A nonsmooth IMC method for mechanical systems with backlash

This paper proposes a discrete-time nonsmooth internal model control （NSIMC） approach for mechanical transmission systems described by so-called sandwich system with backlash. In this method, a dynamic compensator is introduced to compensate for the effect of the input linear subsystem. Thus, the sandwich systems with backlash can be simplified as a pseudo-Hammerstein system with backlash. The corresponding NSIMC strategy is designed to control this system. The design procedure of the controller is presented based on the analysis on the robust stability by considering the model errors involved with the effect of backlash as well as the compensated error of the input linear subsystem. Moreover, as the model is switched among the different operating zones, the robust filters are proposed to guarantee the robust stability and satisfactory control performance of the system.     

时滞系统的神经网络预测控制

针对时滞系统的特点和采用神经网络单值预测控制存在的不足,提出了多步超前预测与补偿的控制算法,有效地增加了控制力度,改善了动态性能,并论述了增加的预测与补偿步数与稳定的关系。     

Robust Adaptive Output Control of Uncertain Nonlinear Plants With Unknown Backlash Nonlinearity

In this note, we consider a class of uncertain dynamic nonlinear systems preceded by unknown backlash nonlinearity. The control design is achieved by introducing a smooth inverse function of the backlash and using it in the controller design with backstepping technique. For the design and implementation of the controller, no knowledge is assumed on the unknown system parameters. It is shown that the proposed controller not only can guarantee stability, but also transient performance     

一种改进的神经网络非线性预测控制

从建立神经网络非线性预测模型出发,针对BP网络存在收敛速度慢,容易陷入局部最小的缺点,该文在BFGS拟牛顿法的基础上,提出了一种基于并行拟牛顿优化算法的并行拟牛顿神经网络。该并行拟牛顿优化算法采用两个含有不同参数的拟牛顿校正公式,在每次迭代过程中,利用这两个不同的校正公式得到相应的搜索方向,并通过不精确搜索法求取最优步长,最后根据一性能指标取最优的一个搜索方向和相应的步长对网络各层之间的权值进行修正。Matlab仿真结果表明,同BP神经网络和BFGS拟牛顿神经网络相比,该神经网络具有收敛速度快、模型精度高的特点,更适合于实时非线性控制。     

Operator-based robust control for nonlinear uncertain systems with unknown backlash-like hysteresis

In this paper, operator based robust control for nonlinear uncertain system with unknown backlash-like hysteresis is considered. In detail, a continuous backlash-like hysteresis operator is proved to be corresponding to a one-to-one operator, that is, it is suitable to be used in operator theoretic based control theory. Moreover, an internal model control (IMC) structure with one parallel compensating operator is proposed for nonlinear uncertain system with unknown backlash-like hysteresis. Based on the proposed control scheme, the designed system is robustly stable and the desired output tracking performance can be realized simultaneously. Finally, a simulation example about nonlinear plant preceded by backlash is given to show the design procedure of the proposed method.     

Stable adaptive fuzzy control of nonlinear systems preceded by unknown backlash-like hysteresis

This paper deals with adaptive control of nonlinear dynamic systems preceded by unknown backlash-like hysteresis nonlinearities, where the hysteresis is described by a dynamic equation. By utilizing this dynamic model and by combining a fuzzy universal function approximator with adaptive control techniques, a stable adaptive fuzzy control algorithm is developed without constructing a hysteresis inverse. The stability of the closed-loop system is shown using Lyapunov arguments. The effectiveness of the proposed method is demonstrated through simulations.     

基于Preisach模型的迟滞系统建模与控制

针对一种复杂的非线性系统一迟滞系统,研究了基于KP算子Preisach模型对迟滞系统进行建模的方法。利用Preisach模型与其边界线之间的映射关系,建立了容易在线更新的迟滞模型。基于Preisach模型进行迟滞非线性系统的控制,采用PID方法来控制一类带有未知非线性特性迟滞的单输入单输出非线性系统。对迟滞非线性系统的建模与控制进行的数值仿真研究结果表明,该迟滞非线性系统的建模和控制方法具有理论意义和应用价值。     

Adaptive Tracking Control for Nonlinear Systems with a Class of Input Nonlinearities

An adaptive tracking control approach is presented for nonlinear systems with a class of input nonlinearities. A generalized model has been developed for a class of non‐smooth nonlinearities that include dead‐zone, backlash and ‘backlash‐like’ hysteresis. By using the developed model and Nussbaum‐gain technique, the problem of input nonlinearity is solved perfectly. The proposed method is available even when the designer is uncertain about the type of input nonlinearities mentioned above, and the knowledge on the bounds of these nonlinearity parameters is not required. Furthermore, it is proved that all closed‐loop signals are bounded and the tracking error converges to a small residual set asymptotically. Two simulation examples are provided to demonstrate the effectiveness of the proposed method.     

