A study of robust controller and observer design method for a rolling object and beam system

This paper deals with a robust control problem for a ball and beam system with an uncertainty. At first, we clarify the effect of a measurement error in the beam rotational angle and its differential value. It is expressed as additional terms in the state and input matrix of the state equation, which is called as a structured uncertainty. For this system, a robust tracking controller and a robust state observer are applied. Both components are designed based on a robust control, which is called guaranteed cost control. This is a kind of cost minimization method for designing problem of a linear feedback system. The controller is obtained as the solution of the matrix algebraic Riccati like equation, which is referred to as stochastic algebraic Riccati equation. The nominal system performance is degraded due to the influence of the uncertainty, but it is able to design a system with robustness for disturbance. Next, we consider the design problem of a state observer to estimate all state variables form the output signal easy to measure, like rotation angle of the beam. For the design problem of the state observer, we consider dual problem of the original system. Consequently, our proposed system estimates the whole state vector, and using estimated state values, it controls the ball to the desired position. Both components have robustness for the uncertainty. Numerical result shows the validity of our proposed method.     

A systematic approach for robust repetitive controller design

In this paper, a methodology for the synthesis of repetitive controllers to ensure periodic reference tracking and harmonic disturbance rejection is cast in a robust control framework. Specifically, the Lyapunov–Krasovskii theory is applied to derive LMI-based conditions for designing a state feedback control law with guaranteed stability and performance properties for system parameter variations. Practical experiments in commercial uninterruptible power supplies – UPS are considered to illustrate and discuss some practical implementation aspects of the proposed method.     

Adaptive fuzzy robust tracking controller design via small gain approach and its application

An adaptive fuzzy robust tracking control (AFRTC) algorithm is proposed for a class of nonlinear systems with the uncertain system function and uncertain gain function, which are all the unstructured (or nonrepeatable) state-dependent unknown nonlinear functions arising from modeling errors and external disturbances. The Takagi-Sugeno type fuzzy logic systems are used to approximate unknown uncertain functions and the AFRTC algorithm is designed by use of the input-to-state stability approach and small gain theorem. The algorithm is highlighted by three advantages: 1) the uniform ultimate boundedness of the closed-loop adaptive systems in the presence of nonrepeatable uncertainties can be guaranteed; 2) the possible controller singularity problem in some of the existing adaptive control schemes met with feedback linearization techniques can be removed; and 3) the adaptive mechanism with minimal learning parameterizations can be obtained. The performance and limitations of the proposed method are discussed. The uses of the AFRTC for the tracking control design of a pole-balancing robot system and a ship autopilot system to maintain the ship on a predetermined heading are demonstrated through two numerical examples. Simulation results show the effectiveness of the control scheme.     

Energy-based robust controller design for flexible spacecraft

This paper presents a class of non-model2based position controllers for a kind of flexible spacecraft. With the controllers, one can achieve not only the closed-loop stability of the original distributed parameter system, but also the asymptotic stability of the truncated system, which is obtained through representing the deflection of the appendage by an arbitrary finite number of flexible modes. The system dynamics are not explicitly involved in the controller design and stability proof. Instead, only a very basic system energy rehtionship of the flexible spacecraft is utilized. The controllers possess several remarkable advantages over the traditional model-based ones. Numerical simulations are carried out on a kind of spacecraft with one flexible appendage and satisfactory results are obtained.     

A robust adaptive performance enhancement controller using setmembership identification

A robust direct adaptive control scheme is proposed to enhance the performance of a fixed nominal controller. The key idea lies in the introduction of a set membership constraint in the estimation process. The set membership constraint results in an adaptive scheme that has a built-in discriminator to discard incoming data that carry little or no information content on the actual plant. The proposed scheme, which uses only informative data to refine the parameter estimates, is more robust than conventional methods that continuously update the parameter estimates     

Tuning an adaptive controller using a robust control approach

This article proposes a new technique for the tuning of a discrete adaptive controller that is designed based on Lyapunov stability concepts. The tuning is based on the minimisation of a performance index that can be calculated from a generalised eigenvalue problem (GEVP) using LMI's (Linear Matrix Inequalities). The proposed technique results in an adaptive controller with time-varying tuning gains. The solution is based on an approximation of the optimal dual adaptive control problem. The tuning technique was used to perform on-line control of a first-order system and an isothermal and a non-isothermal CSTR. The results show that the proposed approach provides better performance than an adaptive algorithm with the same structure, but with constant adaptation gains. Also, the proposed algorithm is shown to be superior to an adaptive controller based on a Recursive Least Squares (RLS) estimator during sudden changes in model parameters.     

