Decentralised control of chromatographic simulated moving bed processes based on wave front reconstruction

The behaviour of chromatographic simulated moving bed processes is described by the movement of concentration profiles through a circle of separation columns. A closed-loop control manipulates the profiles in order to meet demands concerning specified product purity and disturbance attenuation. If steep wave fronts of the concentration profiles occur, the controlled variables undergo fast changes in case of a transient of the process. In this case, a reconstruction of the wave fronts is necessary for a successful control.A simple and effective decentralised controller structure is proposed based on cascaded discrete-time PI controllers. On-line product purity measurements and the reconstructed wave fronts are used for control purposes. Two kinds of process models are used: a rigorous model for dynamic simulations, and strongly simplified plant models for the design of the wave front reconstruction and the controller. The latter models are identified based on experimental step tests with the reference plant and numerical simulations. The performance of the control system is evaluated by numerical simulations.     

State Observation and Diagnosis of Discrete-Event Systems Described by Stochastic Automata

The problems ofstate observation and diagnosis are solved for discrete–eventsystems, which are described by stochastic automata. As manysystems are not observable in the sense that it is possible toreconstruct the state unambiguously, the observation problemis set up as the problem of determining the smallest possibleset of states that are compatible with the measured input andoutput sequences. The diagnostic problem is shown to be, in principle,an observation problem. Conditions for the observability anddiagnosability of stochastic automata are presented. The resultsare illustrated by examples.     

Sensor and actuator fault diagnosis of systems with discrete inputs and outputs

The paper describes a method for detecting and identifying faults that occur in the sensors or in the actuators of dynamical systems with discrete-valued inputs and outputs. The model used in the diagnosis is a stochastic automaton. The generalized observer scheme (GOS), which has been proposed for systems with continuous-variable inputs and outputs some years ago, are developed for discrete systems. This scheme solves the diagnostic problem as an observation problem, which is set up here for discrete-event systems. As the system under consideration is described by a stochastic automaton rather than a differential equation, the mathematical background and the diagnostic algorithms obtained are completely different from the well-known observers developed for continuous-variable systems. The GOS is extended here by a fault detection module to cope with plant faults that are different from actuator or sensor faults. The diagnostic algorithm consists of two steps, the first detecting the existence of a fault and the second isolating possible sensor or actuator faults or identifying plant faults. The results are applied to quantized systems whose discrete inputs and outputs result from a quantization of the continuous-variable input and output signals. Experimental results illustrate the proposed diagnostic method.     

Discrete-event models of quantized systems for diagnosis

The paper concerns the model-based diagnosis of continuous-variable systems whose state can only be measured through a quantizer. The diagnosis is based on the investigation whether the observed discrete input and output sequences are consistent with a discrete-event model of the quantized system. The paper describes a necessary and sufficient condition for the discrete-event model to be suitable for diagnosis. This condition is independent of the specific model form and of the diagnostic algorithm applied to the model. Within a hierarchy of models with increasing accuracy all of which satisfy this modelling requirement the quality of the diagnostic result increases. The results are illustrated by an example.     

Leader–follower synchronisation of autonomous agents with external disturbances

The synchronisation problem is investigated for multiple linear agents with external disturbances that are guided by a leader with different dynamics. A method is presented for designing a networked controller that synchronises the agents. First, a general dynamic controller with two inputs is proposed that introduces the model of the leader as an internal reference model into the control loop of all the following agents. Second, the two inputs to the local controllers of the followers are designed by H_∞ control theory such that the resulting closed-loop system achieves the output synchronisation with a desired disturbance attenuation performance. The proposed method is applied to the leader–follower synchronisation of vehicles in a platoon.     

Dependable control of uncertain linear systems based on set-theoretic methods

This article concerns the feedback control of discrete-time systems subject to disturbances and uncertainties in both model parameters and signal measurements. The uncertainties are assumed to be unknown but bounded and thus characterised by closed intervals or sets. The main result is a new approach to design a feedback controller keeping the system state in a target set. First, a method is proposed that computes minimal enclosures of the set of reachable states, which are consistent with the uncertain input and output measurements and the system dynamics. Then, a control method to keep the current state set in the target set is developed, which extends control techniques based on invariant polyhedra. The method is illustrated by a mobile robot experiment.     

Control reconfiguration after actuator failures by Markov parameter matching

Two novel linear control reconfiguration methods for plants subject to actuator failures are described. The common idea is to place a reconfiguration block between the faulty plant and the nominal controller in order to re-route the signals around the broken actuator. The first method uses a computationally simple static reconfiguration block. It recovers the nominal plant input/output-behaviour by assigning the faulty plant the same Markov parameters as the faultless plant. The second method concerns the design of the feedforward part in the virtual actuator using the idea and results of the first approach. The virtual actuator is a dynamical reconfiguration block. Existence conditions and solution algorithms are provided, and it is shown that both approaches guarantee the closed-loop stability if the existence conditions are met. An experimental study demonstrates the practical usability of the proposed approaches.     

Stability analysis and controller synthesis for hybrid dynamical systems

Wherever continuous and discrete dynamics interact, hybrid systems arise. This is especially the case in many technological systems in which logic decision-making and embedded control actions are combined with continuous physical processes. Also for many mechanical, biological, electrical and economical systems the use of hybrid models is essential to adequately describe their behaviour. To capture the evolution of these systems, mathematical models are needed that combine in one way or another the dynamics of the continuous parts of the system with the dynamics of the logic and discrete parts. These mathematical models come in all kinds of variations, but basically consist of some form of differential or difference equations on the one hand and automata or other discrete-event models on the other hand. The collection of analysis and synthesis techniques based on these models forms the research area of hybrid systems theory, which plays an important role in the multi-disciplinary design of many technological systems that surround us. This paper presents an overview from the perspective of the control community on modelling, analysis and control design for hybrid dynamical systems and surveys the major research lines in this appealing and lively research area.     

Modelling and decentralized control of a multizone crystal growth furnace

The controller of a crystal growth furnace with 15 heating zones must have a decentralized structure. It is shown that each control station must necessarily satisfy a certain robustness property and that the design of the whole decentralized controller can be replaced by the problem of designing the control stations separately from each other as robust centralized controllers. As a basis for this, it is shown that the model can be considerably reduced. Although the zones are strongly coupled it will be seen here that, owing to structural properties of the plant, the furnace can be described by a model which has regard to only three zones. Experimental results with furnace illustrate the modelling and design methods used.