Stability Analysis of Parallel Fuzzy P ＋ Fuzzy I ＋ Fuzzy D Control Systems

The study presented in this paper is in continuation with the paper published by the authors on parallel fuzzy proportional plus fuzzy integral plus fuzzy derivative (FP + FI + FD) controller. It addresses the stability analysis of parallel FP + FI + FD controller. The famous"small gain theorem" is used to study the bounded-input and bounded-output (BIBO) stability of the fuzzy controller. Sufficient BIBO-stability conditions are developed for parallel FP + FI + FD controller. FP + FI + FD controller is derived from the conventional parallel proportional plus integral plus derivative (PID) controller. The parallel FP + FI + FD controller is actually a nonlinear controller with variable gains. It shows much better set-point tracking, disturbance rejection and noise suppression for nonlinear processes as compared to conventional PID controller.     

On robust stability of LTI fractional-order delay systems of retarded and neutral type

This paper deals with the analysis of robust BIBO-stability of LTI fractional order delay systems in the presence of real parametric uncertainties. Two large classes of these systems, namely retarded and neutral types, are considered. Two theorems are given to check the robust BIBO-stability of these two families of fractional order systems. One of these theorems provides necessary and sufficient conditions for the case of retarded type and another one presents only sufficient conditions for the case of neutral type. Furthermore, upper and lower bounds (cutoff frequencies) are provided for drawing the value sets. To illustrate the results, two numerical examples are presented.     

Controller tuning freedom under plant identification uncertainty: double Youla beats gap in robust stability

In iterative schemes of identification and control one of the particular and important choices to make is the choice for a model uncertainty structure, capturing the uncertainty concerning the estimated plant model. Structures that are used in the recent literature encompass e.g. gap metric uncertainty, coprime factor uncertainty, and the Vinnicombe gap metric uncertainty. In this paper, we study the effect of these choices by comparing the sets of controllers that guarantee robust stability for the different model uncertainty bounds. In general these controller sets intersect. However in particular cases the controller sets are embedded, leading to uncertainty structures that are favourable over others. In particular, when restricting the controller set to be constructed as metric-bounded perturbations around the present controller, the so-called double Youla parametrization provides a set of robustly stabilizing controllers that is larger than corresponding sets that are achieved by using any of the other uncertainty structures. This is particularly of interest in controller tuning problems.     

Robust control for nonlinear motor-mechanism coupling system using wavelet neural network

A robust controlled toggle mechanism, which is driven by a permanent magnet (PM) synchronous servo motor is studied in this paper. First, based on the principle of computed torque control, a position controller is developed for the motor-mechanism coupling system. Moreover, to relax the requirement of the lumped uncertainty in the design of a computed torque controller, a wavelet neural network (WNN) uncertainty observer is utilized to adapt the lumped uncertainty online. Furthermore, based on the Lyapunov stability a robust control system, which combines the computed torque controller, the WNN uncertainty observer and a compensated controller is proposed to control the position of the motor-mechanism coupling system. The computed torque controller with WNN uncertainty observer is the main tracking controller, and the compensated controller is designed to compensate the minimum approximation error of the uncertainty observer. Finally, simulated and experimental results due to a periodic sinusoidal command show that the dynamic behaviors of the proposed robust control system are robust with regard to parametric variations and external disturbances.     

冷带轧机厚控系统自适应鲁棒输出反馈动态控制器设计

冷带轧机厚控系统可被认为是一个受外界干扰的线性不确定时滞系统.本文首先设计了标称系统下的鲁棒输出反馈动态控制器,以改善闭环系统的动静态性能;其次,在系统不需要满足不确定性匹配条件的情况下,将参数和外部扰动不确定性综合考虑.应用Lyapunov稳定性理论设计了系统不确定性上界参数的自适应估计器和系统的自适应控制器,保证了闭环系统的渐近稳定性,减小了设计的保守性;两者结合实现了板带出口厚度的有效控制.最后通过一个仿真实例说明本文所提出的自适应鲁棒控制器的有效性.     

Hybrid control for speed sensorless induction motor drive

The dynamic response of a hybrid-controlled speed sensorless induction motor (IM) drive is introduced. First, an adaptive observation system, which comprises speed and flux observers, is derived on the basis of model reference adaptive system (MRAS) theory. The speed observation system is implemented using a digital signal processor (DSP) with a high sampling rate to make it possible to achieve good dynamics. Next, based on the principle of computed torque control, a computed torque controller using the estimated speed signal is developed. Moreover, to relax the requirement of the lumped uncertainty in the design of a computed torque controller, a recurrent fuzzy neural network (RFNN) uncertainty observer is utilized to adapt the lumped uncertainty online. Furthermore, based on Lyapunov stability a hybrid control system, which combines the computed torque controller, the RFNN uncertainty observer and a compensated controller, is proposed to control the rotor speed of the sensorless IM drive. The computed torque controller with RFNN uncertainty observer is the main tracking controller and the compensated controller is designed to compensate the minimum approximation error of the uncertainty observer instead of increasing the rules of the RFNN. Finally, the effectiveness of the proposed observation and control systems is verified by simulated and experimental results     

