Compact Form Dynamic Linearization Based Model-Free Adaptive Control for Magnetic Suspension Active Vibration Isolation System

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.

The complicated physical and chemical reactions in the internal complex operating environment of smelting process and the Blast Furnace (BF) have led to the difficulty of establishing the model-based controllers. Therefore, model free control methods should be used that meet the actual needs of the engineering systems. However, due to the sparse characteristic of the molten iron quality (MIQ) data in BF ironmaking, traditional model free adaptive control based MIQ control methods cannot control such a complex industrial system with strong nonlinear time-varying dynamics. In this paper, an extended and compact form dynamic linearization (CFDL) based model free adaptive predictive control (MFAPC) scheme (CFDL-MFAPC) is proposed for multivariate MIQ indices by generalizing the CFDL-MFAPC method only for SISO system to MIMO system. Two groups of verification experiments are performed to evaluate the performance of the controller. The results show that the proposed method has not only a better control performance than the compared traditional CFDL based model free adaptive control method and data-driven model predictive control (MPC) method, but also can guarantee the bounded-input bounded-output stability of the MIQ output of the control system for BF ironmaking process.

Model-Free Control Design for Nonlinear Mechanical Systems

In this paper, the current application status of gas turbine control technology is introduced, it presents the model free control theory and method in perspective of definition of model free control and model free adaptive control algorithms mainly existed and its advantages. This paper introduces some unsolved problems by using traditional control approaches. It gives reasons why the model free is suitable for the control of gas turbine. Afterwards, it describes how the model free adaptive control technology is applied to gas turbine and its related techniques in detail in this paper. In this part, it could provide theoretical foundation for applying model free control in actual gas turbine control system. Finally, conclusions and issues needed further research are put forward at the end of this paper.

In order to solve the dynamic modeling and parameter identification problems of unmanned vehicles trajectory tracking control, a mathematical model of unmanned vehicle trajectory tracking is designed based on the data-driven model-free adaptive control method, which does not depend on the precise dynamic model of the unmanned vehicle. The model-free adaptive control method is extended to the unmanned vehicle trajectory tracking control, and the model-free controller is designed and applied to the driverless vehicle trajectory tracking control. Aiming at the problem that the general compact form dynamic linearization model-free adaptive control (CFDL-MFAC) algorithm cannot converge in vehicle trajectory tracking control, combined with the dynamic characteristics of unmanned vehicles, an improved model-free adaptive control algorithm is proposed in this paper. The simulation results verify the effectiveness and feasibility of the algorithm. Mathematical simulation results show that the improved model-free adaptive algorithm of the designed unmanned vehicle is effective and can effectively implement the trajectory tracking control of the unmanned vehicle. At the same time, the design of the controller does not depend on the kinematics and dynamics models of the unmanned vehicle, and it has high control accuracy.

This book categorizes the wide area of data-driven model-free controllers, reveals the exact benefits of such controllers, gives the in-depth theory and mathematical proofs behind them, and finally discusses their applications. Each chapter includes a section for presenting the theory and mathematical definitions of one of the above mentioned algorithms. The second section of each chapter is dedicated to the examples and applications of the corresponding control algorithms in practical engineering problems. This book proposes to avoid complex mathematical equations, being generic as it includes several types of data-driven model-free controllers, such as Iterative Feedback Tuning controllers, Model-Free Controllers (intelligent PID controllers), Model-Free Adaptive Controllers, model-free sliding mode controllers, hybrid model‐free and model‐free adaptive‐Virtual Reference Feedback Tuning controllers, hybrid model-free and model-free adaptive fuzzy controllers and cooperative model-free controllers. The book includes the topic of optimal model-free controllers, as well. The optimal tuning of model-free controllers is treated in the chapters that deal with Iterative Feedback Tuning and Virtual Reference Feedback Tuning. Moreover, the extension of some model-free control algorithms to the consensus and formation-tracking problem of multi-agent dynamic systems is provided. This book can be considered as a textbook for undergraduate and postgraduate students, as well as a professional reference for industrial and academic researchers, attracting the readers from both industry and academia.

Hydrometallurgy technology can directly deal with low grade and complex materials, improve the comprehensive utilization rate of resources, and effectively adapt to the demand of low carbon and cleaner production. A series of cascade continuous stirred tank reactors are usually applied in the gold leaching industrial process. The equations of leaching process mechanism model are mainly composed of gold conservation, cyanide ion conservation, and kinetic reaction rate equations. The derivation of the theoretical model involves many unknown parameters and some ideal assumptions, which leads to difficulty and imprecision in establishing the accurate mechanism model of the leaching process. Imprecise mechanism models limit the application of model-based control algorithms in the leaching process. Due to the constraints and limitations of the input variables in the cascade leaching process, a novel model-free adaptive control algorithm based on compact form dynamic linearization with integration (ICFDL-MFAC) control factor is first constructed. The constraints between input variables is realized by setting the initial value of the input to the pseudo-gradient and the weight of the integral coefficient. The proposed pure data-driven ICFDL-MFAC algorithm has anti-integral saturation ability and can achieve faster control rate and higher control precision. This control strategy can effectively improve the utilization efficiency of sodium cyanide and reduce environmental pollution. The consistent stability of the proposed control algorithm is also analyzed and proved. Compared with the existing model-free control algorithms, the merit and practicability of the control algorithm are verified by the practical leaching industrial process test. The proposed model-free control strategy has advantages of strong adaptive ability, robustness, and practicability. The MFAC algorithm can also be easily applied to control the multi-input multi-output of other industrial processes.

