Mode Control For Nonlinear Systems Research Articles

Adaptive prescribed-time sliding mode control of nonlinear systems with unknown dynamics

One of the main difficulties for application of sliding mode control is the presence of chattering. It is a well known fact that the amplitude of chattering is proportional to the magnitude of discontinuous control. The problem can be alleviated by making the magnitude as small as possible while still ensuring the existence of the sliding mode. In this paper, a novel predefined-time single layer adaptive scheme based on equivalent concept with a relaxed assumption about unknown dynamics is proposed for dynamically tuning the gain associated with the control magnitude, and applying this scheme in sliding mode control algorithms enables decreasing the control action magnitude to the minimum possible value remaining the characteristic of finite-time convergence. Simulation results are shown to verify the effectiveness of the designed scheme.

Exponential super-twisting control for nonlinear systems with unknown polynomial perturbations

The study focuses on the control of nonlinear dynamic systems in the presence of parameter uncertainties, unmodeled dynamics, and external disturbances. The lumped perturbation is assumed to be bounded within a polynomial in the system state with the polynomial parameters and degrees unknown a priori such that it accommodates a quite wider range dynamic systems. Based on the studies in recent super-twisting algorithm designs and the idea from adaptive sliding mode control for nonlinear systems with uncertainties, we propose a novel adaptive super-twisting algorithm with exponential reaching law, or exponential super-twisting algorithm (ESTA), for the high-stability and acceptable accuracy control of the aimed nonlinear dynamics. The stability analysis and practical finite-time (PFT) convergence are proven using Lyapunov theory and an intuitive analysis of the control behaviour. Simulations are performed to compare the proposed ESTA with the existing super-twisting method and the traditional proportional integral differential control. The simulation results demonstrate the effectiveness of the proposed ESTA in terms of the fastest settling time and the smallest overshoot.

Fast finite time fractional-order robust-adaptive sliding mode control of nonlinear systems with unknown dynamics

This study investigates the fast finite-time robust-adaptive terminal sliding-mode control of nonlinear affine high order (NAHO) systems based on fractional-order control approach. It is considered in this paper that dynamic parameters of the nonlinear system are completely unknown. To do this, at first a high-order fractional order sliding surface is proposed. Then, considering that there is no any information about dynamics of system due to the large amount of uncertainties and unmolded dynamics, a finite-time fractional-order adaptive sliding-mode controller is devised to achieve finite-time stability with quick convergence of system output to its desired trajectory. A stable adaptive law is also designed to estimate the system’s unknown dynamic parameter vector. This is worth to mention that using the designed control law, finite time convergence is obtained in a more real condition where the dynamic parameters of the system are unknown and because of using a fractional order sliding surface, the chattering phenomena is less than ordinary terminal sliding mode controller. The developed Lyapunov theory has been employed to prove the stability of the closed-loop system. The simulation results are demonstrated on a cable robot with unknown dynamics to validate the effectiveness of the control law.

Neuroadaptive global sliding mode control for nonlinear systems and its application

AbstractOne type of adaptive controller on the basis of an original dual‐loop recursive fuzzy neural network (DRFNN) with two closed loop structures for a kind of nonlinear dynamic systems is designed in this paper. Though the conventional FNN could approximate arbitrary smooth functions, the inner network parameters need to be set up in advance. Usually, the setting of the base width and central vector are lack of theoretical guidance to some degree and need to be debugged many times. However, the initial values of the center vector and the base width can be arbitrarily set and stable to optimal ones in the light of adaptive mechanism of the proposed dual recursive FNN. Besides, the dynamic dual recursive FNN possesses the ability of storing more beneficial information through constructing signal back loops, meanwhile accuracy of the approximation is higher than the traditional FNN. Furthermore, the learning speed and detection accuracy can be improved due to the fact that expert knowledge is a priori knowledge in the network structure by including if‐then rules of this FNN. To validate effectiveness of the developed scheme, simulations and three suits of experiments are carried out on a set of active power filter to demonstrate that this presented global sliding mode control using DRFNN can achieve expected performance. Eventually, some comparisons among FNN and the proposed DRFNN are implemented to suggest the dual recursive FNN can obtain more superior properties.

Design of a Deep Neural Network-Based Integral Sliding Mode Control for Nonlinear Systems Under Fully Unknown Dynamics

In this letter a novel deep neural network based integral sliding mode (DNN-ISM) control is proposed for controlling perturbed systems with fully unknown dynamics. In particular, two DNNs with an arbitrary number of hidden layers are exploited to estimate the unknown drift term and the control effectiveness matrix of the system, which are instrumental to design the ISM controller. The DNNs weights are adjusted according to adaptation laws derived directly from Lyapunov stability analysis, and the proposal is satisfactorily assessed in simulation relying on benchmark examples.

