Symbolic control of linear systems based on symbolic subsystems

This paper describes an approach to the control of continuous systems through the use of symbolic models describing the system behavior only at a finite number of points in the state space. These symbolic models can be seen as abstract representations of the continuous dynamics enabling the use of algorithmic controller design methods. We identify a class of linear control systems for which the loss of information incurred by working with symbolic subsystems can be compensated by feedback. We also show how to transform symbolic controllers designed for a symbolic subsystem into controllers for the original system. The resulting controllers combine symbolic controller dynamics with continuous feedback control laws and can thus be seen as hybrid systems. Furthermore, if the symbolic controller already accounts for software/hardware requirements, the hybrid controller is guaranteed to enforce the desired specifications by construction thereby reducing the need for formal verification.     

Robust and adaptive control: fidelity or an open relationship?

Robust and adaptive control are essentially meant to solve the same control problem. Given an uncertain LTI model set with the assumption that the controlled plant slowly drifts or occasionally jumps in the allowed model set, find a controller that satisfies the given servo and disturbance rejection specifications. Specifications on the transient response to a sudden plant change or “plant jump” are easily incorporated into the robust control problem, and if a solution is found, the robust control system does indeed exhibit satisfactory transients to plant jumps. The reason to use adaptive control is its ability, when the plant does not jump, to maintain the given specifications with a lower-gain control action (or to achieve tighter specifications), and also to solve the control problem for a larger uncertainty set than a robust controller. Certainly equivalence-based adaptive controllers, however, often exhibit insufficient robustness and unsatisfactory transients to plant jumps. It is therefore suggested in this paper that adaptive control always be built on top of a robust controller in order to marry the advantages of robust and adaptive control. The concept is called adaptive robust control. It may be compared with gain scheduling, two-time scale adaptive control, intermittent adaptive control, repeated auto-tuning, or switched adaptive control, with the important difference that the control is switched between robust controllers that are based on plant uncertainty sets that take into account not only the currently estimated plant model set but also the possible jumps and drifts that may occur until the earliest next time the controller can be updated.     

Synthesis of supervisory controllers for hybrid systems based onapproximating automata

The paper concerns the synthesis of supervisory controllers for a class of continuous-time hybrid systems with discrete-valued input signals that select differential inclusions for continuous-valued state trajectories and event-valued output signals generated by threshold crossings in the continuous state space, the supervisor is allowed to switch the input signal value when threshold events are observed. The objective is to synthesize a nonblocking supervisor such that the set of possible sequences of control and threshold event pairs for the closed-loop system lies between given upper and lower bounds in the sense of set containment. We show how this problem can be converted into a supervisor synthesis problem for a standard controlled discrete-event system (DES). A finite representation may not exist for the exact DES model of the hybrid system, however. To circumvent this difficulty, we present an algorithm for constructing finite-state Muller automata that accept outer approximations to the exact controlled threshold-event language, and we demonstrate that supervisors that solve the synthesis problem for the approximating automata achieve the control specifications when applied to the original hybrid system     

Multi-model predictive control of an industrial C3/C4 splitter

In this paper, the application of a linear predictive controller to an industrial distillation column that presents a nonlinear behavior is described. The system is represented by a set of linear approximating models, where each model corresponds to a possible operating point of the system. The control sequence computed by the control algorithm is based on a min–max optimization problem where the controller cost is minimized for the worst process model. The control algorithm makes use of a particular form of the state-space model, which preserves the structure of conventional model predictive control controllers that are based on the step response model. The performance of the proposed controller applied to an industrial system is illustrated with results of the real system at typical plant conditions with the controller performing as a regulator and as an output reference tracker.     

H∞-optimal controller discretization

A redesign method for discretizing a continuous-time controller is proposed. The resulting hybrid control system, for example with continuous-time plant and discrete-time controller, is stable, and performance including the system's inter-sampling behaviour can be optimized by approximating some chosen reference transfer function of the continuous-time control system. In order to obtain a tractable problem, the continuous-time part of the hybrid system and the reference transfer function are approximated by a discrete-time system with arbitrary fast sampling. After lifting the resulting periodic system, the approximation problem can be formulated as a standard H_∞-problem which is solved using standard software for H_∞-controller design.     

基于二维混合模型的最优重复控制方法

针对一类线性系统,提出一种基于连续／离散二维混合模型的最优重复控制设计新方法．通过独立地 考虑重复控制系统连续的控制行为与离散的学习行为,建立了重复控制系统的连续／离散二维混合模型,并将重复 控制器设计问题转化为一类连续／离散二维系统的镇定问题．在此基础上,应用最优控制原理,对给定的性能指标 泛函,获得了最优重复控制律．通过调节性能指标泛函中的相关参数,可以对控制和学习行为进行独立的调节．最 后,通过数值仿真验证了所提方法的有效性．     

Modelling and motion control of a mechatronic system using BGM with intelligent controllers

In this research paper, a mechatronics system such as a pan tilt platform (PTP) has been considered for motion control under intelligent controllers. A proportional-derivative (PD) controller is considered for comparison of results obtained from fuzzy and hybrid controllers. The trajectory following performance of the mechatronics system is found against these controllers. The results of simulations show that hybrid fuzzy controller reduce the tracking error effectively in lesser settling time. The intelligent controllers require knowledge base of error and derivative of error to compensate the PTP dynamics. The intelligent controllers have similar trends as the PD controllers and compensated both electrical and mechanical dynamics. The PD controller requires position measurement. The intelligent controllers have knowledge base consisting of position and velocity data. Thus intelligent controllers have position measurement along with knowledge base for position control system. The best results were achieved with hybrid fuzzy controllers. They meet the desired specifications.     

