Control design for recycled, multi unit processes

An integrated multi-unit chemical plant presents a challenging control design problem due to the existence of recycling streams. In this paper, we develop a framework for analyzing the effects of recycling dynamics on closed-loop performance from which a systematic design of a decentralized control system for a recycled, multi-unit plant is established. In the proposed approach, the recycled streams are treated as unmodelled dynamics of the “unit” model so that their effects on closed-loop stability and performance can be analyzed using the robust control theory. As a result, two measures are produced: (1) the ν-gap metric, which quantifies the strength of recycling effects, and (2) the maximum stability margin of “unit” controller, which represents the ability of the “unit” controller to compensate for such effects. A simple rule for the “unit” control design is then established using the combined two measures in order to guarantee the attainment of good overall closed-loop performances. As illustrated by several design examples, the controllability of a recycled, multi unit process under a decentralized “unit” controller can be determined without requiring any detailed design of the “unit” controller because the simple rule is calculated from the open-loop information only.     

Variable structure exponential stabilization of chained systems based on the extended nonholonomic integrator

In this paper, a new variable structure control strategy for exponentially stabilizing chained systems is presented based on the extended nonholonomic integrator model, the discontinuous coordinate transformation and the “reaching law method” in variable structure control design. The proposed approach converts the stabilization problem of an n-dimensional chained system into the pole-assignment problem of an (n−3)-dimensional linear time-invariant system and consequently simplifies the stabilization controller design of nonholonomic chained systems.     

Parameter dependent H∞ control by finite dimensional LMI optimization: application to trade‐off dependent control

In this paper, we consider the design of an H_∞ trade‐off dependent controller, that is, a controller such that, for a given Linear Time‐Invariant plant, a set of performance trade‐offs parameterized by a scalar θ is satisfied. The controller state space matrices are explicit functions of θ. This new problem is a special case of the design of a parameter dependent controller for a parameter dependent plant, which has many application in Automatic Control. This last design problem can be naturally formulated as a convex but infinite dimensional optimization problem involving parameter dependent Linear Matrix Inequality (LMI) constraints. In this paper, we propose finite dimensional (parameter independent) LMI constraints which are equivalent to the parameter dependent LMI constraints. The parameter dependent controller design is then formulated as a convex finite dimensional LMI optimization problem. The obtained result is then applied to the trade‐off dependent controller design. A numerical example emphasizes the strong interest of our finite dimensional optimization problem with respect to the trade‐off dependent control application. Copyright © 2005 John Wiley & Sons, Ltd.     

Short-Period Communication and the Role of Zero-Order Holding in Networked Control Systems

We discuss controller design for a networked control system (NCS) in which a stochastic linear time invariant (LTI) plant communicates with a controller over a shared medium. The medium supports a limited number of simultaneous connections between the controller and the plant's sensors and actuators, possibly subject to transmission delays. We restrict communication to periodic medium access sequences which preserve the structural properties of the plant, thus decoupling the selection of the communication from that of the controller. Using the plant's controllability/observability indices as a guide for allocating access, we show that the period of the sequences in question can be shorter than previously established. In addition, we explore the use of sequences designed for a simple NCS model, in which sensors and actuators are “ignored” by the controller when they are not actively communicating, in a more complex, but practical, setting that includes zero-order holding. We include a numerical experiment that illustrates our results in the context of LQG control.      

Anti-windup via constrained regulation with observers

A method is presented for the output-feedback control of discrete-time linear systems with hard constraints on state and control variables. Prior work has shown that optimal controllers for constrained systems take the form of a nonlinear feedback law acting on a set-valued state estimate. In this paper, conventional state estimation schemes are used. A nonlinear control law is derived which views the state estimation error as a disturbance. The resulting control law is then used in conjunction with the conventional observer, rather than set-valued observer, to achieve the desired constrained regulation. The significantly reduced real-time computations come at the cost of restricting the controller structure and thereby introducing possible conservatism in the achievable performance. The results are specialized to the problem of anti-windup for systems with control saturations. A “measurement governor” scheme is introduced that alters plant measurements in such a way to improve performance in the presence of controller saturations.     

A decade of progress in iterative process control design: from theory to practice

One of the most active areas of research in the nineties has been the study of the interplay between system identification and robust control design. It has led to the development of “control-oriented identification design”, the paradigm being that, since the model is only a tool for the design of a controller, its accuracy (or its error distribution) must be tuned towards the control design objective. This observation has led to the concept of “iterative identification and control design” and, subsequently, to model-free iterative controller design, in which the controller parameters are iteratively tuned on the basis of successive experiments performed on the real plant, leading to better and better closed-loop behaviour. These iterative methods have found immediate applications in industry; they have also been applied to the optimal tuning of PID controllers. This paper presents the progress that has been accomplished in iterative process control design over the last decade. It is illustrated with some applications in the chemical industry.     