Control technology for wheeled mobile robots is one of the core focuses in the current field of robotics research. Within this domain, model-free adaptive control (MFAC) methods, with their advanced data-driven strategies, have garnered widespread attention. The unique characteristic of these methods is their ability to operate without relying on prior model information of the control system, which showcases their exceptional capability in ensuring closed-loop system stability. This paper extensively details three dynamic linearization techniques of MFAC: compact form dynamic linearization, partial form dynamic linearization and full form dynamic linearization. These techniques lay a solid theoretical foundation for MFAC. Subsequently, the article delves into some advanced MFAC schemes, such as dynamic event-triggered MFAC and iterative learning MFAC. These schemes further enhance the efficiency and intelligence level of control systems. In the concluding section, the paper briefly discusses the future development potential and possible research directions of MFAC, aiming to offer references and insights for future innovations in control technology for wheeled mobile robots.

As an excellent Vibration absorption technology, magnetic suspension vibration isolation technology has many advantages, for instance, no abrade, small time delay, and not easy to lose effectiveness. A magnetic suspension isolator (MSVI) is designed for a passive vibration isolation system with complex excitation, and it is added to the original system to become an active vibration isolation system. for purpose of solve the problem of inaccurate modeling caused by the hysteretic behavior of MSVI, a hybrid training method based on artificial neural network (ANN) is proposed to improve the accuracy of the model. Based on the optimized model, an LQR control model is proposed. The objective function of the control model is to minimize the sum of the weighted squares of the forces. In order to realize optimal control of LQR model, the values of Q matrices and R matrices can be obtained through multi-population genetic algorithm (MPGA). The control model is simulated under different types of excitations such as sinusoidal, sweep, random and impulse signal. By comparing the simulation data of the system without control and after control, it is proved that the system using the control method in this paper has better vibration reduction effect.

In this paper, we use recursive least squares method for magnetic single layer vibration isolation system identification to get the system transfer function matrix. By considering the fitting degree, pole-zero, the step response to adjust the order of model and noise structure for optimizing the model Identification. Applying the system transfer function matrix to the magnetic active vibration control system to improve the isolation effect. The results showed that: significantly improved isolation effect, verify the validity of this identification model for magnetic single isolation system.

In this paper, the performance of three model-free control approaches on a multi-input, multi-output (MIMO) nonlinear system with constant and time-varying references is compared. The first control algorithm is model-free adaptive control (MFAC). The second is a modified version of MFAC (MMFAC) designed to handle delays in the system by incorporating the output error difference (over two sample time steps) in the control input. The third approach, model-free adaptive predictive control (MFAPC) with a one-step-ahead forecast of the system input, is obtained by using predictions of the outputs based on the data-based linear model. The experimental device used is an MIMO three-tank system (3TS) assumed to be an interconnected system with multiple coupled single-input, single-output (SISO) subsystems with unmeasurable couplings. The novelty of this contribution is that each coupled SISO partition is assumed to be controlled independently using a decoupled control algorithm, leading to fewer control parameters compared to a centralized MIMO controller. Additionally, both parameter tuning for each controller and performance evaluation are conducted using an evaluation criterion considering energy consumption and accumulated tracking error. The results demonstrate that almost all the proposed model-free controllers effectively control an MIMO system by controlling its SISO subsystems individually. Moreover, the predictive features in the decoupled MFAPC contribute to more accurate tracking of time-varying references. The utilization of tracking error differences helps in reducing energy consumption.

Magnetic suspended vibration isolator was designed and applied to multi-degree of freedom vibration isolation system. Stiffness and damping of magnetic suspended vibration isolator based on stiffness control was deduced. The operating condition of magnetic suspended vibration system was analyzed and mathematic model was constructed. The mathematic model of base motion was incorporated into the theoretical model and simulation model of the magnetic suspended vibration isolator. The stiffness and damping of the whole vibration-isolating system are varied by the way of adjusting the stiffness and damping of the magnetic suspension isolator. Force transmissibility, input force, and output force response of magnetic suspended vibration isolation system, respectively under chirp exciting signal and dual-frequency exciting signal were simulated. The simulation results indicate that the floating raft isolation system under active fuzzy controller can remarkably suppress vibration in the wide range of frequency and is remarkably better than those of passive isolation.

Low-frequency vertical vibration isolation systems play important roles in precision measurements to reduce seismic and environmental vibration noise. Several types of active vibration isolation systems have been developed. However, few researches focus on how to optimize the test mass install position in order to improve the vibration transmissibility. An active low-frequency vertical vibration isolation system based on an earlier instrument, the Super Spring, is designed and implemented. The system, which is simple and compact, consists of two stages: a parallelogram-shaped linkage to ensure vertical motion, and a simple spring-mass system. The theoretical analysis of the vibration isolation system is presented, including terms erroneously ignored before. By carefully choosing the mechanical parameters according to the above analysis and using feedback control, the resonance frequency of the system is reduced from 2.3 to 0.03 Hz, a reduction by a factor of more than 75. The vibration isolation system is installed as an inertial reference in an absolute gravimeter, where it improved the scatter of the absolute gravity values by a factor of 5. The experimental results verifies the improved performance of the isolation system, making it particularly suitable for precision experiments. The improved vertical vibration isolation system can be used as a prototype for designing high-performance active vertical isolation systems. An improved theoretical model of this active vibration isolation system with beam-pivot configuration is proposed, providing fundamental guidelines for vibration isolator design and assembling.

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.

In this paper, the model-free adaptive control (MFAC) method which is based on compact form dynamic linearization (CFDL) of multiple input and multiple output (MIMO) nonlinear systems is applied to the control of Puma560 manipulator. The controller design requires only the input and output data of the system. The simulation results verify the effectiveness of the model-free adaptive control method. Based on the structure of the controller, the function of controller parameters is analysed. By adding external disturbances, the anti-interference of Puma560 based on model-free adaptive control can be verified. The model free adaptive controller is optimized.