On ultimate boundedness around non-assignable equilibria of linear time-invariant systems

In this note we investigate the following questions: given a (finite-dimensional) linear time-invariant (LTI) multivariable system and a constant desired value for its output, say y_?. Assume there is no assignable equilibrium point corresponding to y_?. How “close” to y_? can we ultimately keep the output using LTI static state-feedback stabilizing controllers? Can this neighborhood of y_? be reduced with dynamic, nonlinear, time-varying controllers? Our main contributions are the proof that the optimal ultimate boundedness neighborhood is achieved with LTI static state-feedback, the explicit computation of the neighborhood's size and the proof, under some reasonable rank assumptions, that the system has non-assignable values for the output if and only if it has a transmission zero at zero. Interestingly, there is no connection between this problem and the more familiar concepts of controllability and observability.     

Reliable regulation in decentralised control systems

This article addresses the design of decentralised regulators which supply the control systems with signal tracking and disturbance rejection. This property has to be attained, to the maximum possible extent, even when instrumentation faults occur, thus causing the opening of some feedback loops. The problem is tackled for LTI asymptotically stable plants, subject to perturbations, under the assumption that the Laplace transforms of the exogenous signals have multiple poles on the imaginary axis. The proposed regulator is composed of an LTI nominal controller supervised by a reconfiguration block. Once the actions of the reconfiguration block have been settled, the synthesis of the nominal controller is reformulated as a suitable regulation problem. A constructive sufficient condition for its solvability is established. This condition turns out to be also necessary if the exogenous signals are polynomial in time.     

Robust output regulation for nonlinear systems with nonpolynomial nonlinearity under nonlinear exosystems

This paper studies a robust output regulation problem with nonlinear exosystems without the assumption that the solution to the regulator equations along the trajectory of the exosystems should be polynomial. Based on the extended concepts of steady-state generator and internal model, a set of sufficient conditions for the solvability of the problem are given. Thus, the result developed in this paper can allow the robust output regulation problem with nonlinear exosystems to accommodate much more general nonlinear given plants including those which contain nonpolynomial nonlinearity.     

Tracking and regulation in the behavioral framework

Given a plant together with an exosystem generating the disturbances and the reference signals, the problem of asymptotic tracking and regulation is to find a controller such that the plant variable tracks the reference signal regardless of the disturbance acting on the system. If a controller achieves this design objective, we call it a regulator for the plant with respect to the given exosystem. In this paper, we formulate the asymptotic tracking and regulation problem in the behavioral framework, with control by interconnection.     

Repetitive control for systems with uncertain period-time

Repetitive control is useful if periodic disturbances act on a control system. Perfect (asymptotic) disturbance rejection is achieved if the period-time is exactly known. For those cases where the period-time changes and cannot be measured directly by an auxiliary signal, a robust repetitive controller structure is proposed. It uses multiple memory-loops in a certain feedback configuration, such that small changes in period-time do not diminish the disturbance rejection properties. The robust repetitive controller shows good implementation results for a tracking control problem of a Compact Disc player.     

Adaptation and regulation with signal detection implies internal model

This note provides a simple result showing, under suitable technical assumptions, that if a system Σ adapts to a class of external signals , in the sense of regulation against disturbances or tracking signals in , then Σ must necessarily contain a subsystem which is capable of generating all the signals in . It is not assumed that regulation is robust, nor is there a prior requirement for the system to be partitioned into separate plant and controller components. Instead, one assumes that a “signal detection” property holds.     

自适应仿人智能控制控制策略研究

在分析自适应仿人智能控制结构的基础上,重点研究了多模态控制策略,充分利用系统误差、误差的变化、被控对象的输入量的变化和模型误差四个信息,并以被控对象的输入量的变化和模型误差作为仿人智能控制器和内模控制器之间的协调参数,使控制器的快速性、平稳性、鲁棒性和抗扰性得到极大改善。仿真试验证明在该控制结构下的控制策略非常有效。     

Nonlinear control for robust rejection of periodic disturbances

Consider a linear plant with a strictly proper rational transfer function and an input which is a known periodic waveform of unknown amplitude and phase. In the case when the periodic waveform has infinitely many non-zero harmonics, it is pointed out that for a wide class of linear, time-invariant (infinite-dimensional) controllers, it is not possible to robustly stabilize the plant and achieve asymptotic rejection of the disturbance. For a specific linear plant and a triangular wave disturbance, it is shown by construction that the problem is soluble with a nonlinear controller. Robustness is measured using the gap metric robust stability margin.     

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.     

Generalized control systems,boundary control systems,and delayed control systems

We investigate the relationships between the three classes of systems mentioned in the title: we show that systems with delays in control are a special instance of boundary control systems, and a boundary control system produces a generalized control system when projected onto its (unstable) eigenspaces. We use this observation to investigate the action of feedback on the dynamical behavior of systems with boundary controls. In particular, the well-known fact that spectral controllability is necessary and sufficient for a system with delays in control to be stabilizable is derived from a general rather than from anad hoc method. This paper was written according to the programs of the GNAFA-CNR group, with the financial support of the Italian “Ministero della Pubblica Istruzione.”     

Robustness for time-varying systems

We consider robust optimization for time-varying systems in terms of perturbations of fractional representations. Upper and lower bounds are given for the maximal radius of the operator ball around a given plant which can be stabilized by a single compensator. In the time-invariant case, these numbers are equal.     