一类多不确定性系统鲁棒H∞控制器的LMI设计方法

对同时具有加型参数不确定性以及积分二次约束(IQC,integral quadratic constraint) 不确定性环节的一类线性系统,给出设计其鲁棒H∞状态反馈控制器和动态输出反馈降阶控制 器的设计方法.在具体推导过程中,首先基于动态耗散理论,考虑了无输入情况下系统只具不 确定性闭环环节时的鲁棒H∞稳定性问题.然后基于这一条件,针对典型的无源类和有限增益 类不确定性,推出了系统同时具有多不确定性时进行鲁棒H∞状态反馈控制器和动态输出反馈降 阶控制器设计的充分条件.所有可解条件都可化为标准的LMI(1inear matrix inequality)求解.     

基于非脆弱控制器设计的不确定模糊系统稳定性研究

研究不确定动态模糊系统的稳定性问题.提出一类不确定T-S动态模糊系统的非脆弱控制问题,并进行了控制器设计.首先给出不确定T-S动态模糊系统的模型;然后利用Lyapunov函数方法,研究连续不确定动态模糊系统的非脆弱控制器设计,得到基于LMI的不确定动态模糊系统的全局渐近稳定性条件.通过对一级倒立摆的不确定模糊非脆弱控制器设计的实例,表明了设计方法的可行性和有效性.     

Fuzzy Sliding Mode Control For Ship Roll Stabilization

A fuzzy sliding mode controller is proposed in this study for ship roll stabilization. Ship dynamic models usually contain large uncertainty. Sliding mode control is well known for its good robustness to large uncertainty. However, the required uncertainty bound is usually difficult to estimate. A fuzzy logic is designed here for the upper bound estimation of the uncertainty coming mostly from the wave excitation. As a result, the uncertainty‐related parameters in the sliding mode controller are automatically tuned by fuzzy logic according to the encountered wave amplitude. The present controller has the advantage that smaller control efforts are required for the anti‐capsizing purpose under the same sea states. A numerical example is investigated to confirm the analysis.     

大柔性飞行器的自适应姿态控制设计

研究系统存在不确定性的大柔性飞行器的姿态跟踪控制问题.针对高阶大柔性飞行器模型,使用平衡实现方法对其降阶,并通过奇异值对比分析系统降阶前后特性.基于降阶模型,设计LQR-PI控制器作为基线控制器.考虑不确定性,利用李雅普诺夫稳定性理论设计模型参考自适应控制器,并对比两种方法的控制效果.仿真结果显示,所提方案对包含不确定性的系统具有较好的控制效果,能使系统完成期望的姿态跟踪目标.     

网络化控制系统中鲁棒控制器的设计与优化

针对网络化控制系统,提出了新型的延迟状态变量模型,考虑到模型的不确定因素和外 部扰动,推出了鲁棒控制器存在的条件,并给出了该控制器设计和性能优化的方法。仿真结果表明, 该控制器对所有允许的网络延迟、模型不确定性和外部扰动,具有良好的性能。     

Neural-network hybrid control for antilock braking systems

The antilock braking systems are designed to maximize wheel traction by preventing the wheels from locking during braking, while also maintaining adequate vehicle steerability; however, the performance is often degraded under harsh road conditions. In this paper, a hybrid control system with a recurrent neural network (RNN) observer is developed for antilock braking systems. This hybrid control system is comprised of an ideal controller and a compensation controller. The ideal controller, containing an RNN uncertainty observer, is the principal controller; and the compensation controller is a compensator for the difference between the system uncertainty and the estimated uncertainty. Since for dynamic response the RNN has capabilities superior to the feedforward NN, it is utilized for the uncertainty observer. The Taylor linearization technique is employed to increase the learning ability of the RNN. In addition, the on-line parameter adaptation laws are derived based on a Lyapunov function, so the stability of the system can be guaranteed. Simulations are performed to demonstrate the effectiveness of the proposed NN hybrid control system for antilock braking control under various road conditions.     

