On Model-Free Adaptive Control and Its Stability Analysis

This study investigates the design of an automatic carrier landing system that takes into account nonlinearity, internal parameter uncertainty, and external disturbance. The flight controller design utilises a modified data-driven model-free adaptive control (MFAC) by considering the changing rate of the tracking error in the controller. The MFAC system is implemented in the angular rate control subsystem, using the virtual equivalent dynamic linearization data model and the time-varying pseudo-partial derivative (PPD) estimate method. These algorithms are developed solely based on the input/output measurements of the carrier-based aircraft. The adaptive estimation method enhances the robustness to internal parameter uncertainty and external disturbance. The simulation results convincingly demonstrate the efficacy of the suggested controller in the automatic carrier landing system.

Data-driven model-free adaptive attitude control of partially constrained combined spacecraft with external disturbances and input saturation

This paper presents a new control scheme for an omnidirectional mobile manipulator (OMM) combining model free adaptive control (MFAC) with neural network. The proposed control approach only uses input-output (I/O) data and can achieve effective trajectory tracking and excellent robust performance. Firstly, a dynamic linearization data model is derived for OMM based on pseudo-partial derivative (PPD), using I/O data. Then a radial basis function neural network (RBFNN) is applied to approximate uncertainties and estimation errors of PPD in the data model. In particular, the weights of RBFNN are updated by concurrent learning. Since concurrent learning uses current data and rich historical stack data concurrently for adaptation, parameter convergence can be achieved without persistence of excitation condition. Moreover, in order to improve the convergence rate of MFAC, proportional-derivative feedback is incorporated into the typical MFAC design. Finally, extensive simulations are conducted to verify the effectiveness and robustness of the proposed control design.

Model-Free Control Design for Nonlinear Mechanical Systems

Aiming at the robustness issue in high-speed trains (HSTs) operation control, this article proposes a model-free adaptive control (MFAC) scheme to suppress disturbance. Firstly, the dynamic linearization data model of train system under the action of measurement disturbance is given, and the Kalman filter (KF) based on this model is derived under the minimum variance estimation criterion. Then, according to the KF, an anti-interference MFAC scheme is designed. This scheme only needs the input and output data of the controlled system to realize the MFAC of the train under strong disturbance. Finally, the simulation experiment of CRH380A HSTs is carried out and compared with the traditional MFAC and the MFAC with attenuation factor. The proposed control algorithm can effectively suppress the measurement disturbance, and obtain smaller tracking error and larger signal to noise ratio with better applicability.

For launch vehicles, many traditional control methods are facing the challenge of modeling due to various perturbations and large-scale change of structural parameters existed during the launching process. With the features of simple structure and adaptive tracking, Model-free Adaptive Control (MFAC), as one of the data-driven control methods, is firstly used to design the attitude controller with the restrictions on control inputs for a launch vehicle in this paper. By virtue of the virtual dynamic linearization data model of the launch vehicle, the attitude controller can be designed just depending on the input-output data of the launch vehicle without requirement of any physical model. Simulation is conducted to demonstrate the effectiveness and robustness of MFAC method by comparing with PID method under the circumstance with the engine failures.

In control theory, traditional methods are basically relied on the mathematical model of a plant to design suitable control schemes. First, the model has to be successfully developed which reflects precisely the system dynamic behaviors within certain operating conditions. Theoretically, based on the true assumed plant model, the controller design and system stability analysis can be carried out. On the other hand, since the last few decades an alternative control strategy, which only utilizes the available input-output information from the closed-loop system to analyze and design controllers, has been proposed. This novel data-driven or model-free control method can reduce efforts spending on the system modeling tasks. In addition, by using directly the updated system data the unknown time-varying parameters of the given system/process and design controller are estimated and corrected continuously at each operating point. These updated parameters are necessary to determine the required control input energy. In this thesis, a recently developed data-driven control method called model-free adaptive control (MFAC) will be intensively investigated to acquire further control performance improvements by applying the method to the field of vibration reduction. The main principle of MFAC is replacement of the unknown complicated dynamical characteristics of the initial (nonlinear) system by an equivalent linearized model based on the on-line updated system input-output data. Hence, the assumed system model is built up at each discrete-time instant during the system operation. To design control, the identified parameters from the local dynamic model should be utilized explicitly. This research will develop different modified/improved MFAC strategies which can be effectively applied to a class of complex mechanical systems for vibration reduction purpose. Traditional MFAC often uses conventional projection algorithm to estimate and update the unknown system parameters of the linearized data model. To improve on-line estimation accuracy, in this thesis, recursive least-squares algorithm (RLSA) will be applied. Furthermore, the tracking control performance of MFAC can be improved by minimizing not only the current output error amplitudes, but also the error variations within a fixed-length of time window from the past. As a result, a modified control input law will be generated. In addition, compact-form dynamic linearization (CFDL) has been considered in MFAC design as a simplified technique for system linearization. In this work, the CFDL concept will be applied not only to the unknown (nonlinear) plant but also to an assumed nonlinear controller. Subsequently, a linearized controller structure is derived, in which a matrix of unknown controller parameters needs to be estimated. By proposing a modified objective function of the controller parameter matrix, an improved estimation algorithm for updating these parameters on-line is introduced. Moreover, based on the fundamentals of MFAC and generalized model predictive control, modified model-free adaptive predictive control programs are proposed, in which RLSA and its modification can be implemented for parameter estimation instead of using traditional projection algorithm. Another dynamic linearization technique called partial-form dynamic linearization (PFDL) is implemented to the MFAC design for multivariable systems. In this contribution, an improved PFDL-based data-driven control strategy will be developed. A partial-form data model of the original system is constructed locally which contains a set of unknown parameter matrices namely pseudo-jacobian matrix. These matrices are recursively updated by using the measured system input-output signals. In addition to known approaches, in this study, on-line parameter estimation based on the recursive least-squares method is applied to the PFDL model. For control realization, a modified PFDL-based control input equation is proposed by considering minimization of the tracking error differences. To verify control effectiveness, the proposed controllers will be executed to reduce the free-vibrations of an elastic ship-mounted crane due to the non-zero initial excitation of the payload. The crane is represented as a typical complex and flexible system, in which the in-plane oscillations of the elastic boom and the payload must be reduced or eliminated to increase the crane safety operation. Simulation results demonstrate that, the angular displacements of the output signals as well as the payload are reduced significantly within a short length of time by using the modified model-free controllers. Additionally, the proposed MFAC programs work effectively and better control results are obtained when varying several design controller parameters in comparison with conventional methods.

