Optimal second order sliding mode control for nonlinear uncertain systems

In this paper, a chattering free optimal second order sliding mode control (OSOSMC) method is proposed to stabilize nonlinear systems affected by uncertainties. The nonlinear optimal control strategy is based on the control Lyapunov function (CLF). For ensuring robustness of the optimal controller in the presence of parametric uncertainty and external disturbances, a sliding mode control scheme is realized by combining an integral and a terminal sliding surface. The resulting second order sliding mode can effectively reduce chattering in the control input. Simulation results confirm the supremacy of the proposed optimal second order sliding mode control over some existing sliding mode controllers in controlling nonlinear systems affected by uncertainty.     

Temporally local recurrent radial basis function network for modeling and adaptive control of nonlinear systems

In this paper, a novel temporally local recurrent radial basis function network for modeling and adaptive control of nonlinear systems is proposed. The proposed structure consists of recurrent hidden neurons having weighted self-feedback loops and a weighted linear feed-through from the input layer directly to the output layer neuron(s). The dynamic back-propagation algorithm is developed and used for updating the parameters of the proposed structure. To improve the performance of learning algorithm, discrete Lyapunov stability method is used to develop an adaptive learning rate scheme. This scheme ensures the faster convergence of the parameters and maintains the stability of the system. A total of 5 complex nonlinear systems are used to test and compare the performance of the proposed network with other neural network structures. The disturbance rejection tests are also carried out to check whether the proposed scheme is able to handle the external disturbance/noise signals effects or not. The obtained results show the efficacy of the proposed method.     

Optimal second order sliding mode control for linear uncertain systems

In this paper an optimal second order sliding mode controller (OSOSMC) is proposed to track a linear uncertain system. The optimal controller based on the linear quadratic regulator method is designed for the nominal system. An integral sliding mode controller is combined with the optimal controller to ensure robustness of the linear system which is affected by parametric uncertainties and external disturbances. To achieve finite time convergence of the sliding mode, a nonsingular terminal sliding surface is added with the integral sliding surface giving rise to a second order sliding mode controller. The main advantage of the proposed OSOSMC is that the control input is substantially reduced and it becomes chattering free. Simulation results confirm superiority of the proposed OSOSMC over some existing.     

Continuous higher-order sliding mode control with time-varying gain for a class of uncertain nonlinear systems

This paper presents a continuous higher-order sliding mode (HOSM) control scheme with time-varying gain for a class of uncertain nonlinear systems. The proposed controller is derived from the concept of geometric homogeneity and super-twisting algorithm, and includes two parts, the first part of which achieves smooth finite time stabilization of pure integrator chains. The second part conquers the twice differentiable uncertainty and realizes system robustness by employing super-twisting algorithm. Particularly, time-varying switching control gain is constructed to reduce the switching control action magnitude to the minimum possible value while keeping the property of finite time convergence. Examples concerning the perturbed triple integrator chains and excitation control for single-machine infinite bus power system are simulated respectively to demonstrate the effectiveness and applicability of the proposed approach.     

A new discrete-time robust adaptive time-delay control for a class of uncertain nonlinear strict-feedback systems using sliding mode

This paper presents a new discrete-time adaptive second-order sliding mode control with time delay estimation (TDE) for a class of uncertain nonlinear time-varying strict-feedback systems. The existing researches on time delay control (TDC) are conventionally established based on a stability criterion that is subject to the infinitesimal time delay assumption. Recently, this criterion was rejected and a new criterion was proposed for the development of a controller for systems with fully known dynamics. In this study, this approach is extended to uncertain systems. Specifically, a new criterion is developed for the stability of the TDE-error within an adaptive robust controller design without the infinitesimal time delay assumption. With the proposed adaptive robust control, there is no need for determination of uncertainties upper-bounds. Simulation results illustrate the efficacy of the proposed controller.     

Actuator fault tolerant control using adaptive RBFNN fuzzy sliding mode controller for coaxial octorotor UAV

In this paper, a robust controller for a Six Degrees of Freedom (6 DOF) coaxial octorotor helicopter control is proposed in presence of actuator faults. Radial Base Function Neural Network (RBFNN), Fuzzy Logic Control approach (FLC) and Sliding Mode Control (SMC) technique are used to design a controller, named Fault Tolerant Control (FTC), for each subsystem of the octorotor helicopter. The proposed FTC scheme allows avoiding difficult modeling, attenuating the chattering effect of the SMC, reducing the rules number of the fuzzy controller, and guaranteeing the stability and the robustness of the system. The simulation results show that the proposed FTC can greatly alleviate the chattering effect, good tracking in presence of actuator faults.     