On the computation of the gap metric for LTV systems

In this paper, we consider the robust stabilization problem for linear discrete time-varying (LTV) systems using the gap metric. In particular, we show that the time-varying (TV) directed gap reduces to an operator with a TV Hankel plus Toeplitz structure. Computation of the norm of such an operator can be carried out using an iterative scheme involving a TV Hankel operator defined on a space of Hilbert–Schmidt causal operators. The “infimization” in the TV directed gap formula is shown to be, in fact, a minimum by using duality theory. The latter holds as well in the time-invariant case.     

Input-state model matching and ripple-free response for dual-rate systems

In this paper, we address the model matching problem for dual-rate systems where the controller output is generated at a faster rate than the measurement update rate. The model matching problem that has been studied in the literature requires the input-output properties of the closed-loop multirate system to match those of a desired single-rate linear time-invariant (LTI) system. In this paper, we consider the model matching problem from the input-state viewpoint: given a desired LTI system, find conditions and provide a controller design procedure to achieve matching between the closed-loop system and the desired system state variables at the measurement update rate. We provide a solution to this problem using a particular time-varying controller structure. In addition, we give conditions to avoid ripples in the steady-state output of the continuous-time plant; in particular, we show that some constraints on the input matrix of the desired system have to be posed. Numerical examples are given to illustrate the proposed method.     

H controller design for pure delay and other distributed systems

In this paper we consider the design of a rational stabilizing controller for a weighted two-block H problem with a distributed plant, with emphasis on the case of a pure delay plant and first order weights. The optimal controller for such a problem is, in general, distributed and requires rational approximation. We propose a simple suboptimal design procedure, which is based on Pade approximation with two crucial modifications: (i) high frequency performance is modified using a first-order approximated inverse; (ii) an additional one-point interpolation condition is imposed to restore stability at a critical imaginary unstable pole. The design trade-offs are discussed, with an example.     

A cognitivist model for decision support: COGITA project, a problem formulation assistant

The formulation of a problem may be defined as a process of acquisition and organization of knowledge related to a given situation, on which a decision maker projects some action. The assistance in the problem formulation that we may expect within decision support systems is difficult to design and to implement. This is mainly due to the frequent lack of attention to a sufficiently formalized conceptual framework which would consider the decision with a more cognition sciences oriented approach. In the first part, we will present an instrumental model for the study of decision processes as an attempt to simulate the cognitive process of knowledge acquisition and organization carried out by a decision maker facing a problematic situation. Considering its epistemological foundations, this model can be named “cognitivist model”. Within this model, the decision is defined as a cognitive construction which we call “decisional construct”. It consists of the elaboration of one or several abstract representations of the problematic situation (formulation phase), and the design of operational models (solving phase). In the second part, we will present the COGITA project, which consists of the design and realization of an environment for the development of problem formulation assistance systems. The modelization and simulation of cognitive processes call for relevant techniques originating either in artificial intelligence or in connectionism. We will show which are the main characteristics, potentials, limits and complementarity of these techniques and why their integration is fundamental and necessary to the simulation of the cognitive process associated with the formulation. COGITA is a hybrid system currently under development which tends to integrate symbolic artificial intelligence techniques and connectionist models in a cooperative hybridation the general architecture of which is presented.     

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.     

Design of optimal controllers for spatially invariant systems with finite communication speed

We consider the problem of designing optimal distributed controllers whose impulse response has limited propagation speed. We introduce a state-space framework in which all spatially invariant systems with this property can be characterized. After establishing the closure of such systems under linear fractional transformations, we formulate the H₂ optimal control problem using the model-matching framework. We demonstrate that, even though the optimal control problem is non-convex with respect to some state-space design parameters, a variety of numerical optimization algorithms can be employed to relax the original problem, thereby rendering suboptimal controllers. In particular, for the case in which every subsystem has scalar input disturbance, scalar measurement, and scalar actuation signal, we investigate the application of the Steiglitz–McBride, Gauss–Newton, and Newton iterative schemes to the optimal distributed controller design problem. We apply this framework to examples previously considered in the literature to demonstrate that, by designing structured controllers with infinite impulse response, superior performance can be achieved compared to finite impulse response structured controllers of the same temporal degree.     

Sensor management for tracking smart targets

We consider the problem of tracking a “smart” target. That is, a target that is aware it is being tracked and modifies its behaviour accordingly. To track such targets effectively it is necessary to modify the behaviour of the tracking sensor in response to the target. We consider that the best framework for such a problem is that of a mathematical game. In this paper, we consider an idealised version of this problem that illustrates some of the issues that can occur when attempting to track a smart target and the utility of a game theoretic framework.     