Design of a discrete robust controller using a first-order model approximation

In this paper, a discrete controller with integral action is designed for a linear time invariant stable process based upon a first-order model approximation. Sufficient conditions in the form of simple inequalities are derived to ensure asymptotic stability. It is shown that this condition becomes both necessary and sufficient in the special case where the control interval approaches the open-loop settling time. The stability criterion is a closed-form inequality equation that is well suited for real-time calculation of the admissible controller parameter space.     

A robust direct adaptive controller

This paper proposes a new direct adaptive control algorithm which is robust with respect to additive and multiplicative plant unmodeled dynamics. The algorithm is designed based on the reduced-order plant, which is assumed to be minimum phase and of known order and relative degree, but is analyzed with respect to the overall plant which, due to the unmodeled dynamics, may be nonminimum phase and of unknown order and relative degree. It is shown that if the unmodeled dynamics are sufficiently small in the low-frequency range, then the algorithm guarantees boundedness of all signals in the adaptive loop and "small" residual tracking errors for any bounded initial conditions. In the absence of unmodeled dynamics, the residual tracking error is shown to be zero.     

An ellipsoid algorithm for probabilistic robust controller design

In this paper, a new iterative approach to probabilistic robust controller design is presented, which is applicable to any robust controller/filter design problem that can be represented as an LMI feasibility problem. Recently, a probabilistic Subgradient Iteration algorithm was proposed for solving LMIs. It transforms the initial feasibility problem to an equivalent convex optimization problem, which is subsequently solved by means of an iterative algorithm. While this algorithm always converges to a feasible solution in a finite number of iterations, it requires that the radius of a non-empty ball contained into the solution set is known a priori. This rather restrictive assumption is released in this paper, while retaining the convergence property. Given an initial ellipsoid that contains the solution set, the approach proposed here iteratively generates a sequence of ellipsoids with decreasing volumes, all containing the solution set. At each iteration a random uncertainty sample is generated with a specified probability density, which parameterizes an LMI. For this LMI the next minimum-volume ellipsoid that contains the solution set is computed. An upper bound on the maximum number of possible correction steps, that can be performed by the algorithm before finding a feasible solution, is derived. A method for finding an initial ellipsoid containing the solution set, which is necessary for initialization of the optimization, is also given. The proposed approach is illustrated on a real-life diesel actuator benchmark model with real parametric uncertainty, for which a robust state-feedback controller is designed.     

A robust stochastic adaptive controller

The adaptive tracking problem is considered for discrete-time stochastic systems consisting of a modeled part being a stable ARMAX process and unmodeled dynamics dominated by a small constant ϵ multiplied by a quantity independent of ϵ but tending to infinity as the past input, output, and noise grow. The adaptive control law proposed is switched at stopping times and is disturbed by a sequence of random vectors bounded by an arbitrary small but fixed constant σ. It is shown that the closed-loop system is globally stable, the estimation errors for parameters contained in the modeled part of the order ϵ, and the tracking error differs from the minimum tracking error for systems without unmodeled dynamics by value of O(ϵ² )+O(σ²)     

A robust adaptive tracking controller using neural networks for a class of nonlinear systems

A neural networkbased robust adaptive tracking control scheme is proposed for a class of nonlinear systems. It is shown that, unlike most neural control schemes using the back-propagation training technique, one hidden layer neural controller is designed in the Lyapunov sense, and the parameters of the neural controller are then adaptively adjusted for the compensation of unknown dynamics and nonlinearities. Using this scheme, not only strong robustness with respect to unknown dynamics and nonlinearities can be obtained, but also asymptotic error convergence between the plant output and the reference model output can be guaranteed. A simulation example based on a one-link non-linear robotic manipulator is given in support of the proposed neural control scheme.     

A simple robust PI/PID controller design via numerical optimization approach

This paper presents a simple but effective method for designing robust PI or PID controller. The robust PI/PID controller design problem is solved by the maximization, on a finite interval, of the shortest distance from the Nyquist curve of the open loop transfer function to the critical point-1. Simulation studies are used to demonstrate the effectiveness of the proposed method.     

