Precision preview-based stable-inversion for nonlinear nonminimum-phase systems: The VTOL example

This article quantifies the importance of the future desired trajectory in determining the exact-output-tracking input for nonlinear, nonminimum-phase systems by using system inversion techniques. It is intuitive that the effect of the desired output's distant-future values, on the output-tracking input at the current time instant, should be small. Therefore, at a current time instant (t_c), preview information of the desired output in a finite-time window [t_c,t_c+T_p] should be sufficient to compute the output-tracking input with an arbitrarily small prescribed error, if the preview time T_p is sufficiently large. The contribution of this article is the quantification of the needed preview time T_p by using the benchmark VTOL aircraft model as an example. Additionally, simulation results are presented to evaluate the efficacy of the finite-preview-based stable-inversion approach.     

ISE-optimal nonminimum-phase compensation for nonlinear processes

This work concerns the optimal regulation of single-input–single-output nonminimum-phase nonlinear processes. The problem of calculation of an ISE-optimal, statically equivalent, minimum-phase output for nonminimum-phase compensation is formulated using Hamilton–Jacobi theory and the normal form representation of the nonlinear system. A Newton–Kantorovich iteration is developed for the solution of the pertinent Hamilton–Jacobi equations, which involves solving a Zubov equation at each step of the iteration. The method is applied to the problem of controlling a nonisothermal CSTR with Van de Vusse kinetics, which exhibits nonminimum-phase behaviour.     

Optimal tracking control for nonlinear large-scale systems with persistent disturbances

This paper studies the optimal control with zero steady-state error problem for nonlinear large-scale systems affected by external persistent disturbances. The nonlinear large-scale system is transformed into N nonlinear subsystems with interconnect terms. Based on the internal model principle, a disturbance compensator is constructed such that the ith subsystem with external persistent disturbances is transformed into an augmented subsystem without disturbances. According to the sensitivity approach, the optimal tracking control law for the ith nonlinear subsystem can be obtained. The optimal tracking control law for the nonlinear large-scale systems can be obtained. A numerical simulation shows that the method is effective.     

带有持续扰动的时滞非线性大系统的最优跟踪控制

研究具有外界持续扰动的时滞非线性大系统的无静差最优跟踪控制问题.将时滞非线性大系统分解为带有互联项的N个时滞非线性子系统,基于内模原理对子系统构造扰动补偿器,将带有外部持续扰动的子系统化为无扰动的增广系统.通过灵敏度法求解不含时滞的两点边值问题,得到子系统的最优跟踪控制律,截取最优跟踪控制律的前N项作为次优控制律来近似系统的最优控制律.仿真实例表明了该设计方法的有效性.     

时滞双线性系统的最优跟踪控制

研究带有时滞项的双线性系统的最优跟踪控制.依据求解规律转化成两点边值问题.通过采用迭代逐次逼近法,能够得到收敛与原系统最优控制律的序列.由于控制律含有外系统变量导致控制律物理不可实现,则采用状态重构解决这一问题.仿真结果表明该方法对解决这类问题有较好的鲁棒性及快速性.     

Optimal MPC for tracking of constrained linear systems

Model predictive control (MPC) is one of the few techniques which is able to handle constraints on both state and input of the plant. The admissible evolution and asymptotic convergence of the closed-loop system is ensured by means of suitable choice of the terminal cost and terminal constraint. However, most of the existing results on MPC are designed for a regulation problem. If the desired steady-state changes, the MPC controller must be redesigned to guarantee the feasibility of the optimisation problem, the admissible evolution as well as the asymptotic stability. Recently, a novel MPC has been proposed to ensure the feasibility of the optimisation problem, constraints satisfaction and asymptotic evolution of the system to any admissible target steady-state. A drawback of this controller is the loss of a desirable property of the MPC controllers: the local optimality property. In this article, a novel formulation of the MPC for tracking is proposed aimed to recover the optimality property maintaining all the properties of the original formulation.     

Adaptive output feedback consensus tracking for linear multi-agent systems with unknown dynamics

In this paper, the consensus tracking problem with unknown dynamics in the leader for the linear multi-agent systems is addressed. Based on the relative output information among the agents, decentralised adaptive consensus protocols with static coupling gains are designed to guarantee that the consensus tracking errors converge to a small neighbourhood around the origin and all the signals in the closed-loop dynamics are uniformly ultimately bounded. Moreover, the result is extended to the case with dynamic coupling gains which are independent of the eigenvalues of the Laplacian matrix. Both of the protocols with static and dynamic coupling gains are designed by using the relative outputs, which are more practical than the state-feedback ones. Finally, the theoretical results are verified through an example.     