A data-driven distributed formation control algorithm is proposed for an unknown heterogeneous non-affine nonlinear discrete-time MIMO multi-agent system (MAS) with sensor fault. For the considered unknown MAS, the dynamic linearization technique in model-free adaptive control (MFAC) theory is used to transform the unknown MAS into an equivalent virtual dynamic linearization data model. Then using the virtual data model, the structure of the distributed model-free adaptive controller is constructed. For the incorrect signal measurements due to the sensor fault, the radial basis function neural network (RBFNN) is first trained for the MAS under the fault-free case, then using the outputs of the well-trained RBFNN and the actual outputs of MAS under sensor fault case, the estimation laws of the unknown fault and system parameters in the virtual data model are designed with only the measured input-output (I/O) data information. Finally, the boundedness of the formation error is analyzed by the contraction mapping method and mathematical induction method. The effectiveness of the proposed algorithm is illustrated by simulation examples.

The frequency response model of the microgrid (MG) is necessary for the design of the controller when performing secondary frequency control. However, due to such factors as the widespread application of commercial power sources, it is difficult to obtain micro-source models, which naturally increases the difficulty of controller design through mechanism modeling methods. Therefore, this paper proposes a secondary frequency control strategy for islanded MG based on model-free adaptive control (MFAC). Firstly, the problem of secondary frequency control is transformed into the target frequency tracking problem. Then, the model-free adaptive control algorithm and pseudo partial derivative (PDD) estimation and reset algorithm are designed based on the dynamic linear data model of the control system. Further, the regulation of the frequency is realized. This method is independent of the mathematic model of MG and only needs to use the input and output data during the operation of the MG without complex controller parameter tuning. It also has strong adaptability and portability for different MGs. Simulation results verify the effectiveness of the proposed scheme.

The flexible integrated joint (FIJ) is a key part of the collaborative robots, which has the characteristics of lightweight and highly integration. The force control is pivotal for achieving compliant interactions with environments and humans, such as impendence control and force tracking control. However, the controller design for force control of the flexible joint is a challenging issue with unmodeled uncertainties, nonlinear friction, time-varying load and other disturbances forced by environments in general. In this paper, a control scheme based on model-free adaptive control (MFAC) was developed for the force control of the FIJ. First, the model of the FIJ was transformed into a virtual dynamic linearization data model by a dynamic linearization approach. Second, a MFAC algorithm was designed for force control of the FIJ, including its corresponding pseudo gradient estimating algorithm and pseudo gradient resetting algorithm. To evaluate the performance of the proposed method, the experiments including zero force tracking and step force tracking were carried out in this research. The experimental results show that the developed control approach can get a high performance as the dynamical parameters of the FIJ are time-varying and uncertain.

In this article, a model-free adaptive control (MFAC) algorithm based on full form dynamic linearization (FFDL) data model is presented for a class of unknown multi-input multi-output (MIMO) nonaffine nonlinear discrete-time learning systems. A virtual equivalent data model in the input-output sense to the considered plant is established first by using the FFDL technology. Then, using the obtained data model, a data-driven MFAC algorithm is designed merely using the inputs and outputs data of the closed-loop learning system. The theoretical analysis of the monotonic convergence of the tracking error dynamics, the bounded-input bounded-output (BIBO) stability, and the internal stability of the closed-loop learning system is rigorously proved by the contraction mapping principle. The effectiveness of the proposed control algorithm is verified by a simulation and a quad-rotor aircraft experimental system.

