracking the output signal is showcased, outperforming conventional controllers with remarkable improvements. The system achieves 0.001 steady-state error, 0% overshoot and settling time of approximately 8.9 s, which is good enough in the context of standalone fuel cell applications.

Improved data-driven high-order model-free adaptive iterative learning control with fast convergence for trajectory tracking systems

The data-driven high-order pseudo-partial derivative-based model-free adaptive iterative learning control (HOPPD-MFAILC) is always slow to converge and difficult to have excellent tracking results. To address the problem, an improved high-order pseudo-partial derivative-based model-free adaptive iterative learning control (iHOPPD-MFAILC) with fast convergence is proposed. First, to reduce the impact of the initial value of the pseudo-partial derivative (PPD) on the convergence speed of the algorithm, the initial PPD is corrected by introducing the high-order model estimation error. Second, to reduce the influence of system noise on the control performance, the original HOPPD-MFAILC control law is improved by introducing time-varying iterative proportional and time-varying iterative integral terms. Then, the convergence of the proposed improved control algorithm is demonstrated by theoretical analysis. Finally, simulations and experiments on the ball screw motion system show that the proposed iHOPPD-MFAILC can track the desired trajectory better. In addition, iHOPPD-MFAILC has better robustness in the noisy environment and achieves better convergence as well as trajectory tracking performance under different initial PPD conditions. The proposed control scheme has excellent application potential in precision motion control.