State estimation and fuzzy sliding mode control of nonlinear Markovian jump systems via adaptive neural network

This paper deals with the problem of Takagi-Sugeno fuzzy model-based state estimation and sliding mode control for nonlinear systems through an adaptive neural network, in which the system parameters follow the Markovian switching rules. In order to deal with the unknown local nonlinearity, a multi-layer neural network is used for the nonlinear function approximation. First, a Lebesgue fuzzy observer with adaptive compensator is designed based on state-dependent fuzzy rules. Second, an integral sliding surface is proposed, based on which the obtained sliding mode dynamics has good property of sliding mode manifold. Third, an H∞ performance with stochastic stability of the sliding mode dynamics and error dynamics are developed in the form of linear matrix inequality. Moreover, reachability of sliding surface in finite-time and maintenance of sliding motion are realized by constructing a fuzzy sliding mode controller. Finally, a simulation study is added to show the validity of the proposed results on the robot manipulator model.

Optimization-based adaptive neural sliding mode control for nonlinear systems with fast and accurate response under state and input constraints

The high-performance control requires the system to be stable, fast and accurate simultaneously. However, various systems (e.g., motors, industrial robots) generally face technical challenges such as nonlinearities, uncertainties, external disturbances and physical constraints, which make it difficult to reach the hardware potential of the systems to track the desired trajectories when satisfying the high-performance control requirements. Therefore, take a two-order nonlinear system for example, an optimization-based adaptive neural sliding mode control based on a two-loop control structure is proposed in this paper, where the outer and inner loops are designed separately to achieve different control requirements. Namely, the outer loop is designed as a model predictive control (MPC)-based optimization problem, which can optimize the desired trajectories to meet the state and input constraints, and maximize the converging speed of transient response as fast as possible, and the inner loop is designed with a recurrent neural network (RNN)-based adaptive neural sliding mode controller, which can guarantee the tracking of the replanned desired trajectories from outer loop as accurate as possible. The stability of the system is guaranteed by Lyapunov theorem, the optimal tracking performance is achieved under nonlinearities, uncertainties, external disturbances and physical constraints, and comparative simulation with a motor system is carried out to verify the effectiveness and superiority of the proposed approach.

RBF Neural Network Sliding Mode Control for Passification of Nonlinear Time-Varying Delay Systems with Application to Offshore Cranes.

This paper is devoted to studying the passivity-based sliding mode control for nonlinear systems and its application to dock cranes through an adaptive neural network approach, where the system suffers from time-varying delay, external disturbance and unknown nonlinearity. First, relying on the generalized Lagrange formula, the mathematical model for the crane system is established. Second, by virtue of an integral-type sliding surface function and the equivalent control theory, a sliding mode dynamic system can be obtained with a satisfactory dynamic property. Third, based on the RBF neural network approach, an adaptive control law is designed to ensure the finite-time existence of sliding motion in the face of unknown nonlinearity. Fourth, feasible easy-checking linear matrix inequality conditions are developed to analyze passification performance of the resulting sliding motion. Finally, a simulation study is provided to confirm the validity of the proposed method.

Fuzzy Estimator Indirect Terminal Sliding Mode Control of Nonlinear Systems Based on Adaptive Continuous Barrier Function

In this paper, the theory of control is considered on nonlinear systems. A closed-loop controller with a strong idea has been introduced to track system states and guarantee asymptotically stability. The proposed method is the indirect terminal sliding mode control technique based on adaptive and fuzzy rules, which has used the continuous barrier function as a new approach in its design to improve the performance of this controller. One of the significant challenges in the sliding mode control method is the chattering phenomenon due to the discontinuous sign function in the control law. In the proposed approach, the control law is obtained continuously and smoothly due to the mentioned continuous function and subsequently solves the chattering problem. Another feature of the proposed method is the asymptotical stability of the system dynamics within finite time, which is proved based on the Lyapunov function. The proposed Lyapunov function includes the function of fractional power of a sliding surface. On the other hand, the obtained control law using the sliding mode method is estimated using the fuzzy system. The adaptive approach adjusts the fuzzy law parameters and the unknown bound of external disturbance.