Adaptive control of system involving complex hysteretic nonlinearities: a generalised Prandtl–Ishlinskii modelling approach

In this article an adaptive control approach is proposed for a class of nonlinear systems preceded by unknown hysteretic nonlinearities, which is described by a generalised Prandtl–Ishlinskii (P-I) model. The main feature is that the generalised P-I hysteresis model is counted in the controller design without constructing a hysteresis inverse. The developed controller guarantees the global stability of the system and tracking a desired trajectory to a certain precision is achieved. The effectiveness of the proposed control approach is demonstrated through simulation example.     

基于迟滞算子的非平滑三明治系统自适应控制

针对一类具有非平滑的迟滞三明治系统, 提出一种基于神经网络的自适应控制方法. 首先利用神经网络做出了前端动态模块的逆系统实现前端动态模块的近似补偿, 这样将迟滞三明治系统转化成一般的迟滞非线性系统. 然后提出一个迟滞算子将迟滞的多映射转化成一一映射, 基于这个迟滞算子设计了神经网络自适应控制器, 通过Lyapunov方法证明了系统的稳定性并推导出神经网络的权值自适应调整律和控制律. 最后通过仿真验证了该方案的有效性.     

A data‐driven bilinear predictive controller design based on subspace method

In this paper, a new data‐driven model predictive control (MPC), based on bilinear subspace identification, is considered. The system's nonlinear behavior is described with a bilinear subspace predictor structure in an MPC framework. Thus, the MPC formulation results in a fixed structure objective function with constraints regardless of the underlying nonlinearity. For unconstrained systems, the identified subspace predictor matrices can be directly used as controller parameters. Therefore, we design optimization algorithms that exploit this feature. The open‐loop optimization problem of MPC that is nonlinear in nature is solved with series quadratic programming (SQP) without any approximations. The computational efficiency already demonstrated with the current formulation presents further opportunities to enable online control of nonlinear systems. These improvements and close integration of modeling and control also eliminate the intermediate design step, which provides a means for data‐driven controller design in generalized predictive controller (GPC) framework. Finally, the proposed control approach is illustrated with a verification study of a nonlinear continuously stirred tank reactor (CSTR) system. Copyright © 2011 John Wiley and Sons Asia Pte Ltd and Chinese Automatic Control Society     

Neural‐network‐based predictive controller design: An application to temperature control of a plastic injection molding process

This paper presents a neural‐network‐based predictive control (NPC) method for a class of discrete‐time multi‐input multi‐output (MIMO) systems. A discrete‐time mathematical model using a recurrent neural network (RNN) is constructed and a learning algorithm adopting an adaptive learning rate (ALR) approach is employed to identify the unknown parameters in the recurrent neural network model (RNNM). The NPC controller is derived based on a modified predictive performance criterion, and its convergence is guaranteed by adopting an optimal algorithm with an adaptive optimal rate (AOR) approach. The stability analysis of the overall MIMO control system is well proven by the Lyapunov stability theory. A real‐time control algorithm is proposed which has been implemented using a digital signal processor, TMS320C31 from Texas Instruments. Two examples, including the control of a MIMO nonlinear system and the control of a plastic injection molding process, are used to demonstrate the effectiveness of the proposed strategy. Results from both numerical simulations and experiments show that the proposed method is capable of controlling MIMO systems with satisfactory tracking performance under setpoint and load changes. Copyright © 2010 John Wiley and Sons Asia Pte Ltd and Chinese Automatic Control Society     

An adaptive output feedback dynamic surface control for a class of nonlinear systems with unknown backlash‐like hysteresis

This paper is devoted to the output feedback control for a class of nonlinear systems with unknown backlash‐like hysteresis at the input. Based on a high‐gain observer, an adaptive dynamic surface control scheme is proposed which is able to mitigate the effect of the hysteresis, to eliminate the explosion of terms inherent in backstepping control, and in particular, by introducing an initialization technique, to guarantee the _∞ performance of the system's tracking error. Another advantage of the proposed scheme is that the adaptive law is needed only at the first design step, which greatly simplifies the design procedure and makes our control easy to implement. Copyright © 2011 John Wiley and Sons Asia Pte Ltd and Chinese Automatic Control Society     

基于未知Prandtl-Ishlinskii回滞的一类不确定非线性系统自适应逆控制

针对带有回滞驱动的一类不确定非线性系统,通过把Prandtl-Ishhnskii模型分解为一个离散的Prandtl-Ishlinskii算子和一个小的有界误差项,采用反步递推的设计方法,实现自适应逆控制器的设计.所设计的自适应逆控制器能保证闭环系统全局稳定.仿真结果进一步证明该控制方法的有效性.     

