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.     

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.     

Output feedback decentralized control of large-scale systems using weighted sensitivity functions minimization

This paper considers the problem of achieving stability and desired dynamical transient behavior for linear large-scale systems, by decentralized control. It can be done by making the effects of the interconnections between the subsystems arbitrarily small. Sufficient conditions for stability and diagonal dominance of the closed-loop system are introduced. These conditions are in terms of decentralized subsystems and directly make a constructive H_∞ control design possible. A mixed H_∞ pole region placement is suggested, such that by assigning the closed-loop eigenvalues of the isolated subsystems appropriately, the eigenvalues of the overall closed-loop system are assigned in desirable range. The designs are illustrated by an example.     

An Effective Coalgebraic Bisimulation Proof Method

The bisimulation “up-to-…” technique provides an effective way to relieve the amount of work in proving bisimilarity of two processes. This paper develops a fresh and direct approach to generalize this set-theoretic “up-to-...” principle to the setting of coalgebra theory. The notion of consistent function is introduced, as a generalization of Sangiorgi's sound function. Then, in order to prove that there are only bisimilar pairs in a relation, it is sufficient to find a morphism from it to the “lifting” of its image under some consistent function. One example is given showing that every self-bisimulation in normed BPA is just such a relation. What's more, we investigate the connection between span-bisimulation and ref-bisimulation. As a result, λ-bisimulation turns out to be covered by our new principle.     

Decentralized preview control for multiple disturbance rejection in HVAC systems

A decentralized preview controller is designed for temperature control of multizone indoor environmental spaces. A two-zone space heating system is considered. The physical system consists of a boiler, heat pumps, distribution network and two environmental zones. By assuming that the outdoor temperature variations are “previewable”, a decentralized preview controller is designed by using a parameter optimization method. The output responses of the resulting decentralized closed-loop bilinear system acted upon by single and multiple disturbances with and without preview action are compared. Also, results showing the robustness property of the controller, and the 24-hour building operation with unoccupied and occupied setpoint tracking using preview control are given.     

Simple analytic rules for model reduction and PID controller tuning

The aim of this paper is to present analytic rules for PID controller tuning that are simple and still result in good closed-loop behavior. The starting point has been the IMC-PID tuning rules that have achieved widespread industrial acceptance. The rule for the integral term has been modified to improve disturbance rejection for integrating processes. Furthermore, rather than deriving separate rules for each transfer function model, there is a just a single tuning rule for a first-order or second-order time delay model. Simple analytic rules for model reduction are presented to obtain a model in this form, including the “half rule” for obtaining the effective time delay.     

A convex characterization of distributed control problems in spatially invariant systems with communication constraints

In this paper we consider the problem of distributed controller design in spatially invariant systems for which communication among sites is limited. In particular, the controller is constrained so that information is propagated with a delay that depends on the distance between subsystems—a structure we refer to as “funnel” causality. We show that the problem of optimal design can be cast as a convex problem provided that the plant has a similar funnel-causality structure, and the propagation speeds in the controller are at least as fast as those in the plant. As an example, we consider the case of the wave dynamics with limited propagation speed control.     

Value function-based approach to the scheduling of multiple controllers

Both gain scheduling and multiple model based control approaches are considered to be practical approaches for control of industrial nonlinear processes. However, the former ignores system dynamics and the latter is specific to the type of controller design and limited in its scope of application as practiced in industry. This paper proposes a value function-based strategy for switching among local controllers, thereby providing an effective global control policy for the entire operating regions. The suggested method selects the best one among a set of available control policies at each time step by evaluating the “value” function associated with the successive state when a particular control action instructed by a candidate policy is taken for a give state. The value function, which maps a state to its associated discounted infinite horizon cost-to-go, is obtained by solving the dynamic programming in an approximate way using closed-loop simulation or operational data and a function approximator. The proposed approach has the advantages that candidate controllers are general and the switching is performed not by a fixed heuristic rule but rigorously via dynamic programming. From the viewpoint of dynamic programming, the approach helps alleviate the curse of dimensionality with respect to the state space and action space. Optimal or approximately optimal switching rules can be learned without a model, which defines the state transitional rule. The approach is demonstrated on several different nonlinear control examples.     

