An Algebraic Method for Pole Placement in Multivariable Systems

This paper considers the pole placement in multivariable systems involving known delays by using dynamic controllers subject to multirate sampling. The controller parameterizations are calculated from algebraic equations which are solved by using the Kronecker product of matrices. It is pointed out that the sampling periods can be selected in a convenient way for the solvability of such equations under rather weak conditions provided that the continuous plant is spectrally controllable. Some overview about the use of nonuniform sampling is also given in order to improve the system's performance.     

An indirect adaptive pole place for MIMO systems based on multirate sampling of the plant output

The use of multirate-output controllers in order to achieveadaptive pole placement in linear multiple-input multiple-outputsystems with unknown parameters is investigated for the firsttime. Multirate-output controllers contain a multirate samplingmechanism with different sampling period at each system output.Such {acute} control allows us to assign the poles of the sampledclosed-loop system arbitrarily in desired locations, and doesnot make assumptions on the plant other than controllability,observability, and the knowledge of two sets of structural indices,namely the controllability and the observability indices. Anindirect adaptive control scheme based on these sampled-datacontrollers is proposed, which estimates the controller parameterson line. Using the proposed adaptive algorithm, the problemof adaptive pole placement is reduced to the determination ofa fictitious static state-feedback controller, due to the meritsof dynamic multirate-output controllers. Known techniques resortto the direct computation of dynamic controllers. The controllerdeterminations here is based on the transformation of the discreteanalogue of the systems under control to a phase-variable canonicalform prior to the applications of the control design procedure.The solution of the problem can be obtained by a quite simpleutilization of the concept of state similarity transformation,whereas known techniques usually require the solution of matrixpolynomial Diophantine equations. Moreover, persistent excitationof the continuous-time plant is provided without assuming anyspecial richness of the reference signals.     

An Algebraic Method for Pole Placement in Multivariable Systems

This paper considers the pole placement in multivariable systems involving known delays by using dynamic controllers subject to multirate sampling. The controller parameterizations are calculated from algebraic equations which are solved by using the Kronecker product of matrices. It is pointed out that the sampling periods can be selected in a convenient way for the solvability of such equations under rather weak conditions provided that the continuous plant is spectrally controllable. Some overview about the use of nonuniform sampling is also given in order to improve the system's performance.     

Discrete model reference adaptive control of continuous-time linear multi-input multi-output systems via multirate sampled-data controllers

The use of multirate sampled-data controllers for linear multivariable time-invariant systems with unknown parameters is investigated. Such controllers contain periodically time-varying elements and a multirate sampling mechanism with different sampling periods at each system input. Their application to unknown continuous-time linear multi-input, multi-output systems results in a sampled closedloop system for which an arbitrary discrete-time transfer function matrix can be assigned, as is shown in the present paper. The contribution of the present paper is twofold: the use of multirate sampled-data controllers in the area of model reference adaptive control; and the application, for the first time, of periodically varying controllers for model reference adaptive control of multi-input, multi-output systems.The work described in this paper has been partialy funded by the General Secretariat for Research and Technology of the Greek Ministry of Industry, Research, and Technology and by the Heracles General Cement Company of Greece.     

Hardware-in-the-loop experimental study on a fractional order networked control system testbed

Networked Control Systems (NCS) are of great interest in many industries because of their convenience in data sharing and manipulation remotely. However, there are several problems along with NCS itself due to the uncertainties in network communication. One issue inherent to NCS is the network-induced delays which may deteriorate the performance and may even cause instability of the system. Therefore a controller which can make the plant stable at large values of delay is always desirable in NCS systems. Our past work on Optimal Fractional Order Proportional Integral (OFOPI) controller showed that fractional order PI controllers have larger jitter margin (maximum value of delay for which system is stable) for lag-dominated systems when compared to traditional Proportional Integral Derivative (PID) controllers, whereas integer order PID controllers have larger jitter margin for delay-dominated systems. This paper aims at the design process of a tele-presence controller based on OFOPI tuning rules. To illustrate this, an extensive experimental study on the real-time Smart Wheel networked speed control system is performed using hardware-in-the-loop control. The real-time random delay in the world wide network is collected by pinging different locations, and is considered as the delay in our simulation and experimental systems. Comparisons are made with existing integer order PID controller. It is found that the proposed OFOPI controller is a promising controller and has faster response time than the traditional integer order PID controllers. Since the plant into consideration viz. the Smart Wheel is a delay-dominated system, it is verified that PID achieves larger jitter margin as compared to OFOPI tuning rules. Simulation results and real-time experiments showing comparisons between OFOPI and OPID tuning rules prove the significance of this method in NCS.     

