Global robust output regulation for a class of nonlinear systems

The problem of global robust output regulation is solved for a class of nonlinear systems driven by a linear neutrally stable exosystem. The proposed scheme makes use of a dynamic controller which processes information from the regulated error only. Robust regulation is achieved for every initial condition in the state space, and for all possible values of the uncertain parameter vector and the exogenous signal ranging over arbitrary compact sets. The regulator synthesis is based upon a recursive procedure, and takes advantage of both the special normal form of the plant equations and the passivity property of the internal model.     

Global nonlinear output regulation: Convergence-based controller design

In this paper we present output-feedback controllers solving the global output regulation problem for a class of nonlinear systems. The proposed controllers are based on the notion of convergent systems. The presented solution extends well-established results on the linear output regulation problem and the local nonlinear output regulation problem to the global case. For Lur’e systems, which are not necessarily in the output-feedback form, the proposed controllers can be found by solving the regulator equations and certain linear matrix inequalities. For systems in the output-feedback form with uncertain parameters and uncertain nonlinearities we provide a robust regulator that does not rely on the minimum phaseness assumption on the system, which is crucial in the previous regulator designs for output-feedback systems. The results are illustrated by examples.     

Matched disturbance suppression for nonlinear systems stabilizable by logic-based feedback

We focus on a class of nonlinear systems that can be stabilized at a desired compact set by means of logic-based continuous feedback and we show how to design regulators that are robust to matched exosystem-generated disturbances. The proposed design methodology, of interest also for purely continuous-time systems, combines recent advances in the field of hybrid control systems and output regulation for nonlinear systems. As an illustrative example, the problem of global stabilization of a 6-DOF rigid body affected by a force periodic disturbance of uncertain amplitude, phase and frequency is presented.     

Implicit fault-tolerant control: application to induction motors

In this paper we propose an innovative way of dealing with the design of fault-tolerant control systems. We show how the nonlinear output regulation theory can be successfully adopted in order to design a regulator able to offset the effect of all possible faults which can occur and, in doing so, also to detect and isolate the occurred fault. The regulator is designed by embedding the (possible nonlinear) internal model of the fault. This idea is applied to the design of a fault-tolerant controller for induction motors in presence of both rotor and stator mechanical faults.     

Semi-global robust output regulation of minimum-phase nonlinear systems based on high-gain nonlinear internal model

We consider the assumption of existence of the general nonlinear internal model that is introduced in the design of robust output regulators for a class of minimum-phase nonlinear systems with rth degree (r ≥ 2). The robust output regulation problem can be converted into a robust stabilisation problem of an augmented system consisting of the given plant and a high-gain nonlinear internal model, perfectly reproducing the bounded including not only periodic but also nonperiodic exogenous signal from a nonlinear system, which satisfies some general immersion assumption. The state feedback controller is designed to guarantee the asymptotic convergence of system errors to zero manifold. Furthermore, the proposed scheme makes use of output feedback dynamic controller that only processes information from the regulated output error by using high-gain observer to robustly estimate the derivatives of the regulated output error. The stabilisation analysis of the resulting closed-loop systems leads to regional as well as semi-global robust output regulation achieved for some appointed initial condition in the state space, for all possible values of the uncertain parameter vector and the exogenous signal, ranging over an arbitrary compact set.     

A reduction paradigm for output regulation

The goal of this paper is to provide a reduction paradigm for the design of output regulators which can be of interest for nonlinear as well as linear uncertain systems. The main motivation of the work is to provide a systematic design tool to deal with non‐minimum‐phase uncertain systems for which conventional high‐gain stabilization methods are not effective. The contribution of the work is two‐fold. First, this work extends a previous reduction paradigm for output regulation of nonlinear systems. Furthermore, in the case of the uncertain controlled dynamics being linear, we show how the proposed framework leads to a number of systematic design tools of interest for non‐minimum‐phase linear systems affected by severe uncertainties. A numerical control example of a linearized model of an inverted pendulum on a cart is presented. Copyright © 2007 John Wiley & Sons, Ltd.     

Synchronisation control of electric motors through adaptive disturbance cancellation

A master–slave synchronisation control problem is addressed for current-fed DC and permanent magnet synchronous motors with all uncertain parameters. A measurable exogenous rotor position reference signal, which belongs to the class of biased sinusoidal signals with uncertain bias, amplitude, angular frequency, phase, is to be tracked without assuming its a priori knowledge. An innovative modification of disturbance cancellation techniques allows to prove that an output feedback adaptive nonlinear control scheme, which simply generalises the classical internal-model-based input law, solves the aforementioned problem, with an overall stability proof concerning the entire closed-loop system. The practical effectiveness of the proposed approach is illustrated by experimental results.     

