Robust Control Of Nonlinear Systems Research Articles

Sliding Mode Control Based on Jaya Algorithm of Phase Shift for Two-Rotor Vibration Unit

In this paper, a sliding mode control based on the Jaya algorithm o f phase shift for a two-rotor vibration unit is presented. A two-rotor vibration unit is a highly nonlinear system that has many applications in practical systems. The control problem for this model is to design controllers to ensure phase shift according to the desired value and synchronize the speed of the two rotors. To solve this problem, the authors use the PI controllers for synchronizing the speed of the two rotors and the sliding mode controller for the phase shift. PI control is an effective method to design controllers for practical systems. Besides, Sliding Mode Control (SMC) is one of the most effective methods for designing robust controllers for nonlinear systems affected by external disturbances. However, defining the coefficients of PI controllers and sliding mode controllers is the challenge for researchers. In this study, the Jaya algorithm is used to find the coefficients of these controllers that guarantee the desired phase shift of two rotors, the synchronizing speed of two rotors, and the limitation of control laws. The simulation results are illustrated to show the effectiveness of the proposed method.

Optimal Robust Control of Nonlinear Systems with Unknown Dynamics via NN Learning with Relaxed Excitation.

This paper presents an adaptive learning structure based on neural networks (NNs) to solve the optimal robust control problem for nonlinear continuous-time systems with unknown dynamics and disturbances. First, a system identifier is introduced to approximate the unknown system matrices and disturbances with the help of NNs and parameter estimation techniques. To obtain the optimal solution of the optimal robust control problem, a critic learning control structure is proposed to compute the approximate controller. Unlike existing identifier-critic NNs learning control methods, novel adaptive tuning laws based on Kreisselmeier's regressor extension and mixing technique are designed to estimate the unknown parameters of the two NNs under relaxed persistence of excitation conditions. Furthermore, theoretical analysis is also given to prove the significant relaxation of the proposed convergence conditions. Finally, effectiveness of the proposed learning approach is demonstrated via a simulation study.

Safe optimal robust control of nonlinear systems with asymmetric input constraints using reinforcement learning

Safe optimal robust control of nonlinear systems with asymmetric input constraints using reinforcement learning

Fixed‐time fuzzy adaptive robust H∞ control for nonstrict‐feedback nonlinear systems with input saturation and output constraints

SummaryThis paper focuses on the design of fixed‐time fuzzy adaptive robust control of nonlinear systems in a nonstrict‐feedback form that includes output constraints, input saturation, and external disturbance. Fuzzy systems have been utilized to deal with uncertainties and non‐linearity in the system dynamic model. By introducing novel control and adaptive rules, there is no need to approximate the input saturation function with the hyperbolic tangent function. A Barrier Lyapunov Function (BLF) ensures that systems outputs do not violate the defined constraints. By combining the backstepping and BLF method, asymptotic convergence of tracking error signal to zero in fixed‐time is proved. At the same time, index is also met in dealing with the disturbance effects. Finally, the simulation results of the proposed control method in two examples confirm its effectiveness.

Observer-based finite-time robust control for nonlinear systems with different power Hamiltonian functions

This work uses the Hamiltonian function approach to investigate the observer-based finite-time robust control problem of a broad nonlinear system and presents various new results. To begin, the Hamiltonian technique is used to convert the original system to its equivalent form, and then the observer system is designed. Afterward, utilizing the technology and the Lyapunov method, we investigate the finite-time control issue and give several finite-time stabilization results based on the observer method. Finally, a real unmanned vehicle is used to verify the performance of the observer-based finite-time robust stabilization controller. Different from the existing literature on the Hamiltonian method, the Hamiltonian function in this article has different powers, which implies that the results developed in this article have a wider range of application.

A composite adaptive robust control for nonlinear systems with model uncertainties

AbstractThis article is concerned with a composite adaptive robust control (CARC) for non‐strict feedback nonlinear systems with model uncertainties including parametric uncertainties and uncertain nonlinearities. It is assumed that the model uncertainties of the nonlinear system are bounded but unknown. Firstly, prescribed tracking performance is achieved by the CARC control law even the unknown parameters are time‐varying. This is accomplished firstly by designing a discontinuous projection that confines the unknown parameters in an estimated region. Then the robustness of the closed‐loop system is guaranteed by leveraging the deterministic robust control philosophy. Also, a command filter has been designed to avoid computing complex derivatives of virtual control law in the backstepping procedure. Secondly, a composite adaptation law that intelligently integrates information of both tracking error and prediction error is constructed for improving the performance of controllers. The high adaptation gain of CARC leads to higher parameter convergence speed and smaller tracking errors. Moreover, if the actual parameters are within the design range, asymptotic stability can be achieved in presence of parametric uncertainties only. In addition, exponential convergence of tracking errors and parameters can be shown under certain conditions. Finally, numerical examples are made to validate the superiority and effectiveness of the proposed control scheme.