一类不确定时滞奇异系统的鲁棒非脆弱控制

针对不确定奇异时滞系统，研究了鲁棒非脆弱控制问题。假定不确定性范数有界，设计了基于观测器的控制器，使得闭环系统在不确定性影响下保持鲁棒稳定。仅通过求解相应线性矩阵不等式就可得到鲁棒状态反馈控制器，该控制器不仅对所有容许的系统不确定性使相应的闭环系统渐近稳定，而且满足控制器本身是非脆弱的，达到抑制干扰的效果。     

基于RBF网络的永磁同步电机扰动衰减和速度跟踪

针对永磁同步电机伺服系统速度控制问题,引入削减系统抖振的饱和函数,提出一种解决不确定环境下电机伺服控制系统的速度跟踪控制器。借助RBF网络自适应估计系统中的不确定项,综合反步设计法和滑模控制法的思想,设计控制器。理论分析获证,该受控系统是李亚普诺夫稳定的。数值实验表明,所获控制方案能削弱系统的不确定性干扰,系统输出跟踪能力强。     

Sampled-data controller design for uncertain systems

Presents a sampled-data controller design methodology for uncertain systems. A continuous system with bounded time-varying uncertainty is sampled at intervals of length T. The controller is designed using a Riccati equation approach by neglecting O(T²) uncertainty terms in the discretized system. Stability is verified for this choice of T with the U(T²) terms included. If there exists a stabilizing continuous controller, then there also exists a stabilizing sampled-data controller for a sufficiently small choice of T     

Robust near-optimal output feedback control of non-linear systems

This work proposes a robust near-optimal non-linear output feedback controller design for a broad class of non-linear systems with time-varying bounded uncertain variables. Both vanishing and non-vanishing uncertainties are considered. Under the assumptions of input-to-state stable (ISS) inverse dynamics and vanishing uncertainty, a robust dynamic output feedback controller is constructed through combination of a high-gain observer with a robust optimal state feedback controller synthesized via Lyapunov's direct method and the inverse optimal approach. The controller enforces exponential stability and robust asymptotic output tracking with arbitrary degree of attenuation of the effect of the uncertain variables on the output of the closed-loop system, for initial conditions and uncertainty in arbitrarily large compact sets, provided that the observer gain is sufficiently large. Utilizing the inverse optimal control approach and singular perturbation techniques, the controller is shown to be near-optimal in the sense that its performance can be made arbitrarily close to the optimal performance of the robust optimal state feedback controller on the infinite time-interval by selecting the observer gain to be sufficiently large. For systems with non-vanishing uncertainties, the same controller is shown to ensure boundedness of the states, uncertainty attenuation and near-optimality on a finite time-interval. The developed controller is successfully applied to a chemical reactor example.     

Nonsingular terminal sliding mode control of nonlinear second‐order systems with input saturation

This paper considers the nonsingular terminal sliding mode (TSM) controller design for a nonlinear second‐order system subject to input saturation. A new nonsingular TSM manifold is constructed by integrating the conventional nonsingular TSM manifold with a saturation function. When the bound of the uncertainty is known, based on the designed TSM manifold, a saturated controller can be designed directly for the nonlinear system. When the bound of the uncertainty is unknown, a disturbance observer is first employed to estimate the uncertainty, followed by constructing a composite controller consisting of a bounded feedback controller and a forward compensator. Theoretical analysis shows that under the proposed two control methods, the states of the closed‐loop system will both converge to zero in finite time. Simulation results demonstrate the effectiveness of the proposed methods. Copyright © 2015 John Wiley & Sons, Ltd.     

Feedback linearization control design for systems with fuzzyuncertainty

We derive a state feedback control design for nonlinear systems with fuzzy uncertainty. We use a fuzzy version of the Kolmogorov forward equation and an equivalent deterministic system to represent the effects of the fuzzy uncertainty. Feedback linearization of the equivalent deterministic system cancels both the system nonlinearities and the effects of the fuzzy uncertainty on the state membership function. Our controller obtains asymptotic stability and an approximation to our controller drives the system state to a small bounded set     

基于PI 控制器的线性系统的鲁棒耗散控制

针对参数具有确定性及不确定性的连续系统,给出两种严格耗散PI控制器的设计方法.首先,系统参数确定时,采用线性矩阵不等式方法,导出了类状态反馈和静态输出反馈严格耗散PI控制器存在的充要条件,并由线性矩阵不等式的可行解构造出严格耗散PI控制器增益的显式表达式;然后,考虑系数矩阵均具有范数有界不确定性时的鲁棒严格耗散控制问题,得到相似的结果;最后,通过数值算例表明了所给方法的有效性.     

Robust dissipative control for linear systems with dissipative uncertainty and nonlinear perturbation

This paper focuses on the problem of dissipative control for linear systems which are subjected to dissipative uncertainty and matched nonlinear perturbation. Specifically, quadratic dissipative uncertainty is considered, which contains norm-bounded uncertainty, positive real uncertainty and uncertainty satisfying integral quadratic constraints (IQCs) as special cases. We develop a linear matrix inequality (LMI) approach for designing a robust nonlinear state feedback controller such that the closed-loop system is quadratic dissipative for all admissible uncertainties. Furthermore, under some condition on the dissipative uncertainty, we show that the controller also guarantees the asymptotic stability of the closed-loop system. As special cases, robust H_∞ control and robust passive control problems for systems with nonlinear perturbation and norm-bounded uncertainty (respectively, generalized positive real uncertainty) are solved using the LMI approach.