Diagonal recurrent neural network based adaptive control of nonlinear dynamical systems using lyapunov stability criterion

In this paper adaptive control of nonlinear dynamical systems using diagonal recurrent neural network (DRNN) is proposed. The structure of DRNN is a modification of fully connected recurrent neural network (FCRNN). Presence of self-recurrent neurons in the hidden layer of DRNN gives it an ability to capture the dynamic behaviour of the nonlinear plant under consideration (to be controlled). To ensure stability, update rules are developed using lyapunov stability criterion. These rules are then used for adjusting the various parameters of DRNN. The responses of plants obtained with DRNN are compared with those obtained when multi-layer feed forward neural network (MLFFNN) is used as a controller. Also, in example 4, FCRNN is also investigated and compared with DRNN and MLFFNN. Robustness of the proposed control scheme is also tested against parameter variations and disturbance signals. Four simulation examples including one-link robotic manipulator and inverted pendulum are considered on which the proposed controller is applied. The results so obtained show the superiority of DRNN over MLFFNN as a controller.     

神经滑模控制在转台伺服系统应用

以直流电机为执行机构,分析了飞行仿真转台伺服系统的数学模型。滑模控制具有对系统扰动和参数摄动的自适应性,可实现伺服系统的快速响应,同时有效克服低速状态下摩擦力矩的影响。系统抖振问题是滑模控制的突出问题,利用径向基神经网络的非线性逼近能力,给出以切换函数为网络输入,以滑模控制器为网络输出,构建了神经滑模控制器,软件仿真结果表明所设计的滑模控制器能达到较好的控制品质,有效的克服系统抖振和外部扰动,实现系统低速摩擦补偿。     

Identification of nonlinear dynamic systems using convex combinations of multiple adaptive radius basis function networks

To improve performance of nonlinear adaptive filter based on radius basis function (RBF) networks, a generalized combination scheme is proposed for nonlinear dynamic system identification in this paper. The nonlinear filter proposed is constructed by the convex combination of multiple RBF networks (MCRBF). Its adaptive algorithm with different step sizes is derived by the gradient descent rule, and can overcome the contradiction between convergence speed and precision of the stochastic gradient (SG) algorithm for RBF networks, which is imposed by the selection of a fixed value for the adaption step. Computer simulations demonstrate that the performance of the nonlinear filter proposed is superior to the RBF for nonlinear dynamic system identification in terms of convergence speed, steady state error and tracking capability.     

Model-free adaptive integral terminal sliding mode predictive control for a class of discrete-time nonlinear systems

In this paper, a new model-free adaptive digital integral terminal sliding mode predictive control scheme is proposed for a class of nonlinear discrete-time systems with disturbances. The characteristic of the proposed control approach is easy to be implemented because it merely adopts the input and output data model of the system based on compact form dynamic linearization (CFDL) data-driven technique, while the technique of perturbation estimation is applied to estimate the disturbance term of the system. Moreover, by means of combining model predictive control and CFDL digital integral terminal sliding mode control (CFDL-DITSMC), the CFDL digital integral terminal sliding mode predictive control (CFDL-DITSMPC) method is proposed, which can further improve the tracking accuracy and disturbance rejection performance in comparison with the CFDL model-free adaptive control, neural network quasi-sliding mode control and the CFDL-DITSMC scheme. Meanwhile, the stability of the proposed approach is guaranteed by theoretical analysis, and the effectiveness of the proposed method is also illustrated by numerical simulations and the experiment on the two-tank water level control system.     