Vibration Reduction of a Harmonically Excited Beam with One-sided Spring Using Sliding Computed Torque Control

Vibration reduction of a harmonically excited multi Degree of Freedom (DOF) beam system with a local nonlinearity represented by a one-sided spring is considered. The linear beam system is modeled with a 3-DOF model which is obtained by applying a component mode synthesis method on the linear finite element model of the beam system. The low frequency response of the linear system can be described very accurately while the number of DOFs for the nonlinear analysis is kept small. Vibration reduction is realized in both simulations and experiments by forcing the system at a prescribed excitation frequency from the stable 1/2 subharmonic response of high amplitude towards the coexisting unstable harmonic response of low amplitude using a Sliding Computed Torque Controller (SCTC). The advantage besides the reduction of vibration amplitude is the small control effort needed once the unstable harmonic solution is stabilized. This is due to the fact that the unstable harmonic solution is a natural solution of the uncontrolled system.     

A global state feedback output regulating control for uncertain systems in strict feedback form

A family of single-input, single-output, nonlinear systems in strict feedback form with uncertain constant parameters which appear linearly and belong to a known compact set Π is considered. A global robust output regulation problem via state feedback is addressed and solved under the assumptions that the regulator equations are solvable in Π, the output equation does not depend on uncertain parameters, no modelled disturbances affect the system and the output reference signal is generated by a known exosystem whose state is bounded and available for feedback. Robust adaptive techniques are used to guarantee closed loop boundedness and to achieve, without requiring persistency of excitation, global asymptotic output regulation for a class of feedback linearizable systems which may have unbounded uncertain tracking dynamics or may not have a well-defined global relative degree.     

Limit cycle computation for describing function approximable nonlinear systems with box‐constrained parametric uncertainties

We propose an algorithm to compute the limit cycle set of uncertain non‐rational nonlinear systems with nonlinear parametric dependencies. The proposed algorithm computes the limit cycles for a wide class of uncertain nonlinear systems, where the transfer function of the linear element and describing function of the nonlinear element need to be only continuous with respect to the parameters and continuously differentiable with respect to the amplitude and frequency of periodic input signal. The proposed algorithm guarantees that the limit cycles are reliably computed to a prescribed accuracy, and that none of the actual limit cycle point is missed out irrespective of the tightness of the prescribed accuracy. Moreover, for a prescribed accuracy, the proposed algorithm computes all the limit cycles in a finite number of iterations, and an upper bound for this number is also computable. The algorithm is demonstrated on a challenging non‐rational example with nonlinear parametric dependencies. Copyright © 2005 John Wiley & Sons, Ltd.     

Adaptive Output Regulation of a Class of Nonlinear Output Feedback Systems With Unknown High Frequency Gain

This paper presents an output feedback design approach based on the adaptive control scheme developed for nonlinearly parameterized systems, to achieve global output regulation for a class of nonlinear systems in output feedback form. We solve the output regulation problem without the knowledge of the sign and the value of the high frequency gain a priori. It is not necessary to have both the limiting assumptions that the exogenous signal ω and the unknown parameter μ belong to a prior known compact set and the high frequency gain has a determinate lower and upper bounds. The effectiveness of the proposed algorithm is shown with the help of an example.      

柴油发电机组非线性H2/H∞调速器的研究

船舶电力系统频率的稳定性主要取决于船舶电站柴油机调速系统的转速响应特性. 船舶电站柴油机调速系统是一个非线性控制系统, 为了分析系统的动态特性, 首先建立柴油机调速系统的非线性数学模型, 然后以此为基础设计非线性H2/H∞速器. 将直接反馈线性化和混合H2/H∞控制理论相结合应用于柴油发电机组调速器的设计,把系统的性能要求转化为标准H2/H∞控制问题, 获得了柴油机非线性H2/H∞转速控制律. 计算机仿真结果表明, 设计的非线性H2/H∞调速器有效地提高了系统的动态精度和抑制扰动的能力, 改善了船舶电力系统频率的稳定性.     

一类非线性系统鲁棒自适应控制器

反步设计法是针时不确定非线性系统的进行鲁棒自适应控制器设计的主要方法之一,它主要是靠递推来完成,方法简单,但存在过参数化问题.在反步设计法的基础上,通过引入调节函数,选取合适的虚拟控制律,设计一种鲁棒自适应控制器.然后,利用Lyapunov稳定性理论证明了该设计不仅能够克服过参数化的问题,而且能够保证所设计的系统具有鲁棒自适应稳定性.仿真实例证明了该方法的有效性.     