Robust adaptive control of a class of nonlinear systems including actuator hysteresis with Prandtl-Ishlinskii presentations

This paper deals with robust adaptive control of a class of nonlinear systems preceded by unknown hysteresis nonlinearities. By using a Prandtl-Ishlinskii model with play and stop operators, we attempt to fuse the model of hysteresis with the available control techniques without necessarily constructing a hysteresis inverse. A robust adaptive control scheme is therefore proposed. The global stability of the adaptive system and tracking a desired trajectory to a certain precision are achieved. Simulation results attained for a nonlinear system are presented to illustrate and further validate the effectiveness of the proposed approach.     

含间隙机械系统的混杂模型预测控制器

研究含间隙机械系统的混杂模型预测控制问题.首先,将含间隙机械系统的运行模式分为"间隙模式"和"接触模式".其次,建立了含间隙机械系统的混杂分段仿射 (PWA)模型.然后,利用模型预测控制 (MPC)的方法对约束PWA系统的最优控制进行求解,通过动态规划与多参数二次规划方法,得到了MPC的离线解.最后,通过将分段二次 (PWQ)Lyapunov函数的求解转换成半正定规划,找到了确保闭环控制稳定性的PWQ Lyaplanov函数.跟踪参考速度的实验结果表明,混杂模型预测控制器对含间隙机械系统的跟踪控制具有较好的效果,能够满足小采样时间系统的实时控制要求.     

Robust adaptive tracking control of MIMO nonlinear systems in the presence of actuator hysteresis

Adaptive tracking control of a class of MIMO nonlinear system preceded by unknown hysteresis is investigated. Based on dynamic surface control, an adaptive robust control law is developed and compensators are designed to mitigate the influences of both the unknown bounded external uncertainties and the unknown Prandtl–Islinskii hysteresis. By adopting the low-pass filters, the explosion of complexity caused by tedious computation of the time derivatives of the virtual control laws is overcome. With the proposed control scheme, the closed-loop system is proved to be semi-globally ultimately bounded by the Lyapunov stability theory, and the output of the controlled system can track the desired trajectories with an arbitrarily small error. Finally, numerical simulations are given to verify the effectiveness of the proposed approach.     

Observability and Controllability Analysis for Micro‐Positioning Stage Described by Sandwich Model with Hysteresis

In this paper, an approach for analyzing the observability and controllability of micro‐positioning stage with piezoelectric actuator described by sandwich model with hysteresis is proposed. As hysteresis inherent in piezoelectric actuator is a non‐smooth nonlinear function with multi‐valued mapping, the positioning system is also a non‐smooth dynamic system. The Prandtl‐Ishlinksii (PI) submodel is employed to describe the characteristic of hysteresis embedded in the sandwich system. A linearization method based on non‐smooth optimization is proposed to derive a generalized linearized state‐space function to approximate the non‐smooth sandwich systems within a bounded region around the equilibrium points the system works at. Then, both observability and controllability matrices are constructed and the methods to analyze the observability as well as the controllability of sandwich system with hysteresis are derived. Finally, a simulation example and an application of the proposed method to a micro‐positioning stage with piezoactuator are presented to validate the proposed method.     

BACKLASH COMPENSATION WITH FILTERED PREDICTION IN DISCRETE TIME NONLINEAR SYSTEMS BY DYNAMIC INVERSION USING NEURAL NETWORKS

A dynamics inversion compensation scheme is designed for control of nonlinear discrete‐time systems with input backlash. This paper extends the dynamic inversion technique to discrete‐time systems by using a filtered prediction, and shows how to use a neural network (NN) for inverting the backlash nonlinearity in the feedforward path. The technique provides a general procedure for using NN to determine the dynamics preinverse of an invertible discrete time dynamical system. A discrete‐time tuning algorithm is given for the NN weights so that the backlash compensation scheme guarantees bounded tracking and backlash errors, and also bounded parameter estimates. A rigorous proof of stability and performance is given and a simulation example verifies performance. Unlike standard discrete‐time adaptive control techniques, no certainty equivalence (CE) or linear‐in‐the‐parameters (LIP) assumptions are needed.     

Adaptive variable structure control of a class of nonlinear systems with unknown Prandtl-Ishlinskii hysteresis

Control of nonlinear systems preceded by unknown hysteresis nonlinearities is a challenging task and has received increasing attention in recent years due to growing industrial demands involving varied applications. In the literature, many mathematical models have been proposed to describe the hysteresis nonlinearities. The challenge addressed here is how to fuse those hysteresis models with available robust control techniques to have the basic requirement of stability of the system. The purpose of the note is to show such a possibility by using the Prandtl-Ishlinskii (PI) hysteresis model. An adaptive variable structure control approach, serving as an illustration, is fused with the PI model without necessarily constructing a hysteresis inverse. The global stability of the system and tracking a desired trajectory to a certain precision are achieved. Simulation results attained for a nonlinear system are presented to illustrate and further validate the effectiveness of the proposed approach.