Adaptive sliding mode control for discrete-time multi-input multi-output systems

In this paper, robust adaptive sliding mode tracking control for discrete-time multi-input multi-output systems with unknown parameters and disturbance is considered. The robust tracking controller is comprised of adaptive control and sliding mode control design. Bounded motion of the system around the sliding surface and stability of the global system in the sense that all signals remain bounded are guaranteed. If the disturbance and the reference signal are slowly varying with respect to the sampling frequency, the proposed sliding mode controller can reject the disturbance and output tracking can be approximately achieved. Simulation results are presented to illustrate the proposed approach.     

A genetic-multivariable fractional order PID control to multi-input multi-output processes

A multivariable fractional order PID controller is designed and to get suitable coefficients for the controller, a genetic algorithm with a new topology to generate a new population is proposed. The three parts of the genetic algorithm such as reproduction, mutation, and crossover are employed and some variations in the methods are fulfilled so that a better performance is gained. The genetic algorithm is applied to design FOPID controllers for a multivariable process and the results are compared with the responses of a H_∞ based multivariable FOPID controller. The simulation responses show that in all cases, the genetic-multivariable FOPID controller has suitable performance, and the output of the system has a smaller error. Also, in the proposed method, variations in one output have a smaller effect on another output which is shown the ability of the proposed method to overcome the interaction in the multivariable processes.     

Stable multi-input multi-output adaptive fuzzy/neural control

In this letter, stable direct and indirect adaptive controllers are presented that use Takagi-Sugeno (T-S) fuzzy systems (1985), conventional fuzzy systems, or a class of neural networks to provide asymptotic tracking of a reference signal vector for a class of continuous time multi-input multi-output (MIMO) square nonlinear plants with poorly understood dynamics. The direct adaptive scheme allows for the inclusion of a priori knowledge about the control input in terms of exact mathematical equations or linguistics, while the indirect adaptive controller permits the explicit use of equations to represent portions of the plant dynamics. We prove that with or without such knowledge the adaptive schemes can “learn” how to control the plant, provide for bounded internal signals, and achieve asymptotically stable tracking of the reference inputs. We do not impose any initialization conditions on the controllers and guarantee convergence of the tracking error to zero     

多输入多输出非线性不确定系统连续高阶滑模控制

针对一类MIMO非线性不确定系统,提出一种新的连续高阶滑模控制算法.引入状态反馈使得系统高阶滑模控制问题等效转换为多变量不确定积分链的有限时间稳定问题,首先针对标称系统设计有限时间到达连续控制律,实现系统状态快速收敛,然后采用多变量非解耦形式超螺旋算法克服系统不确定性,实现鲁棒性,最终使得系统控制作用连续、滑模抖振得以大大抑制.基于二次型Lyapunov函数证明系统的有限时间稳定性.针对三阶不确定系统有限时间稳定和气垫船圆形航迹跟踪问题分别进行了仿真,验证了所提算法的有效性、鲁棒性.     

Adaptive fuzzy control for multi-input multi-output nonlinear systems with unknown dead-zone inputs

This paper presents an adaptive fuzzy control scheme for a class of uncertain multi-input multi-output (MIMO) nonlinear systems with the nonsymmetric control gain matrix and the unknown dead-zone inputs. In this scheme, fuzzy systems are used to approximate the unknown nonlinear functions and the estimated symmetric gain matrix is decomposed into a product of one diagonal matrix and two orthogonal matrices. Based on the decomposition results, a controller is developed, therefore, the possible controller singularity problem and the parameter initialization condition constraints problem are avoided. In addition, a dynamic robust controller is employed to compensate for the lumped errors. It is proved that all the signals in the proposed closed-loop system are bounded and that the tracking errors converge asymptotically to zero. A simulation example is used to demonstrate the effectiveness of the proposed scheme.     