Modeling a launch vehicle dynamics accurately is time-consuming since its dynamics is very complex with high nonlinearity, when considering the influence of load variation and other related factors. Model-free adaptive control (MFAC), as a data-driven control method, has been widely used because of its simple controller structure, low-computational burden, and easy implementation. In this paper, a data-driven attitude improved model-free adaptive control (iMFAC) is first applied for a launch vehicle. First, a controller is designed for the launch vehicle by utilizing the MFAC. Then, the initial values of the pseudo gradient (PG) and the reset values of the PG in the designed controller are optimized under the virtual reference feedback tuning (VRFT) framework through the equivalent relationship between the MFAC and the VRFT in controller structure. Finally, the effectiveness and robustness of the applied iMFAC are verified through qualitative and quantitative analysis compared to the MFAC and PID.

Aiming at the problem of poor speed tracking performance in the podded propulsion motor speed control system due to load disturbances, a model-free adaptive iterative learning control (MFAILC) scheme is put forward. Firstly, the mathematical model of a six-phase permanent magnet synchronous motor is built and the expression of propeller load is given. Then the speed equation of the motor is discretized to obtain the dynamic linearization model. Based on the model, a model-free adaptive controller is designed and a pseudo partial derivative (PPD) estimation algorithm is given. Finally, the improved speed controller based on MF AILC is implemented and simulated. According to the simulation results, the proposed algorithm has faster convergence speed, less overshooting, and greater robustness compared with traditional PI control method.

A model free adaptive iterative learning control based fault-tolerant control (MFAILC-FTC) scheme for subway train speed tracking with speed sensor fault and over-speed protection is proposed. Firstly, the train dynamics is transformed into a compact form dynamic linearization (CFDL) data model by applying the concept of pseudo-partial derivative (PPD). If speed sensor fault occurs, the fault function is approximated by the trained RBFNNs under normal condition and the output data of the train system with fault, which serves as a compensation for the proposed MFAILC-FTC scheme. Then, over-speed protection mechanism is developed to ensure that the train operates within safe speed range. Furthermore, the constraint on traction/braking force is also taken into account. Through rigorous mathematical analysis, it is proved that the proposed MFAILC-FTC method with over-speed protection mechanism can ensure the train speed tracking error converges along the iteration axis, which implies the train operates safely and reliably. Finally, the simulation results further demonstrate the effectiveness of the proposed algorithm. <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">Note to Practitioners</i> —Subway train as a practical engineering system with short distance between two stations, starts and stops frequently, has the outstanding repetitive operation pattern, and it is unavoidable subject to speed sensor fault, aerodynamic issues, constraint on output speed and traction/braking force. Nevertheless, few works have considered these factors simultaneously, and a lot of data contain valuable operation information are generated during the train operation, this motives the work of this note. On account of the repetitive operation features of subway trains, the control schemes of speed trajectory tracking are handled under MFAILC framework, which is a pure data-driven model free control methodology. By constructing the RBFNNs-based fault function estimation mechanism, a robust compensation term is designed in the fault-tolerant controller. Taking the safe operation of subway trains into account, an over-speed protection term with trigger mechanism is added to the fault-tolerant controller. To further enhance the application, the constraint on traction/braking force is addressed as well. Without requirement of the train dynamics model, the theoretical analyses and simulation results have confirmed the effectiveness and the feasibility of the proposed data-driven control approach. In the future work, we will focus on verifying the proposed control strategy and addressing some other practical problems, for instance, the energy-efficiency and exogenous disturbances during the train operation.

pH neutralization reaction process plays a crucial role in Waste Water Treatment Process (WWTP). Traditional PID Proportion Integral Differential, (or even advanced PID control) algorithms have poor performance on WWTP due to the strong non-linearity, large time lag, and large inertia characteristics of pH neutralization. Therefore, finding a superior control method to maintain the pH value of wastewater within the normal range will greatly help to improve the efficiency and effectiveness of wastewater treatment. The chemical reaction mechanism of pH neutralization reaction process is first analyzed, and a mechanistic model of pH neutralization reaction process is developed based on the reaction of ions during acid-alkali neutralization and the electric balance equation. Then, combining the characteristics of generalized predictive control and Model-Free Adaptive Control (MFAC), a Model-Free Adaptive Predictive Control (MFAPC) method based on compact format dynamic linearization is introduced. An Improved Model Free Adaptive PI Predictive Control algorithm (IMFAPC) with proportional (P) and integral (I) algorithms is proposed to further improve the control performance. IMFAPC is proposed on the basis of MFAPC, combining the advantages of generalized predictive control, introducing a PI module consisting of error and error sum, and predicting the PI module, making it possible to produce more accurate constraints on the control inputs, avoiding increasing errors, and improving the control effect of delayed systems at the same time. pH neutralization process simulation experimental results show that compared with the ordinary Model-Free Adaptive Control (MFAC) and MFAPC, the IMFAPC control algorithms has the best performance in terms of accuracy, overshoot, and the robustness.