Robust digital controllers for uncertain chaotic systems: A digital redesign approach

In this paper, a new and systematic method for designing robust digital controllers for uncertain nonlinear systems with structured uncertainties is presented. In the proposed method, a controller is designed in terms of the optimal linear model representation of the nominal system around each operating point of the trajectory, while the uncertainties are decomposed such that the uncertain nonlinear system can be rewritten as a set of local linear models with disturbed inputs. Applying conventional robust control techniques, continuous-time robust controllers are first designed to eliminate the effects of the uncertainties on the underlying system. Then, a robust digital controller is obtained as the result of a digital redesign of the designed continuous-time robust controller using the state-matching technique. The effectiveness of the proposed controller design method is illustrated through some numerical examples on complex nonlinear systems––chaotic systems.     

Online optimization of LTI systems under persistent attacks: Stability,tracking, and robustness

We study the stability properties of a closed-loop system composed of a dynamical plant and a feedback controller, the latter generating control signals that can be compromised by a malicious attacker. We consider two classes of feedback controllers: a static output-feedback controller, and a dynamical gradient-flow controller that seeks to steer the output of the plant towards the solution of a convex optimization problem. In both cases, we analyze the stability properties of the closed-loop system under a class of switching attacks that persistently modify the control inputs generated by the controllers. Our stability analysis leverages the framework of hybrid dynamical systems, Lyapunov-based arguments for switching systems with unstable modes, and singular perturbation theory. Our results reveal that, under a suitable time-scale separation between plant and controllers, the stability of the interconnected system can be preserved when the attack occurs with “sufficiently low frequency” in any bounded time interval. We present simulation results in a power-grid example that corroborate the technical findings.     

Controller design for network‐based Markovian jump systems with unreliable communication links

This article is concerned with observer and controller design for networked control systems, where the considered plant refers to a class of discrete‐time communication delay Markovian jump systems. In the study, random packet losses and output quantization are considered simultaneously. The packet losses considered here includes sensor to controller and controller to actuator sides, which are modeled as two Bernoulli distributed white sequences, respectively. An observer‐based control scheme is developed to stabilize the closed‐loop systems. Finally, an illustrative example is provided to show the applicability of the proposed control method. © 2016 Wiley Periodicals, Inc. Complexity 21: 623–634, 2016     

Digital PID controller design for multivariable analogue systems with computational input-delay

This paper presents a new methodology to design MIMO digitalPID controllers for multivariable analogue systems with computationalinput time-delay. The preliminarily designed analogue PID controlleris refined using a newly developed state-feedback and state-feedforwardLQR approach. The optimally designed closed-loop system withthe refined MIMO analogue PID controller has pre-assigned closed-loopeigenvalues. A prediction-based digital redesign technique isdeveloped to discretize the cascaded MIMO analogue PID controller,such that the states of the digitally redesigned closed-loopsampled-data system with the MIMO digital PID controller areclose to those of the analogously designed closed-loop systemwith the refined MIMO analogue PID controller. The aforementioneddigital redesign technique is further modified based on thepredictive control method to cope with MIMO analogue systemswith input delay.     

Hybrid decentralized maximum entropy control for large-scale dynamical systems

In the analysis of complex, large-scale dynamical systems it is often essential to decompose the overall dynamical system into a collection of interacting subsystems. Because of implementation constraints, cost, and reliability considerations, a decentralized controller architecture is often required for controlling large-scale interconnected dynamical systems. In this paper, a novel class of fixed-order, energy-based hybrid decentralized controllers is proposed as a means for achieving enhanced energy dissipation in large-scale lossless and dissipative dynamical systems. These dynamic decentralized controllers combine a logical switching architecture with continuous dynamics to guarantee that the system plant energy is strictly decreasing across switchings. The general framework leads to hybrid closed-loop systems described by impulsive differential equations. In addition, we construct hybrid dynamic controllers that guarantee that each subsystem–subcontroller pair of the hybrid closed-loop system is consistent with basic thermodynamic principles. Special cases of energy-based hybrid controllers involving state-dependent switching are described, and an illustrative combustion control example is given to demonstrate the efficacy of the proposed approach.     

具有量化误差的多步长非线性采样系统的镇定

该文研究一类非线性控制系统在采样器采样过程中产生量化误差的情况下多步长采样镇定问题. 运用近似DTD方法, 在非线性系统的近似离散时间模型上设计全局状态反馈镇定控制器. 当系统近似误差和采样量化误差被限制在一定的条件下, 可以得到含量化误差的多步长非线性采样系统是半全局实用渐近稳定. 最后, 仿真例子验证了所得结果的有效性.     