Effective transfer function method for decentralized control system design of multi-input multi-output processes

In terms of relative gain and relative frequency, the effective transfer function for independent controller design for multi-input multi-output processes is provided in this paper. Differing from existing equivalent transfer functions, the proposed effective transfer function provides both gain and phase information for decentralized controller design in a simple and straightforward manner. The interaction effects for a particular loop from all other closed loops are directly incorporated into the effective transfer functions in four ways. Consequently, the decentralized controllers can be independently designed by employing the single loop tuning techniques. This design method is simple, straightforward, easy to understand and implement by field engineers. Several multivariable industrial processes with different interaction modes are employed to demonstrate the effectiveness and simplicity of the method.     

Nonlinear disturbance observer-based control for multi-input multi-output nonlinear systems subject to mismatching condition

For a multi-input multi-output (MIMO) nonlinear system, the existing disturbance observer-based control (DOBC) only provides solutions to those whose disturbance relative degree (DRD) is higher than or equal to its input relative degree. By designing a novel disturbance compensation gain matrix, a generalised nonlinear DOBC method is proposed in this article to solve the disturbance attenuation problem of the MIMO nonlinear system with arbitrary DRD. It is shown that the disturbances are able to be removed from the output channels by the proposed method with appropriately chosen control parameters. The property of nominal performance recovery, which is the major merit of the DOBCs, is retained with the proposed method. The feasibility and effectiveness of the proposed method are demonstrated by simulation studies of both the numerical and application examples.     

A self-tuning fuzzy controller for a class of multi-input multi-output nonlinear systems

This paper presents a systematic design procedure of a multivariable fuzzy controller for a general Multi-Input Multi-Output (MIMO) nonlinear system with an input-output monotonic relationship or a piecewise monotonic relationship for each input-output pair. Firstly, the system is modeled as a Fuzzy Basis Function Network (FBFN) and its Relative Gain Array (RGA) is calculated based on the obtained fuzzy model. The proposed multivariable fuzzy controller is constructed with two orthogonal fuzzy control engines. The horizontal fuzzy control engine for each system input-output pair has a hierarchical structure to update the control parameters online and compensate for unknown system variations. The perpendicular fuzzy control engine is designed based on the system RGA to eliminate the multivariable interaction effect. The resultant closed-loop fuzzy control system is proved to be passive stable as long as the augmented open-loop system is input-output passive. Two sets of simulation examples demonstrate that the proposed fuzzy control strategy can be a promising way in controlling multivariable nonlinear systems with unknown system uncertainties and time-varying parameters.     

Adaptive neural practical fixed-time command filtered control for multi-input and multi-output nonlinear systems with dead zones input and unknown control direction

In this article, under the circumstance of dead zones input and unknown control direction, the adaptive practical fixed-time control strategy is presented for a general class of multi-input and multi-output (MIMO) nonlinear systems. The inherent explosion of computational complexity difficulty is eliminated by adopting a command filter technique and the universal approximation properties of radial basis function neural networks (RBFNNs) are applied to model the unknown nonlinear functions. The difficulties of the dynamic surface method and unknown directions can be handled by invoking error compensation mechanism and Nussbaum-type functions, respectively. The uniqueness of the presented control scheme is that the tracking system can achieve the fixed-time stability without relying on the boundedness of dead-zone parameters. The fixed-time convergence of the output tracking error and the semiglobally fixed-time stable of closed-loop system are assured via the developed adaptive fixed-time command filtered controller. Finally, a practical example is supplied to further validate the availability of the presented theoretic result.     

状态与输入受限的二阶多输入多输出非线性系统自适应控制

针对含有状态和输入受限的二阶多输入多输出非线性系统的控制问题,提出了一种自适应控制策略.通过综合利用障碍Lyapunov函数和动态面控制方法的特性,使得系统的状态满足约束条件而且能够减少计算量.此外,为了处理输入约束和系统中的不确定性的影响,分别设计了辅助系统和自适应算法.通过理论分析表明,闭环系统的所有状态都是有界的,而且系统的状态和输入都满足约束条件.最后,通过一个数值仿真算例和一个实际的航天器姿态控制系统的仿真来验证所提出的自适应控制策略的有效性.     