Dynamic Modelling and Performance Optimization-Based Sliding Mode Control of Process Drying in a Convective Tunnel Dryer

In this work, we thoroughly investigate the use of sliding mode control for nonlinear systems, specially its application for the control of dryer designed for drying food products. A dynamic model of the drying process has been developed, experimental measurements presented in this paper are established for different values of drying air temperature and drying air velocity. Two scenario of sliding mode control applied to the hybrid tunnel dryer has been assessed through simulations. At first, a nonlinear sliding mode control with first order sliding surface was tested. In front of the insufficient performance of this control in terms of the presence of chattering phenomenon and static error, it was decided to apply a nonlinear sliding mode control with PI sliding surface. Simulation results show that this latter control approach can obtain excellent control performance with no chattering problem, reducing of static error and a good tracking of trajectory.

Dynamic Modelling and Performance Optimization-Based Sliding Mode Control of Process Drying in a Convective Tunnel Dryer

In this work, we thoroughly investigate the use of sliding mode control for nonlinear systems, specially its application for the control of dryer designed for drying food products. A dynamic model of the drying process has been developed, experimental measurements presented in this paper are established for different values of drying air temperature and drying air velocity. Two scenario of sliding mode control applied to the hybrid tunnel dryer has been assessed through simulations. At first, a nonlinear sliding mode control with first order sliding surface was tested. In front of the insufficient performance of this control in terms of the presence of chattering phenomenon and static error, it was decided to apply a nonlinear sliding mode control with PI sliding surface. Simulation results show that this latter control approach can obtain excellent control performance with no chattering problem, reducing of static error and a good tracking of trajectory.

Adaptive fuzzy backstepping super‐twisting sliding mode control of nonlinear systems with unknown hysteresis

AbstractIn this paper, an adaptive fuzzy backstepping super‐twisting sliding mode control (AFBSTSMC) scheme is proposed for a class of nonlinear systems with unknown hysteresis, unmeasured states, and external disturbances. First, fuzzy logic systems are employed to approximate the unknown nonlinear functions of the controlled systems, and a fuzzy state observer is designed to estimate the unmeasured states. Then, combining the backstepping technique and adaptive sliding mode control with super‐twisting algorithm, the AFBSTSMC scheme is proposed without constructing the hysteresis inverse. The problem of “explosion of complexity” inherent in the conventional backstepping design method is eliminated by utilizing the dynamic surface control technique. Moreover, the chattering phenomenon is significantly reduced by using the developed adaptive fuzzy super‐twisting controller. It is proved that the proposed control scheme can guarantee that all the signals in the closed‐loop system are semi‐globally ultimately uniformly bounded and the observer and tracking errors can converge to a small domain of the origin. Finally, the effectiveness of the presented control scheme is confirmed in two examples including a numerical simulation and an inverted pendulum with unknown hysteresis actuator.

Observer-based integral sliding mode control of nonlinear systems with application to single-link flexible joint robotics

Complex Engineering Systems are generally represented in terms of a set of interconnected systems that their collective/global behaviors/properties are somewhat difficult to be predicted or managed. The context of complex engineering systems is mainly concerned with developing multi-component engineering systems, designs, or algorithms to exploit those unpredictable collective/global behaviors/properties. Complexity in Engineering Systems is in general manifested in component, product, system, interconnections of interacting subsystems or multidisciplinary system designs. In a broad sense, complexity is related to the expected amount of information may need to describe a dynamical system.

Event-triggered observer-based [formula omitted] sliding mode control of nonlinear systems

The problem of sliding mode control for a class of Takagi–Sugeno fuzzy model-based nonlinear one-sided Lipschitz systems is investigated in the paper. Due to the state components are not available, a state observer is designed based on an event-triggering mechanism. Meanwhile, the output measurements transmitted through the communication channels suffer from signal delays. Based on the estimated state, an integral sliding surface is proposed. Then, the sliding mode dynamics is obtained by virtue of equivalent control principle. Further, by constructing appropriate sliding mode controller, the finite-time reachability of predefined sliding surface is surely guaranteed. Moreover, the stability with an H∞ performance analysis of sliding mode dynamics is undertaken via Lyapunov function theory and the criteria are established in terms of LMI. Finally, numerical examples are provided to demonstrate the effectiveness of the proposed method.

Observer-based output feedback integral terminal sliding mode control for nonlinear systems: multi-model approach

In this paper we propose an observer-based output feedback integral terminal sliding mode control for nonlinear systems. The state estimation problem is treated by using the Utkin observer under a multi-model structure. The design of the control law is based on the sliding mode theory using multi-model approach. In fact, we propose two types of multi-model integral terminal sliding mode which are sign integral and fraction integral. The objective of such observer-based control algorithms is to estimate the states of the system and to stabilise the output tracking error to zero. The stability proof is demonstrated by Lyapunov approach. A numerical example of denitrification process is presented in order to validate the performances of the proposed control laws.