Coherent quantum LQG control

Based on a recently developed notion of physical realizability for quantum linear stochastic systems, we formulate a quantum LQG optimal control problem for quantum linear stochastic systems where the controller itself may also be a quantum system and the plant output signal can be fully quantum. Such a control scheme is often referred to in the quantum control literature as “coherent feedback control”. It distinguishes the present work from previous works on the quantum LQG problem where measurement is performed on the plant and the measurement signals are used as the input to a fully classical controller with no quantum degrees of freedom. The difference in our formulation is the presence of additional non-linear and linear constraints on the coefficients of the sought after controller, rendering the problem as a type of constrained controller design problem. Due to the presence of these constraints, our problem is inherently computationally hard and this also distinguishes it in an important way from the standard LQG problem. We propose a numerical procedure for solving this problem based on an alternating projections algorithm and, as an initial demonstration of the feasibility of this approach, we provide fully quantum controller design examples in which numerical solutions to the problem were successfully obtained. For comparison, we also consider the case of classical linear controllers that use direct or indirect measurements, and show that there exists a fully quantum linear controller which offers an improvement in performance over the classical ones.     

Stability and performance analysis of mixed product run-to-run control

Run-to-run control has been widely used in batch manufacturing processes to reduce variations. However, in batch processes, many different products are fabricated on the same set of process tool with different recipes. Two intuitive ways of defining a control scheme for such a mixed production mode are (i) each run of different products is used to estimate a common tool disturbance parameter, i.e., a “tool-based” approach, (ii) only a single disturbance parameter that describe the combined effect of both tool and product is estimated by results of runs of a particular product on a specific tool, i.e., a “product-based” approach. In this study, a model two-product plant was developed to investigate the “tool-based” and “product-based” approaches. The closed-loop responses are derived analytically and control performances are evaluated. We found that a “tool-based” approach is unstable when the plant is non-stationary and the plant-model mismatches are different for different products. A “product-based” control is stable but its performance will be inferior to single product control when the drift is significant. While the controller for frequent products can be tuned in a similar manner as in single product control, a more active controller should be used for the infrequent products which experience a larger drift between runs. The results were substantiated for a larger system with multiple products, multiple plants and random production schedule.     

Certainty equivalence in nonlinear output regulation with unmeasured error

In this article, we consider a nonlinear output regulation problem in which the controlled output and the measured output are not the same. It is assumed that the controlled plant has a single control input, and that it can be transformed into Gauthier–Kupka's observability canonical form. Then, it is shown that a design based on certainty equivalence is effective for determining a controller that solves the given problem.     

A new optimization model to support a bottom-up approach to facility design

The facility layout problem is typically solved in what is referred to as a “top-down approach” of block layout design followed by detailed layout determination. However, a number of research efforts recently have challenged this approach, producing a reformulated bottom-up approach to the facility layout problem. In this paper we consider the bottom-up approach, applying a tighter formulation than prior efforts and investigating the solvability limits of the new model. Empirical testing of the new bottom-up layout model indicates that although this model produces more usable output, as judged by industry experts, it is approximately three times harder to solve. Valid inequalities and special cases are identified to help improve the formulation's solvability.     

On the problem of robust and perfect tracking for linear systems with external disturbances

We consider in this paper the robust and perfect tracking (RPT) problem for multivariable linear systems with external disturbances. The problem is to design a proper controller such that the resulting overall closed-loop system is asymptotically stable and the controlled output almost perfectly tracks a given reference signal with an arbitrarily fast settling time in the face of external disturbances and initial conditions. The contribution of this paper is two-fold: (1) We derive a set of necessary and sufficient conditions under which the RPT problem is solvable; and (2) Under these solvability conditions, we develop algorithms for constructing state and output feedback laws, explicitly parameterized in epsilon, that solve the RPT problem. In our construction of feedback laws, we propose a controller structure which enables us to design a tracking controller without introducing additional integrators regardless of what type the system is.     

Perception-based approach to time series data mining

Time series data mining (TSDM) techniques permit exploring large amounts of time series data in search of consistent patterns and/or interesting relationships between variables. TSDM is becoming increasingly important as a knowledge management tool where it is expected to reveal knowledge structures that can guide decision making in conditions of limited certainty. Human decision making in problems related with analysis of time series databases is usually based on perceptions like “end of the day”, “high temperature”, “quickly increasing”, “possible”, etc. Though many effective algorithms of TSDM have been developed, the integration of TSDM algorithms with human decision making procedures is still an open problem. In this paper, we consider architecture of perception-based decision making system in time series databases domains integrating perception-based TSDM, computing with words and perceptions, and expert knowledge. The new tasks which should be solved by the perception-based TSDM methods to enable their integration in such systems are discussed. These tasks include: precisiation of perceptions, shape pattern identification, and pattern retranslation. We show how different methods developed so far in TSDM for manipulation of perception-based information can be used for development of a fuzzy perception-based TSDM approach. This approach is grounded in computing with words and perceptions permitting to formalize human perception-based inference mechanisms. The discussion is illustrated by examples from economics, finance, meteorology, medicine, etc.