基于极值搜索算法的一类多输入多输出非仿射型非线性系统输出跟踪控制

针对一类状态不可测的多输入多输出非仿射型非线性系统, 提出了基于极值搜索算法的输出跟踪控制方法. 此方法无需设计系统状态观测器, 仅利用系统的输出量和极值搜索向量形成控制律. 应用平均化理论分析平均化系统的稳定性, 然后利用奇异值扰动方法, 证明了所提出的控制方法可以保证闭环系统的稳定性和输出跟踪误差的收敛性. 仿真结果验证了本文方法的有效性.     

Observer design for a class of multi-input multi-output nonlinear systems

In this article, the problem of state observer design for a class of multi-input multi-output nonlinear systems is considered. Via state transformation and the constructive use of a Lyapunov function, the new observer design approach is addressed by introducing a parameter ? in the observer. Some sufficient conditions are given which guarantee the estimation error to asymptotically converge to zero under adaptive conditions. An example is included to illustrate the method.     

Set-point-related indirect iterative learning control for multi-input multi-output systems

A form of iterative learning control (ILC) is used to update the set-point for the local controller. It is referred to as set-point-related (SPR) indirect ILC. SPR indirect ILC has shown excellent performance: as a supervision module for the local controller, ILC can improve the tracking performance of the closed-loop system along the batch direction. In this study, an ILC-based P-type controller is proposed for multi-input multi-output (MIMO) linear batch processes, where a P-type controller is used to design the control signal directly and an ILC module is used to update the set-point for the P-type controller. Under the proposed ILC-based P-type controller, the closed-loop system can be transformed to a 2-dimensional (2D) Roesser s system. Based on the 2D system framework, a sufficient condition for asymptotic stability of the closed-loop system is derived in this paper. In terms of the average tracking error (ATE), the closed-loop control performance under the proposed algorithm can be improved from batch to batch, even though there are repetitive disturbances. A numerical example is used to validate the proposed results.     

An approximate internal model-based neural control for unknown nonlinear discrete processes

An approximate internal model-based neural control (AIMNC) strategy is proposed for unknown nonaffine nonlinear discrete processes under disturbed environment. The proposed control strategy has some clear advantages in respect to existing neural internal model control methods. It can be used for open-loop unstable nonlinear processes or a class of systems with unstable zero dynamics. Based on a novel input-output approximation, the proposed neural control law can be derived directly and implemented straightforward for an unknown process. Only one neural network needs to be trained and control algorithm can be directly obtained from model identification without further training. The stability and robustness of a closed-loop system can be derived analytically. Extensive simulations demonstrate the superior performance of the proposed AIMNC strategy.     

一类具有参数不确定n阶多输入多输出非线性系统的Terminal滑模控制

针对一类具有参数不确定的n阶MIMO非线性系统,提出了一种Terminal滑模控制方案.该方案通过对滑模超平面的选取和Terminal滑模控制律的设计,不但确保了闭环系统滑模阶段的存在性,而且还保证了系统状态误差在有限时间内的收敛性,由于无论何种情况下系统的初始状态均在Terminal滑模面上,从而消除了其他滑模控制方法常有的到达阶段,使得闭环系统具有全局鲁棒性和稳定性.除此之外,重点克服了控制输入的系数函数矩阵与不确定参数的关联问题.仿真结果表明,该控制方案可消除外部扰动及参数不确定的影响,控制系统各状态变量有效地跟踪期望状态.     