Observer-based output feedback integral terminal sliding mode control for nonlinear systems: multi-model approach

In this paper we propose an observer-based output feedback integral terminal sliding mode control for nonlinear systems. The state estimation problem is treated by using the Utkin observer under a multi-model structure. The design of the control law is based on the sliding mode theory using multi-model approach. In fact, we propose two types of multi-model integral terminal sliding mode which are sign integral and fraction integral. The objective of such observer-based control algorithms is to estimate the states of the system and to stabilise the output tracking error to zero. The stability proof is demonstrated by Lyapunov approach. A numerical example of denitrification process is presented in order to validate the performances of the proposed control laws.

Adaptive Smooth Super-Twisting Sliding Mode Control of Nonlinear Systems With Unmatched Uncertainty

This article presents a novel strategy regarding the stabilization control problem for plants with unmatched uncertainties. The methodology is based on Adaptive Smooth Super Twisting Sliding Mode Control. At first, as an initial step, the plant with unmatched uncertainty is transformed into a plant with matched uncertainty. At the second step, the plant with matched uncertainty is decomposed into a unique framework containing the nominal part and some unknown terms (where these unknown terms are computed adaptively). The nominal system is stabilized by using Smooth Super Twisting Sliding Mode Control. The stabilizing controller for the plant with matched uncertainty is designed in a way; it contains some nominal control plus some compensator term. The stability of the said technique is presented impressively. The compensator controller and the adapted laws are derived in such a way that the time derivative of a Lyapunov function becomes strictly negative. The proposed method is tested on a fourth-order plant. The simulation results show the effectiveness and validity of the proposed controller.

Adaptive super-twisting terminal sliding mode control for nonlinear systems with multiple inputs

This paper presents an adaptive super-twisting terminal sliding mode control for uncertain nonlinear systems with multiple inputs. Based on Lyapunov stability theory, the stability of overall uncertain nonlinear system is guaranteed. Under the proposed method, the trajectory of states not only converges to zero in finite time, but also the chattering phenomenon is alleviated without reducing the accuracy of the system performance. Unlike the previous super-twisting algorithm, the proposed method can be applied to higher order uncertain nonlinear systems with multiple inputs, which is more flexible in the application. Finally, the simulation results are given to demonstrate the effectiveness of the proposed method.

Intuitionistic fuzzy adaptive sliding mode control of nonlinear systems

In this paper, Takagi–Sugeno intuitionistic fuzzy adaptive sliding mode control system (TS-IFASMC) is designed for nonlinear systems. We propose an intuitionistic fuzzy method to determine the parameters of the adaptive sliding mode control method which is used to control nonlinear systems. Intuitionistic fuzzy systems are considered as a skilled tool to model uncertainty in systems so they can transfer expert knowledge to control schemes better than the other classical methods, and real-world problems can be handled more effectively with this control method. In the proposed system, control parameters are defined by the intuitionistic fuzzy membership, non-membership, hesitation degrees and an integral sliding mode surface for a robust control performance. The novelty of this study is the use of Takagi–Sugeno type intuitionistic fuzzy system in adaptive sliding mode control method and comparison of performance of this new system with other classical methods. Thus, adaptive sliding mode controller based on the Takagi–Sugeno intuitionistic fuzzy system is obtained to provide robust control performance. Finally, the results support the effectiveness of the presented control scheme.

Orthogonal function‐based equivalent linearization for sliding mode control of nonlinear systems

This paper proposes the equivalent linearization (EL) and sliding mode control (SMC) methods to address nonlinearity and enhance the performance of nonlinear systems subjected to nonstationary random excitations. The EL methods are commonly used to propose approximate solutions for nonlinear systems under random excitations due to the high computational demands in the exact analyses. Considering the application of orthogonal functions in improving the accuracy and efficiency of approximate solutions, an orthogonal block pulse (BP) function is applied to the EL method in this study to approximate the nonlinear system responses under nonstationary random excitations. The SMC, as a robust control method for systems with uncertainties and external disturbances, is capable of achieving reliable and accurate tracking control. This method is applied to effectively reduce the dynamic responses predicted by the proposed EL method under nonstationary random excitations. The proposed approach is tested on single-degree-of-freedom and two-degree-of-freedom Duffing systems subjected to a seismic type excitation. The results indicate that not only the orthogonal function-based EL method can approximate the dynamic responses more accurately, at lower computational cost, and by a high agreement with the exact solution, but also the proposed SMC can improve the performance of nonlinear systems by effectively reducing the responses compared with the linear quadratic regulator control method.