Fault tolerance evaluation of model-free controllers with application to unmanned aerial vehicles

Although important improvements in the area of robust control of nonlinear systems have been presented in the literature, most of the developed controllers suffer from complexity and large dependency on accurate mathematical formulation of the models. Recently, model-free robust control techniques were introduced and have shown good performance when applied to multi-input–multi-output systems. The model-free approach is characterized by the nonuse of any prior knowledge about the underlying structure and/or associated parameters of the dynamical system. Therefore, the major criteria for assessing the effectiveness of these controllers are related to their ability to handle unknown inputs and disturbances, as well as achieving the desired tracking performance in presence of faults and malfunctions. This work considers the development of robust fault-tolerant controllers based on the model-free approach and their application to multirotor unmanned aerial vehicles’ (UAVs) systems. The different controllers based on intelligent proportional-derivative (iPD), intelligent backstepping (iBackstepping), and adaptive control are compared in terms of performance, ease of implementation and parameters tuning. The simulated results, tested on Matlab/Simulink on a full nonlinear model of a hexarotor UAV, validate the theoretical advantages of the adaptive approach with respect to multiple criteria such as improved tracking performance in case of existence of actuators faults when compared to the iPD and iBackstepping control methods at the cost of increased complexity.

The method of multi objective synthesis of nonlinear robust control by multimass electromechanical systems

Aim. Development of the method of multi objective synthesis of nonlinear robust control by multimass electromechanical systems to satisfy various requirements for the operation of multi-mass systems in various modes. Methodology. The problem of multi objective synthesis of nonlinear robust control of multimass electromechanical systems is formulated and the possibility of satisfying various requirements for the operation of such systems in various modes based on the concept of functionally multiple membership of the state vector and the solution of the Hamilton-Jacobi-Isaacs equation is shown. A method for choosing weight matrices with the help the vector of purpose of nonlinear robust control is formed by solving a zero-sum vector antagonistic game has been substantiated and developed. Results. The results multi objective synthesis of nonlinear robust two-mass electromechanical servo systems in which differences requirements for the operation of such systems in various modes were satisfied are given. Based on the results of modeling and experimental studies it is established, that with the help of synthesized robust nonlinear controllers, it is possible to improve of quality indicators of two-mass electromechanical servo system in comparison with the system with standard regulators. Originality. For the first time the method of multi objective synthesis of nonlinear robust control by multimass electromechanical systems to satisfy various requirements for the operation of multimass systems in various modes is developed. Practical value. From the point of view of the practical implementation the possibility of solving the problem of multi objective synthesis of nonlinear robust control systems to satisfy various requirements for the operation of multimass electromechanical systems in various modes is shown.

Particle Filter Design for Robust Nonlinear Control System of Uncertain Heat Exchange Process with Sensor Noise and Communication Time Delay

In this paper, a particle filter design scheme for a robust nonlinear control system of uncertain heat exchange process against noise and communication time delay is presented. The particle filter employs a cluster of particles and associated weights to approximate the posterior distribution of states and is capable of handling nonlinear and non-Gaussian issues. However, when the realistic given noise is much larger than that of the one modeled by the particle filter, the estimated posterior distribution is no longer reliable. Considering that, the exponential weights take the place of the original absolute particle weights in this paper, which act as an adjustment to the particle filter weights for a better state estimation. This adjustment for the weight of the particle filter takes into account the practical significance and can ensure the stability, tracking performance, and continuous operation of the control process incorporated with the particle filter. The simulation verifies the feasibility and usefulness of the method.

Experimental Study on Support Vector Machine-Based Early Detection for Sensor Faults and Operator-Based Robust Fault Tolerant Control

Considering sensor faults for a thermoelectric cooler actuated by Peltier devices, this work proposes an operator-based robust nonlinear fault tolerant controller (FTC) integrated with early fault detection using a support vector machine (SVM). Firstly, a physical model is formulated based on the law of heat transfer, and the estimated model is derived based on Volterra identification. Then, an operator-based robust nonlinear control system is employed to compensate for uncertainties and to eliminate the effects of coupling. Furthermore, FTC integrated with SVM-based early fault detection is designed to improve the safety performance in the case of sensor faults. The simulation results indicate that SVM-based fault detection can shorten the detection time in comparison to the conventional method without the SVM classier. The experiment results are utilized to verify the tracking performance of the proposed FTC method in the case study.

