Model-free Control Research Articles

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.

Model-free Current Predictive Control of Open-winding Permanent Magnet Synchronous Motor

Model-free Current Predictive Control of Open-winding Permanent Magnet Synchronous Motor

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}.

Model-free visual servoing based on active disturbance rejection control and adaptive estimator for robotic manipulation without calibration

PurposeVisual feedback control is a promising solution for robots work in unstructured environments, and this is accomplished by estimation of the time derivative relationship between the image features and the robot moving. While some of the drawbacks associated with most visual servoing (VS) approaches include the vision–motor mapping computation and the robots’ dynamic performance, the problem of designing optimal and more effective VS systems still remains challenging. Thus, the purpose of this paper is to propose and evaluate the VS method for robots in an unstructured environment.Design/methodology/approachThis paper presents a new model-free VS control of a robotic manipulator, for which an adaptive estimator aid by network learning is proposed using online estimation of the vision–motor mapping relationship in an environment without the knowledge of statistical noise. Based on the adaptive estimator, a model-free VS schema was constructed by introducing an active disturbance rejection control (ADRC). In our schema, the VS system was designed independently of the robot kinematic model.FindingsThe various simulations and experiments were conducted to verify the proposed approach by using an eye-in-hand robot manipulator without calibration and vision depth information, which can improve the autonomous maneuverability of the robot and also allow the robot to adapt its motion according to the image feature changes in real time. In the current method, the image feature trajectory was stable in the camera field range, and the robot’s end motion trajectory did not exhibit shock retreat. The results showed that the steady-state errors of image features was within 19.74 pixels, the robot positioning was stable within 1.53 mm and 0.0373 rad and the convergence rate of the control system was less than 7.21 s in real grasping tasks.Originality/valueCompared with traditional Kalman filtering for image-based VS and position-based VS methods, this paper adopts the model-free VS method based on the adaptive mapping estimator combination with the ADRC controller, which is effective for improving the dynamic performance of robot systems. The proposed model-free VS schema is suitable for robots’ grasping manipulation in unstructured environments.

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.

Model-Free Optimal Vibration Control of a Nonlinear System Based on Deep Reinforcement Learning

Optimal control of nonlinear vibration requires precise knowledge of the system and the solution to Hamilton–Jacobi–Bellman (HJB) equation. However, in practical engineering applications, acquiring precise system parameters poses challenges, and the analytical solutions for the HJB equation are difficult to obtain. In this paper, two reinforcement learning algorithms, Twin Delayed Deep Deterministic Policy Gradient (TD3) algorithm and Soft Actor-Critic (SAC) algorithm, are employed to train neural network-based optimal controllers for the van der Pol vibration system in the presence of unknown system parameters. To validate their performance, the controllers undergo testing in a series of experiments, including assessments of free vibration, frequency sweep excitation, and Gaussian noise excitation. The results indicate that both the TD3-trained and SAC-trained neural network-based controller are capable of proficiently suppress the vibration of the van der Pol oscillator. Additionally, these two model-free controllers can approximate the optimal control law which solved based on the dynamic model of the nonlinear system.

Neural network based adaptive robust synchronous control of double-lift overhead crane considering input saturation

This paper proposes a novel model-free controller, considering the double-lift overhead crane system cannot be accurately modeled and affected by external disturbances. Firstly, to improve the convergence speed of the system states, a time-varying sliding mode surface using a sigmoid-like function is proposed. Then, an adjustable weights radial basis function neural network (AWRBFNN) is introduced to estimate and compensate for the unknown dynamics of the system. This AWRBFNN introduces direct and effective model-free properties, but also brings approximation errors. To estimate the uncertain disturbances and the errors of the neural network, an adaptive uncertainty and disturbance estimator (AUDE) is designed. Furthermore, a fast hyperbolic power reaching law is developed to enhance the robustness while suppressing chattering. Considering that the driving capacity of the actual double-lift overhead crane system and the driving motor torque are limited, an innovative continuous auxiliary system is designed to mitigate the effects of the input saturation while reducing overshoot from synchronization errors. Finally, the stability of the control system is analyzed using the Lyapunov stability theory, and the effectiveness and robustness of the control scheme are verified by simulation.