Asymptotic harmonic generator and its application to finite time orbital stabilization of a friction pendulum with experimental verification

A second order sliding mode approach to orbital stabilization is presented and tested on a friction pendulum, operating under uncertain conditions. The quasihomogeneous control synthesis is utilized to design a variable structure controller that drives the pendulum to a model orbit in finite time in spite of the presence of external disturbances with an a priori known magnitude bound. A well-known Van der Pol oscillator is modified to be introduced into the synthesis as a reference model. This modification is made to shape the oscillator limit cycle to a harmonic one, thereby yielding an asymptotic harmonic generator of the periodic motion. The parameters of the asymptotic harmonic generator are shown to specify amplitude and frequency of the limit cycle production and damping of non-linear oscillations of the generator. The resulting closed-loop system is capable of moving from one orbit to another by changing these parameters dynamically. Performance issues of the controller constructed are illustrated in an experimental study.     

具有自适应内模的一类非线性系统输出调节问题

研究一类包含未知非线性项的非线性系统的鲁棒输出调节问题.此类非线性系统由一包含未知参数的线性中性稳定的外系统驱动.首先运用调节器方程组解和标准内模将输出调节问题转化为镇定问题;然后给出控制律镇定闭环系统,同时利用镇定输入项和外系统信息设计出自适应内模方程.控制律使得闭环系统的信号全局最终有界,且误差被调节至预先设定的任意小的精度值.仿真结果验证了所提出设计方法的有效性.     

用谐波-能量平衡法求解单摆方程

应用谐波—能量平衡法求解了强非线性单摆方程,谐波-能量平衡法与经典的摄动法和谐波平衡法不同,不是把微分方程和初始条件分离处理;而是把微分方程和初始条件同时处理.用谐波平衡,将描述动力系统的二阶常微分方程,化为以角频率、振幅为变量的非线性代数方程组,考虑能量平衡,构成角频率、振幅为变量的封闭方程组求得解析解.谐波-能量平衡法将谐波平衡与能量平衡相结合,克服了二者的缺点吸取了二者的优点.实例表明,谐波-能量平衡法方法简单,取较少谐波就可以达到较高的精度.     

A backstepping high-order sliding mode voltage control strategy for an islanded microgrid with harmonic/interharmonic loads

This paper presents a new nonlinear voltage control strategy based on backstepping control and a high-order sliding mode differentiator for an islanded microgrid. The microgrid consists of multiple distributed generation (DG) units with an arbitrary configuration that can be parametrically uncertain or topologically unknown. The proposed controller robustly regulates the microgrid voltages in the presence of parametric uncertainties, unmodeled dynamics, load imbalances, and nonlinear loads with harmonic/interharmonic currents. In contrast to existing methods, the controller does not need to know the frequency of harmonic and interharmonic current of microgrid loads that lead to the reduction of the steady-state error of the voltage controller in the frequency of unknown harmonics and interharmonics. The MATLAB/SimPowerSystems toolbox has verified the proposed control strategy's performance.     

Nonlinear robust state feedback control system design for nonlinear uncertain systems

This paper presents a systematic approach to the design of a nonlinear robust dynamic state feedback controller for nonlinear uncertain systems using copies of the plant nonlinearities. The technique is based on the use of integral quadratic constraints and minimax linear quadratic regulator control, and uses a structured uncertainty representation. The approach combines a linear state feedback guaranteed cost controller and copies of the plant nonlinearities to form a robust nonlinear controller with a novel control architecture. A nonlinear state feedback controller is designed for a synchronous machine using the proposed method. The design provides improved stability and transient response in the presence of uncertainty and nonlinearity in the system and also provides a guaranteed bound on the cost function. An automatic voltage regulator to track reference terminal voltage is also provided by a state feedback equivalent robust nonlinear proportional integral controller. Copyright © 2016 John Wiley & Sons, Ltd.     

多频激励磁悬浮能量采集

研究多频激励下磁力悬浮非线性磁电能量器采集系统的动力学特性.结合谐波平衡法、牛顿迭代法和弧长延伸法近似分析非线性电力耦合的常微分方程组,研究多简谐频激励下系统的非线性稳态幅频响应特征.通过改变激励的频率,研究磁力悬浮非线性振动能量采集器的幅频特性.研究结果表明,多频激励的稳态幅频响应随非线性系数的增大而位移幅频响应的共振峰变小但带宽变宽.另外,还通过对比电学参数对共振响应幅度以及区域的影响,确定了电阻、电感和耦合系数对增强两个共振强度、扩大两个共振区域,也就是提高能量采集的强度和带宽的影响.数值模拟验证了近似解析分析结果.     

Gain scheduled controllers for dynamic systems using sector nonlinearities

In this work we explore the use of gain scheduling for the control of nonlinear systems. The nonlinear system is represented locally by uncertain linear models using sector nonlinearities representation. The uncertain linear models are then used to design a family of robust controllers. We propose a gain scheduling procedure for the problem of guaranteed transition from an actual operating condition to a desired one by constructing a pre-specified path in the state space for the system operating points. As far as we know this problem has not been addressed before. The gain scheduling control procedure given is illustrated in the context of the regulator problem with state feedback.