Robust control of separated shear flows in simulation and experiment

Closed-loop flow control is gaining more and more interest in the last few years. Whereas most of the published results are based on simulation studies, this work explores the synthesis of closed-loop controllers for separated wall-bounded shear flows in experiments. A methodology and first results are presented for the robust control of a flow over a well established benchmark system, namely a backward-facing step. This system can be seen as a simple representation of the situation in a burner or behind a flame holder. Based on numerical solutions of the Navier–Stokes equations and on experimental wind tunnel results, possible candidates for an online determination of an appropriate output variable are proposed. For our purpose, a substitute for the reattachment length is taken as the control variable. Simple black-box models are derived to describe the behaviour of the system in the vicinity of set-points. Based on these, different robust controllers are synthesised. As expected, these controllers show superior behaviour over the open-loop strategies mainly proposed in the flow control literature.     

H Optimal control for linear stochastic systems

The aim of the present paper is to provide an optimal solution to the H² state-feedback and output-feedback control problems for stochastic linear systems subjected both to Markov jumps and to multiplicative white noise. It is proved that in the state-feedback case the optimal solution is a static gain which is also optimal in the class of all higher-order controllers. In the output-feedback case the optimal H² controller has the same order as the given stochastic system. The realization of the optimal controllers depend on the stabilizing solutions of some appropriate systems of Riccati-type coupled equations. An effective iterative convergent algorithm to compute these stabilizing solutions is also presented. The paper gives some illustrative numerical example allowing to compare the results obtained by the proposed design approach with the ones presented in the recent control literature.     

基于非线性控制方法的倒立摆系统控制

应用非线性系统跟踪控制方法对倒立摆系统的控制进行研究.基于非线性系统控制方法对倒立摆系统摆的镇定问题、台车位置调节问题和鲁棒控制问题设计出了具体的控制器.最后给出了在所设计的各种控制器作用下系统的仿真结果,结果表明所设计的控制器对倒立摆系统的稳定控制具有良好的效果.     

Distributed tracking control of networked chained systems

This paper considers distributed tracking control of multiple nonholonomic chained systems using neighbours’ information. With the aid of the cascade structure of each system and properties of persistently excited signals, distributed state feedback tracking controllers and distributed output feedback tracking controllers are proposed such that the tracking errors exponentially converge to zero. To show applications of the proposed results, formation control of wheeled mobile robots is considered. Distributed controllers are obtained with the aid of the proposed theorems. Simulation results verify the effectiveness of the proposed results.     

Distributed optimal control of multiple systems

This article considers distributed optimal control of multiple linear systems. Distributed approximately optimal controllers are proposed for each system with the aid of communications between systems. The proposed controllers make the states of the closed-loop systems exponentially converge to the states of the closed-loop systems with the centralised optimal controllers if the communication digraph is strongly connected. If the communication digraph is switching and there are communication delays, the proposed controllers also make the states of the closed-loop systems exponentially converge to the states of the closed-loop systems with the centralised optimal controllers. Simulation results show effectiveness of the proposed controllers.     

Distributed tracking control of uncertain mechanical systems with velocity constraints

This paper considers the leader‐following control problem of multiple mechanical systems with uncertainty and velocity constraints. So as to deal with the velocity constraints, a reduction procedure is applied to transform the model of each system to a cascaded system. With the aid of the cascade structure of each system and the properties of linear time‐varying systems, distributed robust feedback controllers are proposed such that the state of each follower system asymptotically converges to the state of a leader system with the aid of neighbors' information. So as to reduce the cost of the communication between systems, an event‐triggered leader‐following control problem is also considered, and event‐triggered distributed controllers are proposed. As an application of the proposed results, formation control of wheeled mobile robots is considered, and distributed controllers are obtained with the aid of the results in Theorems 1 and 2. Simulation results show the effectiveness of the proposed results. Copyright © 2017 John Wiley & Sons, Ltd.     

Feedback linearization based control of a rotational hydraulic drive

The technique of feedback linearization is used to design controllers for displacement, velocity and differential pressure control of a rotational hydraulic drive. The controllers, which take into account the square-root nonlinearity in the system's dynamics, are implemented on an experimental test bench and results of performance evaluation tests are presented. The objective of this research is twofold: firstly, to present a unified method for tracking control of displacement, velocity and differential pressure; and secondly, to experimentally address the issue of whether the system can be modeled with sufficient accuracy to effectively cancel out the nonlinearities in a real-world system.     