A Comprehensive Review on Advanced Control Methods for Floating Offshore Wind Turbine Systems above the Rated Wind Speed

This paper presents a comprehensive review of advanced control methods specifically designed for floating offshore wind turbines (FOWTs) above the rated wind speed. Focusing on primary control objectives, including power regulation at rated values, platform pitch mitigation, and structural load reduction, this paper begins by outlining the requirements and challenges inherent in FOWT control systems. It delves into the fundamental aspects of the FOWT system control framework, thereby highlighting challenges, control objectives, and conventional methods derived from bottom-fixed wind turbines. Our review then categorizes advanced control methods above the rated wind speed into three distinct approaches: model-based control, data-driven model-based control, and data-driven model-free control. Each approach is examined in terms of its specific strengths and weaknesses in practical application. The insights provided in this review contribute to a deeper understanding of the dynamic landscape of control strategies for FOWTs, thus offering guidance for researchers and practitioners in the field.

Observer-based model-free controller for the perturbations estimation and attenuation in robotic plants

The model-free controller is a powerful method because it does not require the knowledge of the robotic plant dynamic equation. Since most of the model-free controllers consider variants of the adaptive or reinforcement learning, one observer-based model-free controller could be a different alternative of interest in the researching community. In this study, an observer-based model-free controller is suggested for the perturbations estimation and attenuation in robotic plants, it contains the model-free observer and the model-free controller. The model-free observer based on the high gain method uses the bounds of the perturbations. The model-free controller based on the sliding mode method uses the bounds of the perturbations and gravity terms. The observer-based model-free controller is applied for the perturbations estimation and attenuation in a cylindrical robotic plant, and a scalar robotic plant.

Optimal bipartite consensus control for heterogeneous unknown multi-agent systems via reinforcement learning

This study focuses on addressing optimal bipartite consensus control (OBCC) problems in heterogeneous multi-agent systems (MASs) without relying on the agents' dynamics. Motivated by the need for model-free and optimal consensus control in complex MASs, a novel distributed scheme utilizing reinforcement learning (RL) is proposed to overcome these challenges. The MAS network is randomly partitioned into sub-networks where agents collaborate within each subgroup to attain tracking control and ensure convergence of positions and speeds to a common value. However, agents from distinct subgroups compete to achieve diverse tracking objectives. Furthermore, the heterogeneous MASs considered have unknown first and second-order dynamics, adding to the complexity of the problem. To address the OBCC issue, the policy iteration (PI) algorithm is used to acquire solutions for discrete-time Hamilton-Jacobi-Bellman (HJB) equations while implementing a data-driven actor-critic neural network (ACNN) framework. Ultimately, the accuracy of our proposed approach is confirmed through the presentation of numerical simulations.

A gradient-descent iterative learning control algorithm for a non-linear system

Original iterative learning control (OILC) has been proved a powerful tool in dealing with the model-free control problems by repetitively corrections based on the control error. However, the steady-state error under widely-used proportional-type original iterative learning control (P-type OILC) is highly corresponded to the proportional learning gain, making the algorithm parameter-determined. Therefore, a new gradient-descent iterative learning control (GDILC) algorithm is proposed to achieve a parameter-free approach by simulating the gradient-descent process. First, GDILC problem is formulated mathematically. Next, the idea of the algorithm is proposed, the analyses of the convergence and the steady-state error are conducted and the algorithm is implemented. GDILC will generate a random correction with a gradient-descent upper bound, rather than a correction proportional to the error in P-type OILC. Finally, illustrative and application simulations are conducted to validate the algorithm. Results show that the algorithm will be convergent after adequate iterations under proper corrections. The steady-state error will be less affected by the algorithm parameters under GDILC than that under OILC.