Decentralized adaptive neural prescribed performance control for high-order stochastic switched nonlinear interconnected systems with unknown system dynamics

In this paper, the problem of decentralized adaptive neural backstepping control is investigated for high-order stochastic nonlinear systems with unknown interconnected nonlinearity and prescribed performance under arbitrary switchings. For the control of high-order nonlinear interconnected systems, it is assumed that unknown system dynamics and arbitrary switching signals are unknown. First, by utilizing the prescribed performance control (PPC), the prescribed tracking control performance can be ensured, while the requirement for the initial error is removed. Second, at each recursive step, only one adaptive parameter is constructed to overcome the over-parameterization, and RBF neural networks are employed to tackle the difficulties caused by completely unknown system dynamics. At last, based on the common Lyapunov stability method, the decentralized adaptive neural control method is proposed, which decreases the number of learning parameters. It is shown that the designed common controller can ensure that all the signals in the closed-loop system are semi-globally uniformly ultimately bounded (SGUUB), and the prescribed tracking control performance is guaranteed under arbitrary switchings. The simulation results are presented to further illustrate the effectiveness of the proposed control scheme.     

The application of a radial basis function neural network for predicting the surface roughness in a turning process

This study considers the performance of a radial basis function neural network for predicting the surface roughness in a turning process. A simple algorithm is proposed for finding the upper and lower estimates of the surface roughness. A code is developed that automatically fits the best network architecture for a given training and testing dataset. The validation of the methodology is carried out for dry and wet turning of mild steel using HSS and carbide tools, and is compared to the performance of the studied network with the reported performance of a multi-layer perception neural network. It is observed that the performance of the radial basis function network is slightly inferior compared to multi-layer perceptron neural network. However, the training procedure is simpler and requires less computational time.     

RBF神经网络滑模变结构控制在并联机器人中的应用

并联机器人系统结构复杂,具有强耦合、非线性等特点。滑模变结构控制对参数不确定性和外部扰动具有强鲁棒性,不需要被控对象精确数学模型且基于该方法的控制器设计过程是自然解耦过程,适用于并联机器人控制,但是滑模控制普遍存在抖振问题。鉴于此,该文提出RBF神经网络与滑模控制相结合的控制方法,利用RBF神经网络对滑模控制器切换项的增益进行调节,可以有效地降低滑模控制的抖振,获得较好的控制效果。仿真结果表明,该控制方法跟踪性能好,系统误差小,具有较强的鲁棒性,可以满足并联机器人的控制要求。     

A new fractional-order sliding mode controller via a nonlinear disturbance observer for a class of dynamical systems with mismatched disturbances

This paper investigates the stabilization and disturbance rejection for a class of fractional-order nonlinear dynamical systems with mismatched disturbances. To fulfill this purpose a new fractional-order sliding mode control (FOSMC) based on a nonlinear disturbance observer is proposed. In order to design the suitable fractional-order sliding mode controller, a proper switching surface is introduced. Afterward, by using the sliding mode theory and Lyapunov stability theory, a robust fractional-order control law via a nonlinear disturbance observer is proposed to assure the existence of the sliding motion in finite time. The proposed fractional-order sliding mode controller exposes better control performance, ensures fast and robust stability of the closed-loop system, eliminates the disturbances and diminishes the chattering problem. Finally, the effectiveness of the proposed fractional-order controller is depicted via numerical simulation results of practical example and is compared with some other controllers.     

Design and implementation of continuous finite-time sliding mode control for 2-DOF inertially stabilized platform subject to multiple disturbances

Control performances of inertially stabilized platforms (ISPs) are always affected by various disturbed phenomena such as cross-couplings, mass unbalance, parameter variations, and external disturbances in real applications. To improve the dynamic response and the disturbance rejection ability of the ISP, a continuous finite-time sliding mode control (SMC) approach with cascaded control structure is proposed. By constructing a finite-time disturbance observer, the multiple disturbances are precisely estimated in real time without the complex modeling and calibration work. Under the field oriented control framework, for the stabilized loop subsystem, an improved super-twisting controller incorporating the disturbance estimates is developed whereas for the current loop subsystem, the super-twisting control method is directly employed. Finite-time convergence of the inertial angular rates is guaranteed with the continuous control action such that chattering is alleviated remarkably. Moreover, by utilizing the manner of disturbance compensation, the feedback control gains can be tuning down without sacrificing the disturbance rejection ability. Comparative experiments are performed to verify the effectiveness of the proposed control approach.     