Dynamic Performance Improvement of Doubly Fed Induction Motor Based on Hybrid Computational Technique and Variable Structure Control

The sliding mode control (SMC) methodology based on the theory of variable structure systems has been widely used for robust control of nonlinear systems. Nevertheless, this type of control has an essential inconvenience, which is the chattering phenomenon caused by the discontinuous control part. In order to reduce the effects of the chattering phenomenon, second order sliding mode (SOSM) seems to be a very attractive solution. To eliminate the remains of chattering phenomenon, a new control scheme based on fuzzy second order sliding mode control (FSOSMC) is proposed in this paper. This fuzzy second order sliding mode controller is destined to the speed control of doubly fed induction motor (DFIM) which is based on the decoupling control to enhance robustness under different operating conditions such as load torque and in the presence of parameters variation.
 The simulation results for various scenarios show the performances of the proposed control in terms of, precision, rapidity and stability for the high powers DFIM operating at variable speeds.

Robust force and displacement control of an active landing gear for vibration reduction at touchdown and during taxiing

In this paper, a new approach is proposed to control the dynamic response of a landing gear system subjected to runway force, both on heavy landing conditions and at the taxiing process. The mathematical model of the system is used in a way that covers nonlinear dynamics characteristics of landing gear and nonlinear/nonaffine property of the external actuator. The operation of the landing gear system and its components are described briefly. The desired control system includes two different interior loops for displacement and force control. The inner loop determines the actuator force and the outer loop performs the displacement control. A lumped uncertainty is considered in both displacement and force control loops that represent uncertainties including parametric errors, measurement noises, unmodeled dynamics, disturbance due to runway excitation, and other disturbances. The direct method of Lyapunov is utilized for asymptotic stability analysis of the robust nonlinear control system (RNCS). This system is simulated in MATLAB software and the performance of the proposed controller is analyzed exactly. Besides, the results are compared with a passive system and conventional PID control. The comparison indicates that RNCS works better and more precisely. This method can reduce vibrations at touchdown and taxiing and effectively overcome uncertainty and provide well aircraft handling by decreasing the changes in tire force.

Adaptive neural network control of nonlinear systems with unknown dynamics

In this study, an adaptive neural network control approach is proposed to achieve accurate and robust control of nonlinear systems with unknown dynamics, wherein the neural network is innovatively used to learn the inverse problem of system dynamics with guaranteed convergence. This study focuses on the following three contributions. First, the considered system is transformed into a multi-integrator system using an input–output linearization technique, and an extended state observation technique is used to identify the transformed states. Second, an iterative control learning algorithm is proposed to achieve the neural network training, and stability analysis is given to prove that the network’s predictions converge to ideal control inputs with guaranteed convergence. Third, an adaptive neural network controller is developed by combining the trained network and a proportional-integral controller, and the long-standing challenge of model-based methods for control determination of unknown dynamics is resolved. Simulation results of a virtual control mission and an aerospace altitude tracking mission are provided to substantiate the effectiveness of the proposed techniques and illustrate the adaptability and robustness of the proposed controller.

Direct Optimization Based Compensation Adaptive Robust Control of Nonlinear Systems With State and Input Constraints

Motion control of mechatronic system with state and input constraints while achieving excellent integrated performance, such as robustness, high tracking accuracy, fast response, and slow overshoot, has always been a challenging issue. However, most existing relating studies merely focus on how to ensure stability under constraints, and few take integrated performance into account. In this article, we proposed a direct optimization based compensation adaptive robust control (ARC) approach, which is under a two-loop feedback structure, where the outer loop directly online replans both the model compensation term and the reference that conform to the constraints; and the conventional ARC control law is synthesized in inner loop to ensure guaranteed tracking accuracy when facing nonlinearity, parametric uncertainties, and external disturbances. Motion control of a linear motor was considered through this article as an introductory example. Comparative experiments are carried out and the results further verify the superiority and effectiveness of the proposed scheme.

Command filtered robust control of nonlinear systems with full-state time-varying constraints and disturbances rejection

For the barrier Lyapunov function-based control of full-state time-varying constrained systems via the traditional backstepping technology, due to repeated differentiations of virtual control functions involving time-varying barriers, the adverse effects of “explosion of complexity” caused by the backstepping iteration are more serious, which even makes it impossible to implement for high-order systems. In order to eliminate this negative influence, we take advantage of the command filtered backstepping approach which introduces a command filter to approximate the constructed virtual control law in each procedure of the backstepping design. More importantly, the approximate errors arising from the introduced filters will be removed by constructing a series of compensating signals. Meanwhile, some relatively conservative assumptions will be released compared with existing control strategies. Furthermore, largely unknown external disturbances that may exist in the system will be estimated in real-time via high-gain disturbance observers and then compensated feedforwardly in designing the controller. Specially, the scheme of the resulting control algorithm is simple and online computation time is saved. Finally, the stability of the whole closed-loop system and the control performance is strictly certificated, respectively.