Adaptive output feedback control of a class of multi-input multi-output systems using neural networks

For a class of uncertain multi-input multi-output non-linear systems an adaptive output feedback control methodology is developed using linearly parameterized neural networks. The neural network operates over a tapped delay line of memory units, comprised of system input/output signals. The adaptive laws for neural network parameters are written in terms of a linear observer of the nominal system's error dynamics. Ultimate boundedness of the error signals is shown through Lyapunov's direct method. Simulations illustrate the theoretical results.     

Leave-one-out cross-validation-based model selection for multi-input multi-output support vector machine

As an effective approach for multi-input multi-output regression estimation problems, a multi-dimensional support vector regression (SVR), named M-SVR, is generally capable of obtaining better predictions than applying a conventional support vector machine (SVM) independently for each output dimension. However, although there are many generalization error bounds for conventional SVMs, all of them cannot be directly applied to M-SVR. In this paper, a new leave-one-out (LOO) error estimate for M-SVR is derived firstly through a virtual LOO cross-validation procedure. This LOO error estimate can be straightway calculated once a training process ended with less computational complexity than traditional LOO method. Based on this LOO estimate, a new model selection methods for M-SVR based on multi-objective optimization strategy is further proposed in this paper. Experiments on toy noisy function regression and practical engineering data set, that is, dynamic load identification on cylinder vibration system, are both conducted, demonstrating comparable results of the proposed method in terms of generalization performance and computational cost.     

多输入多输出非线性系统的最小二乘支持向量机广义逆控制

针对神经网络逆控制存在的不足, 对一类模型未知且某些状态量较难测得的多输入多输出(MIMO)非线性系统, 在状态软测量函数存在的前提下, 提出一种最小二乘支持向量机(LSSVM)广义逆辨识控制策略. 通过广义逆将原被控系统转化为伪线性复合系统, 并可使其极点任意配置, 采用LSSVM代替神经网络拟合广义逆系统中的静态非线性映射. 将系统的状态量辨识与LSSVM逆模型辨识结合, 通过LSSVM训练拟合同时实现软测量功能. 最后以双电机变频调速系统为对象, 采用该控制策略进行仿真研究, 结果验证了本文算法的有效性.     

802.11n与ZigBee共存:子载波置零多输入多输出物理层模型

针对802.11n与ZigBee共享ISM频段造成的WiFi与ZigBee信道重叠,进而导致网络间相互干扰使得网络性能下降,以及当前载波侦听多路访问/冲突避免(CSMA/CA）可能导致的频谱资源利用率较低的问题,提出一个采用子载波置零技术的2×2非相干多输入多输出(MIMO）物理层模型。该模型中,为了避免共信道干扰,WiFi发送端在发送数据前首先对其当前使用的信道中可能存在的ZigBee信号进行检测,若检测到ZigBee信号则对已被占用的频谱对应的子载波置零,使用余下频谱不重叠子载波进行通信。接收端对发送端使用的子载波进行识别,并完成后续工作。通过使WiFi与ZigBee信号频谱分离来消除信号间干扰,解决两者共存问题,实现WiFi与ZigBee数据并行传输。在由GNURadio/USRP软件无线电设备和ZigBee节点搭建的实验床上进行的实验结果表明,采用子载波置零技术的2×2非相干MIMO可以获得全带宽发送状态下50%~70%的吞吐量,同时在数据并行传输过程中ZigBee的正确收包百分比达到90%以上。     

一种多输入多输出系统模型辨识方法及其应用

目前的辨识方法一般需要在系统输入端加入激励信号，而且多输入多输出系统的在线辨识仍很困难。本文提出一种基于牛顿迭代法的多输入、多输出对象模型迭代辨识方法，模型参数更新的依据是使模型预测输出与全部采样时刻的对象实际输出之间的均方差递减，直到收敛。这种基于全局数据迭代的辨识方法可进行闭环辨识，无需外加激励信号，适用于多输入多输出对象的在线辨识。对一个两输入、两输出对象模型的仿真研究和某电厂300MW机组负荷被控对象的计算结果表明，辨识效果令人满意。