Self‐triggered state‐feedback control of linear plants under bounded disturbances

This paper addresses the problem of self‐triggered state‐feedback control for linear plants under bounded disturbances. In a self‐triggered scenario, the controller is allowed to choose when the next sampling time should occur and does so based on the current sampled state and on a priori knowledge about the plant. Besides comparing some existing approaches to self‐triggered control available in the literature, we propose a new self‐triggered control strategy that allows for the consideration of model‐based controllers, a class of controllers that includes as a special case static controllers with a zero‐order hold of the last state measurement. We show that our proposed control strategy renders the solutions of the closed‐loop system globally uniformly ultimately bounded. We further show that there exists a minimum time interval between sampling times and provide a method for computing a lower bound for it. An illustrative example with numerical results is included in order to compare the existing strategies and the proposed one. Copyright © 2014 John Wiley & Sons, Ltd.     

Supervisory control of switching control systems

In this paper, the problem of designing a switching policy for an adaptive switching control system is formulated as a problem of supervisory control of a discrete-event system (DES). Two important problems in switching control are then addressed using the DES formulation and the theory of supervisory control under partial observation. First, it is verified whether for a given set of controllers, a switching policy satisfying a given set of constraints on the transitions among controllers exists. If so, then a minimally restrictive switching policy is designed. Next, an iterative algorithm is introduced for finding a minimal set of controllers for which a switching policy satisfying the switching constraints exists. It is shown that in the supervisory control problem considered in this paper, limitations on event observation are the factors that essentially restrict supervisory control. In other words, once observation limitations are respected, limitations on control will be automatically satisfied. This result is used to simplify the proposed iterative algorithm for finding minimal controller sets.     

时滞关联大系统基于分散控制的无源性

无源性不仅是系统的一个重要性质,而且是控制一个系统的重要途径.本文基于分散控制方法研究了关联大系统的无源性.利用Lyapunov-Krasovskii泛函方法和Hamilton函数方法,通过求解线性矩阵不等式(LMIs)得到了分散无源控制器的显式表达.所得到的新的无源性判据和无源控制器的参数是与时滞相关的.当关联时滞已知时,这些新结果的条件易于用Matlab中的LMI工具箱进行验证,因而控制器的设计也容易实现.最后用数值例子说明了所得到定理的有效性和无源控制器的设计过程.     

A receding horizon control approach to sampled-data implementation of continuous-time controllers

We propose a novel way for sampled-data implementation (with the zero order hold assumption) of continuous-time controllers for general nonlinear systems. We assume that a continuous-time controller has been designed so that the continuous-time closed-loop satisfies all performance requirements. Then, we use this control law indirectly to compute numerically a sampled-data controller. Our approach exploits a model predictive control (MPC) strategy that minimizes the mismatch between the solutions of the sampled-data model and the continuous-time closed-loop model. We propose a control law and present conditions under which stability and sub-optimality of the closed loop can be proved. We only consider the case of unconstrained MPC. We show that the recent results in [G. Grimm, M.J. Messina, A.R. Teel, S. Tuna, Model predictive control: for want of a local control Lyapunov function, all is not lost, IEEE Trans. Automat. Control 2004, to appear] can be directly used for analysis of stability of our closed-loop system.     

Distributed model predictive control of an experimental four-tank system

A distributed model predictive control (DMPC) framework is proposed. The physical plant structure and the plant mathematical model are used to partition the system into self-sufficient estimation and control nodes. Local measurements at the nodes are used to estimate the relevant plant states. This information is then used in the model predictive control calculations. Communication among relevant nodes during estimation and control calculations provides improvement over the performance of completely decentralized controllers. The DMPC framework is demonstrated for the level control of an experimental four-tank system. The performance of the DMPC system for disturbance rejection is compared with other control configurations. The results indicate that the proposed framework provides significant improvement over completely decentralized MPC controllers, and approaches the performance of a fully centralized design.     

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.     