High performance robust linear controller synthesis for an induction motor using a multi-objective hybrid control strategy

A robust induction motor control should provide the desired performance in the face of both plant model and controller model uncertainty. In a recent work, Bottura and co-workers, using the field orientation principle, introduced a representation of a nonlinear time-varying induction motor model that admits robust induction motor controller synthesis in the linear _H∞$H_{\infty }$ framework. The present work considers the use of the approach of Bottura et al. for attaining robust performance of the main operating modes–tracking and disturbance rejection–of an induction motor control system under implementation constraints on the control signal magnitude. This approach requires two distinct mode-specific controllers with gains that cannot be bridged without considerable performance degradation. To address this problem, a multi-objective hybrid control design methodology is developed that employs the corresponding mode-specific controller in each mode, and organizes a rapid and smooth steady-state switching, or transfer, between these controllers to permit sequencing of the operating modes, as necessary. Simulation shows that the technique proposed yields controllers with performance minimally affected by an imprecise modeling of an induction motor, as well as a reduced cost controller implementation throughout the entire induction motor operating sequence.     

Long-range predictive adaptive fuzzy relational control

A class of long-range predictive adaptive fuzzy relational controllers is presented. The plant behavior is described over an extended time horizon by a fuzzy relational model which is identified based on input-output closed-loop observations of the plant variables. In this class of adaptive controllers the control law attempts to minimize a quadratic cost over an extended control horizon. When used with linear models, this approach has revealed a significant potential for overcoming the limitations of one-step ahead schemes, such as the stabilization of non-minimum phase plants. Here, a uniform framework is adopted for implementing both the fuzzy model and the fuzzy controller, namely distributed fuzzy relational structures gaining from their massive parallel processing features and from the learning capabilities typical of the connectivist approaches. Issues such as maintenance during the adaptation process of the meaning of linguistic terms used at both fuzzy systems interfaces are addressed, namely by introducing a new design methodology for on-line fuzzy systems interface adaptation. The examples presented reinforce the claim of the usefulness of this new approach.     

Auto-Tuning and Fractional Order Controller Implementation on Hardware in the Loop System

The paper deals with the design of an auto-tuning fractional order proportional-integrative-derivative controllers and its implementation on hardware in the loop simulator for the real-time control of unknown plants. The proposed procedure can be applied to systems with delay and order greater than one, once specifications on cross-over frequency and phase margin are given. The auto-tuning procedure consists of two phases: the first one dedicated to the identification of the process at the desired cross-over frequency and the second one to determine all the parameters of the fractional order proportional-integrative-derivative controllers. The obtained controller ensures an iso-damping response of the plant. Experimental results are given to confirm the effectiveness of the proposed approach and show that the requirements are totally met for the system to be controlled.     

Design of adaptive LQ regulators for MIMO systems based on multirate sampling of the plant output

In this paper, the certainty equivalence principle is used to combine a discrete-time adaptive law with a control structure derived from the linear-quadratic regulation problem. The proposed control structure is mainly based on multirate sampling of the output of the continuous-time plant under control and allows us to regulate the sampled closed-loop system, subject to a quadratic performance criterion, without making assumptions on the plant other than controllability and observability and the knowledge of two sets of structural indices. Using the proposed algorithm, the adaptive regulation problem is reduced to the determination of a fictitious static state feedback controller. Known techniques usually resort to the computation of fullorder adaptive state observers, thus introducing high-order exogenous dynamics in the control loop. Moreover, persistence of excitation and parameter convergence of the plant are provided without making any additional assumption on the system, as compared to known adaptive linear-quadratic regulation schemes.     

Tracking control for switched time-varying delays systems with stabilizable and unstabilizable subsystems

We investigate the tracking control problem for switched linear time-varying delays systems with stabilizable and unstabilizable subsystems. Sufficient conditions for the solvability of the tracking control problem are developed. The tracking control problem of a switched time-varying delays system with stabilizable and unstabilizable subsystems is solvable if the stabilizable and unstabilizable subsystems satisfy certain conditions and admissible switching law among them. Average dwell time approach and piecewise Lyapunov functional methods are utilized to the stability analysis and controller design. By introducing the integral controllers and free weighting matrix scheme, some restricted assumptions imposing on the switched systems are avoided. A simulation example shows the effectiveness of the proposed method.     

一类具有饱和因子的奇异时滞系统的鲁棒保性能控制

研究了具有饱和因子的非线性奇异时滞系统的鲁棒保性能控制问题.目的是设计一个鲁棒控制器和保成本控制器,通过线性矩阵不等式方法(LMI)得出了鲁棒控制器和保性能控制器存在的充分条件.当这些LMI方法是可解时,分别给出了鲁棒控制器和保性能控制器的解析表达式.     

Control of systems with aftereffect in scales of linear controllers with respect to the type of feedback

For control systems with deviating argument, we consider basic problems of qualitative control theory such as problems of stabilization and modal control in scales of linear controllers with respect to the type of feedback, from the simplest difference controllers to integral controllers of general form. We analyze the results obtained in this direction. Special attention is paid to the stabilization of two-dimensional systems by feedback in the form of difference controllers. For the case in which the construction of a difference controller is impossible or too difficult, an integral feedback is used. Unlike the well-known Krasovskii-Osipov method for the construction of integral feedback in delay systems, the suggested method is based on the Paley-Wiener theorem for entire functions of exponential type.