Model-free control of a magnetically supported plate

Established model-based methods often use a combination of state feedback and observer to control complex systems. They rely on detailed mathematical models that are often hard to derive. Nonetheless, such methods may achieve a high level of accuracy, which justifies the cumbersome modelling. An alternative approach is model-free control, in a form introduced by Fliess and Join, where the system is approximated in a short time interval by a low-order differential equation with unknown parts, a so-called ultra-local model. This control method is a powerful tool, but the parametrisation and the concrete implementation may require time, effort, and experience. The present paper investigates the systematic tuning of a model-free controller for a magnetically supported plate that is modelled as an unstable multiple-input multiple-output system. Furthermore, the incorporation of model information into the model-free controller is investigated. These adaptations ultimately improve results by simplifying parameter tuning and interpretation of estimates. Several experiments are carried out on a test bed to show the capabilities of the proposed algorithms for set point stabilisation and trajectory tracking. The effects of the different parameters in the model-free controllers are addressed, and excellent robustness with respect to actuator faults is demonstrated. Filters for estimating derivatives and unknown quantities are designed using an open-source toolbox.

Adaptive model-free fault-tolerant control for autonomous underwater vehicles subject to actuator failure

Adaptive model-free fault-tolerant control for autonomous underwater vehicles subject to actuator failure

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.

Model-Free Predictive Current Controller for Voltage Source Inverters Using ARX Model and Recursive Least Squares

Model-Free Predictive Current Controller for Voltage Source Inverters Using ARX Model and Recursive Least Squares

Adaptive Ultralocalized Time-Series for Improved Model-Free Predictive Current Control on PMSM Drives

Adaptive Ultralocalized Time-Series for Improved Model-Free Predictive Current Control on PMSM Drives

Model-Free Formation Control: Multi-Input Iterative Learning Super-Twisting Approach

Model-Free Formation Control: Multi-Input Iterative Learning Super-Twisting Approach

Curiosity model policy optimization for robotic manipulator tracking control with input saturation in uncertain environment.

In uncertain environments with robot input saturation, both model-based reinforcement learning (MBRL) and traditional controllers struggle to perform control tasks optimally. In this study, an algorithmic framework of Curiosity Model Policy Optimization (CMPO) is proposed by combining curiosity and model-based approach, where tracking errors are reduced via training agents on control gains for traditional model-free controllers. To begin with, a metric for judging positive and negative curiosity is proposed. Constrained optimization is employed to update the curiosity ratio, which improves the efficiency of agent training. Next, the novelty distance buffer ratio is defined to reduce bias between the environment and the model. Finally, CMPO is simulated with traditional controllers and baseline MBRL algorithms in the robotic environment designed with non-linear rewards. The experimental results illustrate that the algorithm achieves superior tracking performance and generalization capabilities.

Ultralocal Model-Free Adaptive Supertwisting Nonsingular Terminal Sliding Mode Control for Magnetic Levitation System

The magnetic levitation technology has attracted blooming attention from all walks of life thanks to its superiorities such as non-contact and active control. While the intrinsic features of open-loop instability and strong nonlinearity, along with the uncertain external disturbance make the levitation control particularly significant and difficult. For speeding up the convergence and obtaining a better stability and disturbance robustness, this paper proposes an ultra-local model-free adaptive super-twisting nonsingular terminal sliding mode control (ULMF-ASTNTSMC) strategy for the magnetic levitation system. Different from the conventional model-based control, ultra-local model-free control breaks the constraint of a precise system model. Therefore, an improved second-order ultra-local model is established for the magnetic levitation system. For the benefit of finite time convergence and non-singularity, the nonsingular terminal sliding mode surface is chosen. As a second-order algorithm, super-twisting (ST) algorithm can fundamentally suppress the chattering effect of the sliding mode control (SMC). An adaptive super-twisting algorithm is designed for the further improvement of the system dynamic response. The stability of the proposed scheme is strictly verified based on the Lyapunov stability theory. Simulation and experimental comparisons with the existing control methods validate the exceeding performance of the proposed strategy under various operating conditions.