Reducing conservatism in the design of a robust gain-scheduled controller for non-linear chemical processes

A robust control approach has been used to design gain-scheduled controllers, which guarantee closed-loop stability and performance. The inherent conservatism of robust control results in smaller ranges of parameters that satisfy the design criteria and consequently in degraded performance. The main focus of this paper is to reduce the conservatism to enhance the efficiency of the robust design method. Two approaches, the use of parameter-dependent Lyapunov condition and calculation of saturation factor bounds, are proposed to reduce the conservatism of the controller design.     

鲁棒后退时域控制中HJI方程的数值解法及控制器设计

本文讨论了由不确定非线性系统鲁棒后退时域控制(robust receding horizon control,RRHC)策略导出的Hamilton-Jacobin-Isaac(HJI)方程的求解,提出了一种新的带反曲变换的有限差分算法计算值函数,所提出算法对HJI方程的求解是一种稳定且收敛的算法.同时提出基于边界值迭代的加速过程,加速优化问题的求解,在花费更少计算时间的前提下,提高计算精度.所求得的值函数可直接应用于一类不确定非线性系统鲁棒后退时域控制器的设计,在控制器设计中,传统鲁棒后退时域控制策略中的有限时域被扩展到无限时域,求得的控制器可实时实现,避免对初始点可解性的依赖以及反复在线优化问题.     

A noniterative method for the design of linear robust controllers

A procedure for determining a linear control law which guarantees asymptotic stability for an uncertain system is derived. Using an elementary matrix identity, an alternative proof of the existence of stabilizing control law for the matched case is provided. Bounds for the rates of decay are established, and by using these bounds it is shown that every trajectory of the closed-loop system can be made to decay at a prespecified exponential rate. The technique is simpler to use than existing techniques since it does not require a numerical procedure, but allows the control law to be obtained from some simple formulas     

Decentralized robust PI controller design for an industrial boiler

This paper presents a new scheme to design decentralized robust PI controllers for uncertain LTI multivariable systems. Sufficient conditions for closed-loop stability and closed-loop diagonal dominance (almost decoupling) of a multivariable system are obtained. Satisfying these conditions and robust performance of the overall system are modeled as local robust performance problems. Then, by appropriately selecting the time constants of the closed-loop isolated subsystems in the IMC (Internal Model Control) strategy, the defined local robust performance problems are solved. To design a decentralized robust PI controller for a real industrial utility boiler, a control oriented nonlinear model for the boiler is identified. The nonlinearity of the system is modeled as uncertainty for a nominal LTI multivariable system. Using the new proposed method, a decentralized PI controller for the uncertain LTI model is designed. The designed controller is applied to the real system. The simulation results show the effectiveness of the proposed methodology.     

Numerical optimization method for HJI equations derived from robust receding horizon control schemes and controller design

This paper addresses how to numerically solve the Hamilton-Jacobin-Isaac(HJI)equations derived from the robust receding horizon control schemes.The developed numerical method,the finite dierence scheme with sigmoidal transformation,is a stable and convergent algorithm for HJI equations.A boundary value iteration procedure is developed to increase the calculation accuracy with less time consumption.The obtained value function can be applied to the robust receding horizon controller design of some kind of uncertain nonlinear systems.In the controller design,the finite time horizon is extended into the infinite time horizon and the controller can be implemented in real time.It can avoid the on-line repeated optimization and the dependence on the feasibility of the initial state which are encountered in the traditional robust receding horizon control schemes.     

A method for a robust optimization of joint product and supply chain design

This paper proposes a method for finding a robust solution to the problem of joint product family and supply chain design. Optimizing product design and the supply chain network at the same time brings substantial benefits. However, this approach involves decisions that can generate uncertainties in the long term. The challenge is to come up with a method that can adapt to most possible environments without straying too far from the optimal solution. Our approach is based on the generation of scenarios that correspond to combinations of uncertain parameters within the model. The performance of designs resulting from these scenario optimizations are compared to the performance of each of the other design scenarios, based on their probability of occurrence. The proposed methodology will allow practitioners to choose a suitable design, from the most profitable to the most reliable.     

基于直接状态空间理论的H∞鲁棒控制器设计方法及实例

鲁棒性是系统的重要性能指标。H∞鲁棒控制能够解决系统存在不确定性时的鲁棒性问题。一般的H∞鲁棒控制器设计方法的计算量偏大。基于直接状态空间理论，通过无迭代的求解两个Riccati方程得到具有鲁棒性的控制器，从而解决了计算量偏大的问题。最后讨论了H∞控制理论的应用。