Plasma magnetic time-varying nonlinear robust control system for the Globus-M/M2 tokamak

This paper is devoted to the development of the magnetic plasma control system for the Globus-M/M2 spherical tokamak (ST) when minor disruptions occur. The novelty of the research is the design of robust cascade multivariable control systems for time-varying plasma models in the presence of nonlinear thyristor current inverters as actuators for plasma position control. A new architecture of coordinated control of plasma position and shape is proposed. Quantitative Feedback Theory is used for the synthesis of robust Single-Input Single-Output (SISO) controllers for plasma position and PF-currents. Multiple-Input Multiple-Output (MIMO) H∞ control is applied to control the plasma shape. The simulation results of the gaps-based MIMO plasma shape control system with the plasma equilibrium reconstruction code in the feedback are shown. The robust stability of the control system is estimated.

Adaptive dynamic programming based robust control of nonlinear systems with unmatched uncertainties

This paper proposes a new approach to address robust control design for nonlinear continuous-time systems with unmatched uncertainties. First, we transform the robust control problem into an equivalent optimal control problem, which allows to simplify the control design. A critic neural network (NN) is then adopted to reformulate the derived Hamilton–Jacobi–Bellman (HJB) equation based on the optimal control methodology. Then, a novel adaptation algorithm is used to online directly estimate the unknown NN weights, so as to achieve the guaranteed convergence. The control system stability and the convergence of the derived control action to the optimal solution can be rigorously proved. Finally, two simulation examples are provided to illustrate the validity and efficacy of the proposed method.

Robust control for nonlinear systems with uncertain time-varying parameters coupled with non-triangular terms

ABSTRACTIn this paper, a robust control scheme is proposed for a class of nonlinear systems which consist of uncertain time-varying parameters that are coupled with non-triangular terms, perturbed nonlinearity, and external disturbance. In order to deal with time-varying parameters, we provide determination process of allowed time-varying parameters utilising a Lyapunov equation. With system analysis associated with perturbed nonlinearity, we show that all states of the controlled system remain bounded by a gain-scaling feedback controller in the presence of external disturbance. Moreover, the ultimate bounds of some system states can be made (arbitrarily) small by adjusting a gain-scaling factor depending on the system nonlinearity. The effectiveness of our control scheme is shown via an application example, with comparison of the existing result.

Designing Intelligent MIMO Nonlinear Controller Based on Fuzzy Cognitive Map Method for Energy Reduction of the Buildings

Designing a suitable controller for air-conditioning systems to reduce energy consumption and simultaneously meet the requirements of the system is very challenging. Important factors such as stability and performance of the designed controllers should be investigated to ensure the effectiveness of these controllers. In this article, the stability and performance of the fuzzy cognitive map (FCM) controller are investigated. The FCM method is used to control the direct expansion air conditioning system (DX A/C). The FCM controller has the ability to do online learning, and can achieve fast convergence thanks to its simple mathematical computation. The stability analysis of the controller was conducted using both fuzzy bidirectional associative memories (FBAMs) and the Lyapunov function. The performances of the controller were tested based on its ability for reference tracking and disturbance rejection. On the basis of the stability analysis using FBAMS and Lyapunov functions, the system is globally stable. The controller is able to track the set point faithfully, maintaining the temperature and humidity at the desired value. In order to simulate the disturbances, heat and moisture load changed to measure the ability of the controller to reject the disturbance. The results showed that the proposed controller can track the set point and has a good ability for disturbance rejection, making it an effective controller to be employed in the DX A/C system and suitable for a nonlinear robust control system.

Finite-time sliding mode and super-twisting control of fighter aircraft

The development of two nonlinear robust higher-order flight control systems for roll-coupled maneuvers of fighter aircraft with uncertain parameters is discussed in this article. The objective is to independently control the output variables (roll angle, pitch angle and sideslip angle) using aileron, elevator and rudder control surfaces. For a nominal model of aircraft, first a finite time stabilizing (FTS) control law, based on the notion of geometric homogeneity, is designed. Then for robust control in the presence of parameter uncertainties, (i) a discontinuous sliding mode (DSM) control law and (ii) a super-twisting (STW) continuous control law is designed. It is shown that in the composite closed-loop system consisting of either (a) the FTS and DSM control laws or (b) the FTS and STW control systems, the output trajectory tracking error and its first-order derivative converge to the origin in finite time. Digital simulation results for a swept-wing fighter aircraft, including the two composite control systems, are obtained. These results show that each of the designed flight controllers accomplishes precise simultaneous large longitudinal and lateral maneuvers, despite uncertainties in the aerodynamic and inertia parameters, turbulence, and partial loss of control surface effectiveness.