Optimal output-transitions for linear systems

This article addresses the optimal (minimum-input-energy) output-transition problem for linear systems. The goal is to transfer the output from an initial value (for all time t?t_i) to a final output value (for all time t?t_f). Previous methods solve this output-transition problem by transforming it into a state-transition problem; the initial and final states (x(t_i),x(t_f), respectively) are chosen and a minimum-energy state-to-state transition problem is solved. However, the choice of the initial and final states can be ad hoc and the resulting output-transition cost (input energy) may not be minimal. The contribution of this article is the solution of the optimal output-transition problem. An example system with elastic dynamics is studied to illustrate the proposed method. Simulation results are presented that show substantial reduction of transition costs with the use of the proposed method when compared to the use of minimum-energy state-to-state transitions.     

Tracking in a class of nonminimum-phase systems with nonlinear internal dynamics via sliding mode control using method of system center

A method of asymptotic output tracking in a class of causal nonminimum-phase uncertain nonlinear systems is considered. Local asymptotic stability of output tracking-error dynamics are provided for the specified class of systems with the nonlinear hyperbolic at the origin internal dynamics forced by a reference output profile and external disturbances defined by a known linear exosystem. The nonlinear vector field of the internal dynamics is expanded in a power series, obtained at a selected operational point in the internal dynamics state space. The presented technique employs some linear algebraic methods and sliding mode control approach. The solution is a complete constructive algorithm.     

Observer-based optimal output tracking for discrete-time systems with multiple state and input delays

The optimal output tracking control (OOTC) problem for a class of discrete-time systems with state and input delays is addressed. An augmented system is constructed such that the OOTC problem can be transformed into a two-point boundary value (TPBV) problem with both advance and delay terms from the necessary optimality conditions. The successive approximating method recently developed is extended to obtain an approximate solution of the TPBV problem, which is then used to obtain a feedforward and feedback tracking controller. An observer is designed for the uncertain reference input such that the feedforward controller is physically realizable. Simulations show the results are effective even with long time-delays. Recommended by Editorial Board member Poo Gyeon Park under the direction of Editor Young Il Lee. This research was supported by the National Natural Science Foundation of China (Grant No. 40776051), the Key Natural Science Foundation of Shandong Province (Grant No. Z2005G01), the Natural Science Foundation of Qingdao City (Grant No. 05-1-JC-94) and the research funds of QingDao University of Science and Technology. Hai-Hong Wang received the Ph.D. degree in Computer Science in July 2007 from Ocean University of China. She presently works in QingDao University of Science and Technology, Qingdao, P.R. China. Her current research interests include analysis and control for time-delay systems and nonlinear systems. Gong-You Tang received the Ph.D. degree in Control Theory and Applications from the South China University of Technology, P. R. China in 1991. He is a Professor at the College of Information Science and Engineering at the Ocean University of China, Qingdao, P. R. China. He is the Editor of the Journal of the Ocean University of China and Control and the Instruments in Chemical Industry. His research interests are in the areas of nonlinear systems, delay systems, large-scale systems, and networked control systems, with emphasis in optimal control, robust control, fault diagnosis and stability analysis.     

Approximate causal output tracking for linear perturbed systems via sliding mode control

ABSTRACT

A new approach to the solution of what is termed causal output tracking problem for linear time-invariant systems in the presence of both matched and unmatched unmodelled disturbances is presented. The proposed solution is addressed through the design of a dynamic steady state estimator based on the desired system structure and an observer, considering the reference as the system output. The unmatched disturbance is estimated and used in the steady state estimator to achieve invariance, while the matched disturbance robustness is provided via sliding mode control using the super-twisting algorithm. A useful application of the presented techniques is output tracking for non-minimum phase systems; thus, the performed simulation results confirm the effectiveness of the proposed control scheme for this kind of systems.     

A new nonlinear output tracking controller via output-feedback

1 Introduction Since the introduction of backstepping design [1], exten- sive research has been investigated on control design for the systems in the triangular structure [1～6], merged with non- linear damping [7], tuning functions [4], MT filters [5] and other techniques. Two classes of output-feedback nonlinear control sys- tems have been investigated intensely: the first is that non- linearities only depend on the measurable states. By output injection, a much simple but effectual observe…     

A new nonlinear output tracking controller via output-feedback

In this paper, the output tracking control is investigated for a class of nonlinear systems when only output is available for feedback. Based on the multivariable analog of circle criterion, an observer is first introduced. Then, the observer-based output tracking controller is constructively designed by using the integral backstepping approach together with completing square. It is shown that, under relatively mild conditions, all the closed-loop signals are uniformly bounded. Meanwhile the system output asymptotically tracks the desired output. A simulation example is given to illustrate the effectiveness of the theoretical results.     