First principle modeling and predictive control of a continuous biodiesel plant

Typically, the large-scale production of biodiesel involves continuous operation plants. Also, the final biodiesel product has to comply with specifications imposed by standards of quality in order to be marketable. These quality constraints must be satisfied during the production at the minimum possible operating cost, in order to make the process economically viable. In this context, a nonlinear model predictive controller (NMPC) is applied to control the oil transesterification section of a continuous biodiesel plant. The controller determines the optimal profiles of the process variables using a nonlinear mechanistic model of the whole transesterification section. The model describes the dynamics of the composition and temperature of the liquid mixture in the reactors and in the decanters, as well as of the decanters interface level. The capability of the proposed NMPC strategy to improve the process economic performance and to enforce the final biodiesel specifications is demonstrated by simulation.     

Safety and Reachability of Piecewise Linear Hybrid Dynamical Systems Based on Discrete Abstractions

In this paper, a novel methodology for analysis of piecewise linear hybrid systems based on discrete abstractions of the continuous dynamics is presented. An important characteristic of the approach is that the available control inputs are taken into consideration in order to simplify the continuous dynamics. Control specifications such as safety and reachability specifications are formulated in terms of partitions of the state space of the system. The approach provides a convenient general framework not only for analysis, but also for controller synthesis of hybrid systems. The research contributions of this paper impact the areas of analysis, verification, and synthesis of piecewise linear hybrid systems.     

Minimization of the L∞-induced norm forsampled-data systems

It is shown that given any degree of accuracy, there exists a standard discrete-time l¹ problem that can be determined a priori whose solution yields a controller that is almost optimal in terms of the hybrid L^∞-induced norm. This is accomplished by first converting the hybrid system into an equivalent infinite-dimensional discrete-time system using the lifting technique in continuous time, and then approximating the infinite-dimensional parts of the system which model the intersample dynamics. A thorough analysis of the approximation procedure is presented, and it is shown that it is convergent at the rate of 1/n . Explicit bounds that are independent of the controller are obtained to characterize the approximation. It is also shown that the geometry of the induced norm for the sampled-data problem is different from that of the standard l¹ norm, and hence there might not exist a linear isometry that maps the sampled-data problem exactly to a standard discrete-time problem     

The real-time supervisory control of an experimental manufacturing system based on a hybrid method

In this paper, the real-time supervisory control of an experimental manufacturing system is reported based on a recently proposed hybrid (mixed PN/automaton) approach. Assuming that an uncontrolled bounded Petri net (PN) model of a (plant) discrete event system (DES) and a set of forbidden state specifications are given, the proposed approach computes a maximally permissive and nonblocking closed-loop hybrid model. The method is straightforward logically, graphically and technologically. This paper particularly shows the applicability of a hybrid (mixed PN/automaton) approach to low-level real-time DES control. To do this, programmable logic controller (PLC) based real-time control of an experimental manufacturing system is considered.     

On the supremal controllable sublanguage in the discrete-eventmodel of nondeterministic hybrid control systems

This paper is concerned with the logical control of hybrid control systems (HCS). It is assumed that a discrete-event system (DES) plant model has already been extracted from the continuous-time plant. The problem of hybrid control system design can then be solved by applying logical DES controller synthesis techniques to the extracted DES plant. Traditional DES synthesis methods, however, are not always applicable since the extracted plant DES will often exhibit nondeterministic transitions. This paper presents an extension of certain DES controller synthesis techniques to the nondeterministic control automaton found in HCS. In particular, this paper derives a formula computing the supremal controllable sublanguage of a given specification language under the assumption that the DES plant exhibits nondeterministic transitions     

A fuzzy controller improving a linear model following controllerfor motor drives

Since the dynamic response trajectory of a traditional fuzzy controller can not be quantitatively controlled, a fuzzy model following controller is proposed in this paper. In the proposed controller, an output feedback linear model following controller (LMFC) is first designed according to the roughly estimated plant model to let its response follow the output generated by a reference model. Then a model following error driven control signal is synthesized such that good model following characteristics can be preserved at various operating conditions. The proposed controller is applied to the speed control of an induction motor drive. Dynamic signal analysis of the model following behavior is made and the procedure for constructing the control algorithms is described in detail. The performance of the drive and the effectiveness of the proposed controller are demonstrated by some simulated and experimental results     