Design of an adaptive super-twisting decoupled terminal sliding mode control scheme for a class of fourth-order systems

This paper proposes an adaptive super-twisting decoupled terminal sliding mode control technique for a class of fourth-order systems. The adaptive-tuning law eliminates the requirement of the knowledge about the upper bounds of external perturbations. Using the proposed control procedure, the state variables of cart-pole system are converged to decoupled terminal sliding surfaces and their equilibrium points in the finite time. Moreover, via the super-twisting algorithm, the chattering phenomenon is avoided without affecting the control performance. The numerical results demonstrate the high stabilization accuracy and lower performance indices values of the suggested method over the other ones. The simulation results on the cart-pole system as well as experimental validations demonstrate that the proposed control technique exhibits a reasonable performance in comparison with the other methods.     

用神经网络结构实现超磁致伸缩智能构件滑模控制

提出了一种利用超磁致伸缩材料(GMM)智能构件精密加工活塞异形孔的方法.采用一种神经网络前馈复合离散滑模变结构控制策略,实现GMM智能构件的精密位移控制,消除了GMM智能构件迟滞非线性的影响.将智能构件的输出位移及其变化率作为小脑模型神经网络(CMAC)输入,构件的输入电流作为网络输出,利用CMAC在线自学习能力建立GMM智能构件的迟滞逆模型;通过离散滑模变结构控制器来消除神经网络的建模近似误差以及外界干扰.仿真结果表明,此控制策略能在线建立智能构件的迟滞逆模型,消除迟滞非线性的影响,控制误差降低到1.5%以内,可实现智能构件的精密位移控制.     

广义径向基函数神经网络在热误差建模中的应用

针对现有的热误差建模方法建模效率低,模型预测精度不理想等问题,提出了广义径向基函数神经网络(RBF)建模方法并将其应用于数控机床热误差建模中。讨论了采用广义RBF神经网络进行热误差建模的原理及步骤。以数控导轨磨床主轴箱系统为例,布置了12个主轴热误差的关键温度测点,测得了2组独立的主轴箱系统热误差数据。将测得的数据分别用于建立主轴箱系统热误差广义RBF神经网络预报模型和验证模型的准确性。研究结果表明,热误差广义RBF神经网络模型具有预测精度高及泛化能力强的优点;与传统的RBF神经网络建模方法相比,提出的广义RBF神经网络建模方法建模效率更高,模型鲁棒性及预测性能更好,是一种可以用于数控机床热误差实时补偿的有效建模方法。     

Optimal adaptive interval type-2 fuzzy fractional-order backstepping sliding mode control method for some classes of nonlinear systems

In this research, a novel adaptive interval type-2 fuzzy fractional-order backstepping sliding mode control (AIT2FFOBSMC) method is presented for some classes of nonlinear fully-actuated and under-actuated mechanical systems with uncertainty. The AIT2FFOBSMC method exploits the advantages of backstepping and sliding mode methods to improve the performance of closed-loop control systems by lowering the tracking error and increasing robustness. To mitigate chattering and the tracking error, a fractional sliding surface is designed. In addition to the fractional sliding surface, an adaptive interval type-2 fuzzy compensator is used to estimate the uncertainty and perturbation of the nonlinear system in order to further reduce chattering caused by switching term as well as to enhance the perturbation rejection. In order to achieve an optimal performance, the multi-tracker optimization algorithm (MTOA) is used. Finally, a number of simulations and experimental tests are carried out to examine the performance of the AIT2FFOBSMC method.     

A new continuous sliding mode control approach with actuator saturation for control of 2-DOF helicopter system

The 2-degree of freedom (DOF) helicopter system is a typical higher-order, multi-variable, nonlinear and strong coupled control system. The helicopter dynamics also includes parametric uncertainties and is subject to unknown external disturbances. Such complicated system requires designing a sophisticated control algorithm that can handle these difficulties. This paper presents a new robust control algorithm which is a combination of two continuous control techniques, composite nonlinear feedback (CNF) and super-twisting control (STC) methods. In the existing integral sliding mode (ISM) based CNF control law, the discontinuous term exhibits chattering which is not desirable for many practical applications. As the continuity of well known STC reduces chattering in the system, the proposed strategy is beneficial over the current ISM based CNF control law which has a discontinuous term. Two controllers with integral sliding surface are designed to control the position of the pitch and the yaw angles of the 2- DOF helicopter. The adequacy of this specific combination has been exhibited through general analysis, simulation and experimental results of 2-DOF helicopter setup. The acquired results demonstrate the good execution of the proposed controller regarding stabilization, following reference input without overshoot against actuator saturation and robustness concerning to the limited matched disturbances.