Robust model predictive control of constrained linear systems with bounded disturbances

This paper provides a novel solution to the problem of robust model predictive control of constrained, linear, discrete-time systems in the presence of bounded disturbances. The optimal control problem that is solved online includes, uniquely, the initial state of the model employed in the problem as a decision variable. The associated value function is zero in a disturbance invariant set that serves as the ‘origin’ when bounded disturbances are present, and permits a strong stability result, namely robust exponential stability of the disturbance invariant set for the controlled system with bounded disturbances, to be obtained. The resultant online algorithm is a quadratic program of similar complexity to that required in conventional model predictive control.     

一类不确定系统鲁棒容错D-稳定性分析

研究不确定系统D-稳定鲁棒容错H∞控制问题.基于连续型执行器故障模式,利用线性矩阵不等式(LMI)给出了系统D-稳定的鲁棒容错输出反馈控制器存在的充分条件,并将动态输出反馈控制器设计方法归结为求解一族线性矩阵不等式组.仿真示例表明,无论执行器是否发生故障,所得到的动态输出反馈控制器不仅保证闭环系统是D-稳定的,而且满足给定的H∞干扰指标,从而验证了所提出的控制器设计方法的有效性.     

Stabilizing decentralized model predictive control of nonlinear systems

This note presents a stabilizing decentralized model predictive control (MPC) algorithm for nonlinear discrete time systems. No information is assumed to be exchanged between local control laws. The stability proof relies on the inclusion of a contractive constraint in the formulation of the MPC problem.     

Robust fault-tolerant self-recovering control of nonlinear uncertain systems

In this paper, the problem of devising a fault-tolerant robust control for a class of nonlinear uncertain systems is investigated. Possible failures of the sensor measuring the state variables are considered, and a robust measure is developed to identify the stability- and performance-vulnerable failures. Based on evaluation of the robust measure, a fault-tolerant robust control will switch itself between one robust control strategy designed under normal operation and another under the faulty condition. It is shown that, under two input-to-state stability conditions, the proposed scheme guarantees not only the desired performance under normal operations but also robust stability and best achievable performance when there is a sensor failure of any kind.     

一类不确定性非线性网络控制系统的扰动抑制

研究受外部持续扰动的一类不确定性非线性网络控制系统的扰动抑制问题.提出一种@状态变量代换,将控制时滞转移到闭环控制回路之外,从而消除了时滞部分对控制系统稳定性的影响.利用内模原理给出了系统无静差扰动抑制补偿器的设计方法,运用Lyapunov稳定性理论和线性矩阵不等式技术,证明了保成本控制律的存在条件,并给出了无静差保成本控制器的设计方法.仿真结果验证了该控制算法的有效性.     

Hierarchical optimal force-position control of complex manufacturing processes

A hierarchical optimal controller is developed in this paper to regulate the machining force and axis positions, simultaneously, in a micro end milling process. The process is divided into two levels of decision making. The bottom level includes the measurable states, which in this work comprises the axis positions. The top level includes the higher order objectives, which can be derived from the bottom level objectives by an aggregation relationship. In this work, the top level's objective is to regulate the machining force. A series of simulations were conducted in which the weighting between the top and the bottom level objectives is adjusted within the feasible range. The results demonstrated that excellent tracking of both axis positions and machining force are achieved during the steady state regardless of the weighting. However, the transient performance of the system could be systematically shaped to achieve better performance of either objective. For the purpose of comparison a decentralized optimal controller was constructed and simulated for the feasible range of controller weights. When the axis position errors were weighted heavily, both controllers were able to regulate the axis errors well, while the hierarchical controller had smaller machining force errors. When the machining force errors were weighted heavily, although the machining force error decreased for the decentralized controller the axis position errors increased significantly. However, with heavy machining force weighting, the hierarchical controller was able to manipulate the axial errors in a way that while the machining force error was reduced, the contour error (i.e., smallest deviation from the tool tip to the desired contour) remained small.     

Overlapping control systems with optimal information exchange

This paper deals with the stabilizability of interconnected systems via linear time-invariant (LTI) decentralized controllers. Given a controllable and observable system with some distinct decentralized fixed modes (DFMs), it is desired to find a suitable control structure (in terms of information flow) for it. Since a decentralized controller consists of a number of non-interacting local controllers, the objective here is to establish certain interactions between the local controllers in order to eliminate the undesirable DFMs. This objective is achieved by translating the knowledge of the system into some bipartite graphs. Then, the notions of minimal sets and maximal subgraphs are introduced, which lead to a simple combinatorial algorithm for solving the underlying problem. The efficacy of the results obtained is demonstrated by an illustrative example.     

Asymptotic tracking in uncertain Volterra systems

This paper studies the robust tracking problem for an uncertain Volterra system via the frequency-domain approach. Based on the knowledge that the steady-state response of a Volterra system under the sinusoidal input contains possibly infinitely many frequency components, it is shown that (1) for any specified finitely many frequency components possibly contained in the steady-state tracking error, there exists a linear controller that robustly annihilates these components; and (2) robust tracking is possible by a linear controller provided that the Volterra system of the closed-loop system is polynomial. These results can be viewed as a nonlinear analog of the well-known linear robust servomechanism theory developed in the 1970s.