Results and perspectives on fault tolerant control for a class of hybrid systems

This article addresses the fault tolerant control (FTC) issue for a class of hybrid systems (HS) modelled by hybrid automata. Two kinds of faults are considered: continuous fault that affects each continuous system mode; discrete fault that affects the switching conditions. In these two faulty cases, the FTC design has two main objectives: (1) maintain the continuous performances including various stabilities of the origin and the output tracking/regulation behaviours along the trajectories of HS; (2) maintain the discrete specifications that have to be followed by HS, e.g. a desired switching sequence. The following three FTC methodologies are considered: FTC for HS with continuous stability goal; FTC for HS with discrete specifications; supervisory FTC design via hybrid control techniques. Some perspectives are also provided. This article provides the readers a survey on the main techniques that can be used to achieve these FTC goals of HS.     

Reference model selection and adaptive control for induction motordrives

An adaptive model-following speed controller for induction motor drives is proposed and implemented. This adaptive controller is easy to implement since, for the controlled plant, only the output signal is fed back. In order to choose a reference model with the desired drive dynamic behavior, a two-degree-of-freedom (2-DOF) controller is designed, using a systematic procedure based on the prescribed drive specifications. The reference model of the adaptive system is chosen as the transfer function of the controlled drive system by the 2-DOF controller in the nominal case. An adaptation signal is augmented to let the prescribed specifications be maintained under a wide range of operating conditions     

Synthesis of controllers for symmetric systems

This article deals with supervisory control problem for coloured Petri (CP) nets. Considering a CP-net, we build a condensed version of the ordinary state-space, namely the symbolic reachability graph (SRG). This latter graph allows to cope with state-space explosion problem for symmetric systems. The control specification can be expressed in terms of either forbidden states or forbidden sequences of transitions. According to these specifications, we derive the controller by applying the theory of regions on the basis of the SRG. Thanks to expressiveness power of CP-nets, the obtained controller to be connected to the plant model is reduced to one single place.     

A multiple model approach for predictive control of nonlinear hybrid systems

This paper presents modeling and control of nonlinear hybrid systems using multiple linearized models. Each linearized model is a local representation of all locations of the hybrid system. These models are then combined using Bayes theorem to describe the nonlinear hybrid system. The multiple models, which consist of continuous as well as discrete variables, are used for synthesis of a model predictive control (MPC) law. The discrete-time equivalent of the model predicts the hybrid system behavior over the prediction horizon. The MPC formulation takes on a similar form as that used for control of a continuous variable system. Although implementation of the control law requires solution of an online mixed integer nonlinear program, the optimization problem has a fixed structure with certain computational advantages. We demonstrate performance and computational efficiency of the modeling and control scheme using simulations on a benchmark three-spherical tank system and a hydraulic process plant.     

On the Reachability Problem for Uncertain Hybrid Systems

In this paper, we revisit the problem of designing controllers to meet safety specifications for hybrid systems, whose evolution is affected by both control and disturbance inputs. The problem is formulated as a dynamic game and an appropriate notion of hybrid strategy for the control inputs is developed. The design of hybrid strategies to meet safety specifications is based on an iteration of alternating discrete and continuous safety calculations. We show that, under certain assumptions, the iteration converges to a fixed point, which turns out to be the maximal set of states for which the safety specifications can be met. The continuous part of the calculation relies on the computation of the set of winning states for one player in a two player, two target, pursuit evasion differential game. We develop a characterization of these winning states (as well as the winning states for the other player for completeness) using methods from nonsmooth analysis and viability theory.     

Hybrid NMPC of supermarket display cases

This paper presents an NMPC of a supermarket refrigeration system. This is a hybrid process involving switched nonlinear dynamics and discrete events, on/off manipulated variables (valves and compressors), continuous controlled variables (goods temperatures) and, finally, several operation constraints. The hybrid controller is based on a parameterization of the on/off control signals in terms of time of occurrence of events instead of using directly binary values; in this way, the optimization problem can be re-formulated as an NLP problem. A rigorous model of a real supermarket refrigeration system is presented, as well as results of the hybrid controller operating on it.     

Digital redesign of uncertain interval systems based on extremal gain/phase margins via a hybrid particle swarm optimizer

In this paper, a hybrid optimizer incorporating particle swarm optimization (PSO) and an enhanced NM simplex search method is proposed to derive an optimal digital controller for uncertain interval systems based on resemblance of extremal gain/phase margins (GM/PM). By combining the uncertain plant and controller, extremal GM/PM of the redesigned digital system and its continuous counterpart can be obtained as the basis for comparison. The design problem is then formulated as an optimization problem of an aggregated error function in terms of deviation on extremal GM/PM between the redesigned digital system having an interval plant and its continuous counterpart, and subsequently optimized by the proposed optimizer to obtain an optimal set of parameters for the digital controller. Thanks to the performance of the proposed hybrid optimizer, frequency-response performances of the redesigned digital system using the digital controller evolutionarily derived by the proposed approach bare a far better resemblance to its continuous-time counter part in comparison to those obtained using existing open-loop discretization methods.