非线性离散系统的近似最优跟踪控制

研究非线性离散系统的最优跟踪控制问题. 通过在由最优控制问题所导致的非线性两点边值问题中引入灵敏度参数, 并对它进行Maclaurin级数展开, 将原最优跟踪控制问题转化为一族非齐次线性两点边值问题. 得到的最优跟踪控制由解析的前馈反馈项和级数形式的补偿项组成. 解析的前馈反馈项可以由求解一个Riccati差分方程和一个矩阵差分方程得到. 级数补偿项可以由一个求解伴随向量的迭代算法近似求得. 以连续槽式反应器为例进行仿真验证了该方法的有效性．     

Self-tuning control of nonminimum-phase systems

The instability that arises from the pole-zero cancellation of elementary self-tuners and most MRAC algorithms has given rise to a misapprehension that nonminimum-phase systems can pose insoluble problems with the application of adaptive control. Since most practical processes exhibit some form of nonminimum-phase behaviour (particularly when controlled digitally) this appeared to restrict the usefulness of self-tuning methods. However, during the last few years new algorithms have been suggested which partly overcome these difficulties and have been shown to be effective in industrial trials. The paper describes the practical features that a self-tuning controller must possess and discusses how plant dead-time and excess continuous-time poles can lead to discrete-time nonminimum-phase zeros. The source of instability of elementary self-tuners is analysed and various suggested approaches for overcoming this problem are reviewed. These include the use of a generalized minimum variance cost-function incorporating control weighting, factorization methods which avoid cancellation of the offending zeros, adaptive control based on state-space linear quadratic Gaussian (LQG) theory, and explicit pole-placement via solution of a Diophantine or Bezoutian equation. Gawthrop's hybrid controller, which avoids those nonminimum-phase zeros due to continuous-time pole excess, is briefly discussed. A series of simulations in which a nonminimum-phase plant is subjected to a pattern of set-point changes is presented to show some of the features of the algorithms. In applications the order of the process is unlikely to be known (or indeed be finite); the pole-placement algorithm which is particularly effective in the known-order case is shown to lack robustness to underspecified order. The use of a large control weighting however restores stability to the generalized minimum-variance controller. The conclusions are that with appropriate design and engineering judgement adaptive control is viable even for nonminimum-phase processes.     

Optimal semistable control for continuous-time linear systems

In this paper, we develop a new H₂ semistability theory for linear dynamical systems. Specifically, necessary and sufficient conditions based on the new notion of weak semiobservability for the existence of solutions to the semistable Lyapunov equation are derived. Unlike the standard H₂ optimal control problem, a complicating feature of the H₂ optimal semistable control problem is that the semistable Lyapunov equation can admit multiple solutions. We characterize all the solutions using matrix analysis tools. With this theory, we present a new framework to design H₂ optimal semistable controllers for linear coupled systems by converting the original optimal control problem into a convex optimization problem.     

Modified reference tracking MPC for constrained linear systems

This article presents a model predictive control for tracking piecewise constant references with a new steady-state parametrisation. The modified algorithm is based on the artificial reference idea, but the number of decision variables is equal to the standard MPC for regulation. The proposed strategy is able to track admissible constant references with an admissible evolution. If the reference is not admissible, the system is steered to the closest admissible stationary point. A modified initialisation algorithm is proposed to recover the enlarged domain of attraction provided by related artificial reference-based strategies. Simulation examples are presented to illustrate the benefits of the proposed strategy.     

Adaptive learning control of linear systems by output error feedback

This paper addresses the problem of designing an output error feedback tracking control for single-input, single-output uncertain linear systems when the reference output signal is smooth and periodic with known period T. The considered systems are required to be observable, minimum phase, with known relative degree and known high frequency gain sign. By developing in Fourier series expansion a suitable unknown periodic input reference signal, an output error feedback adaptive learning control is designed which ‘learns’ the input reference signal by identifying its Fourier coefficients: bounded closed-loop signals and global exponential tracking of both the input and the output reference signals are obtained when the Fourier series expansion is finite, while global exponential convergence of the input and output tracking errors into arbitrarily small residual sets is achieved otherwise. The structure of the proposed controller depends only on the relative degree, the reference signal period, the high frequency gain sign and the number of estimated Fourier coefficients.     

The output regulation problem with stability for linear switching systems: A geometric approach

This work presents a solution for the output regulation problem with quadratic stability under arbitrary switching in linear switching systems. The extension to other stability requirements, like asymptotic stability in particular, is also considered and it is shown to affect only few specific features of the proposed solution. The main reason is that the geometric approach, which is at the basis of the developed methodology, establishes a neat separation between the structural aspects and the stability aspects of the problem. For the same reason, continuous-time systems and discrete-time systems are given a unified treatment as far as the structural issues are concerned, while different technicalities characterize the discussion of the stability issues.