Decentralized voltage control of distributed generation using a distribution system structural MIMO model

The voltage control problem in Low Voltage (LV) distribution systems is becoming increasingly important due to the presence of Distributed Generation (DG). Recently, DG units have been proposed to contribute to voltage control according to a Volt/Var law which does not realize regulation. Moreover, since the existing LV systems are operated in a decentralized way without communication links, the simultaneous response of the controllers of the DG units may result into operational conflicts and instability. To overcome these problems, the present paper illustrates a design methodology for decentralized voltage controllers that act on DG reactive power injections. The controllers are suitable for the LV systems since they ensure voltage regulation and stability by using only local measurements and without information exchanges. The design is based on a proposed structural MIMO model of the distribution system. Robust stability is also analyzed: changes in the operating conditions of the distribution system are modeled as unstructured additive uncertainties affecting the MIMO model. A case study gives evidence of the applicability of the proposed design; the performance of the controllers in terms of both stability and regulation of the nodal voltages of three DG units connected to a LV distribution feeder is tested by numerical simulations; finally, a comparison with a Volt/Var technique is performed.     

离散型自抗扰控制器在四旋翼飞行姿态控制中的应用

本文首先介绍了自抗扰控制器的结构组成,包括跟踪微分器、扩张状态观测器以及非线性状态误差反馈律,及各部分的典型算法.针对四旋翼盘旋系统的姿态控制问题,设计了3种离散型自抗扰控制器,搭建了仿真结构图,并进行了参数整定,得到了优良的仿真结果.进而在实际装置上进行试验,调试出了令人满意的姿态实时控制结果.实时控制结果表明,文中所设计的自抗扰控制器可以满足控制精度及快速性的要求,并且具有抗干扰性能、稳定控制能力以及对非线性强耦合系统的解耦能力.最后,总结并分析了3种自抗扰控制器的优缺点及适用范围.     

Distributed estimation-based tracking control of multiple uncertain non-linear systems

This paper considers the tracking control of multiple uncertain non-linear systems with a desired signal which is not available to each system. An estimation-based controller design approach is proposed. Distributed estimation-based adaptive controllers are proposed with the aid of Lyapunov techniques and results from graph theory. Simulation results show the effectiveness of the proposed controllers.     

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.     

A flexible layered control policy for resource allocation in a sensor grid

The paper proposes a flexible layered control policy for sensor resource allocation in a sensor grid. In order to allocate sensor resources in the system to maximize the sensor grid utility, different controllers are deployed at three levels: a job-level controller, an application group controller, and a sensor grid system controller. At the lowest levels, job-level controllers perform fast, frequent, local adaptation for optimizing a single sensor grid application at a time, while, at the highest levels, sensor grid system controllers perform less frequent control actions to optimize all applications. Sensor grid system control considers all sensor grid applications in response to large system changes at coarse time granularity. Sensor grid system control exploits the interlayer coupling of the resource layer and the application layer to achieve a system-wide optimization based on the sensor grid users’ preferences. Job-level control adapts a single application to small changes at fine granularity. The layered control system uses a set of utility functions to evaluate the performance of sensor grid applications and groups. The control system chooses control actions that would result in a higher level of utility. In the simulation, a performance evaluation of the algorithm is carried out.     

A linear matrix inequality approach to H∞ control

The continuous- and discrete-time H_∞ control problems are solved via elementary manipulations on linear matrix inequalities (LMI). Two interesting new features emerge through this approach: solvability conditions valid for both regular and singular problems, and an LMI-based parametrization of all H_∞-suboptimal controllers, including reduced-order controllers. The solvability conditions involve Riccati inequalities rather than the usual indefinite Riccati equations. Alternatively, these conditions can be expressed as a system of three LMIs. Efficient convex optimization techniques are available to solve this system. Moreover, its solutions parametrize the set of H_∞ controllers and bear important connections with the controller order and the closed-loop Lyapunov functions. Thanks to such connections, the LMI-based characterization of H_∞ controllers opens new perspectives for the refinement of H_∞ design. Applications to cancellation-free design and controller order reduction are discussed and illustrated by examples.     

时延网络化控制系统的H2/H∞混合控制

针对存在多步随机传输时延的网络化控制系统模型 ,研究了其随机稳定性及H₂/H_∞混合控制问题 .在一定的系统通信控制模式下 ,网络传输时延可以建模为一个马尔可夫随机过程 ,通过增广系统状态的方法将原系统转化为一个具有随机跳变系数的离散系统 ,同时通过建立随机跳变Lyapunov函数 ,构建了满足系统随机稳定的H_∞次优和H₂/H_∞混合控制状态反馈控制器 .该控制器可通过求解一组耦合的矩阵不等式而得 .