How auxiliary variables and plant data collection affect closed-loop performance of inferential control

The design of property estimators for inferential control is addressed in this paper, and the effects of the auxiliary variables (estimator’s inputs) and of the approach to collect plant data, used to compute the model coefficients, are investigated. The concept of steady-state closed-loop consistency, which is the ability of an estimator to guarantee low offset in the unmeasured controlled variables, is adopted and theoretical results about this property are derived. It is shown how the selection of auxiliary variables represents the most crucial design step that determines the final closed-loop performance of an inferential control system. When this selection is done on a steady-state closed-loop consistency basis, the closed-loop performance is satisfactory, and it is secondary how the dataset is built. On the other hand, when “inconsistent” inputs are used, the performance is, in general, poor and may be significantly affected (in positive or in negative) by the dataset characteristics.     

Stabilization by output feedback for systems with ISS inverse dynamics

We consider the subclass of the set systems which admit a global normal form where only the output and not its time derivatives appear in the nonlinearities. We prove that, when the inverse dynamics are “input-to-state stable” (ISS) and a finite gain condition is satisfied, global asymptotic stability can be achieved by dynamic output feedback.     

Nonlinear robust H∞ control via dynamic output feedback

The problem on robust H_∞ control for a class of nonlinear systems with parameter uncertainty is studied. Sufficient conditions for the existence of the dynamic output feedback controller are obtained. Under these conditions, the closed-loop systems have robust H_∞-performance. A numerical example is given to illustrate the design of a robust controller using the proposed approach.     

A type theory which is complete for Kreisel's modified realizability

We define a type theory with a strong elimination rule for existential quantification. As in Martin-Löf's type theory, the “axiom of choice” is thus derivable. Proofs are also annotated by realizers which are simply typed λ-terms. A new rule called “type extraction” which extracts the type of a realizer allows us to derive the so-called “independance of premisses” schema. Consequently, any formula which is realizable in HA^ω, according to Kreisel's modified realizability, is derivable in this type theory.     

Price-driven coordination method for solving plant-wide MPC problems

In large-scale model predictive control (MPC) applications, such as plant-wide control, two possible approaches to MPC implementation are centralized and decentralized MPC schemes. These represent the two extremes in the “trade-off” among the desired characteristics of an industrial MPC system, namely accuracy, reliability and maintainability. To achieve optimal plant operations, coordination of decentralized MPC controllers has been identified as both an opportunity and a challenge. Typically, plant-wide MPC problem can be formulated as a large-scale quadratic program (QP) with linking equality constraints. Such problems can be decomposed and solved with the price-driven coordination method and on-line solutions of these structured large-scale optimization problems require an efficient price-adjustment strategy to find an “equilibrium price”. This work develops an efficient price-adjustment algorithm based on Newton’s method, in which sensitivity analysis and active set change identification techniques are employed. With the off-diagonal element abstraction technique and the enhanced priced driven coordination algorithm, a coordinated, decentralized MPC framework is proposed. Several case studies show that the proposed coordination-based decentralized MPC scheme is an effective approach to plant-wide MPC applications, which provides a high degree of reliability and accuracy at a reasonable computational load.     

A bound on closed-loop performance based on finite-frequency response samples

A new, computationally tractable, bound is derived for the level of closed-loop performance achieved by a given finite-dimensional feedback compensator with a plant for which a finite number of frequency response samples are computable. The bound involves quantities reflecting the performance of the controller with a finite-dimensional, nominal model of the plant, quantities that can be determined from the finite number of frequency response samples of the true plant, and quantities related to the complexity (in the sense of Vinnicombe) of all systems involved. This bound can be used to ‘validate’ closed-loop performance in the case that the true plant frequency response samples are of a plant which is not completely known or, to measure the performance of a finite-dimensional controller with a computationally intractable (e.g. infinite-dimensional) model of the true plant.     

Security procedures for program libraries

As computer programming has become more complex, management has become more concerned about its own ability to exercise appropriate control over the programmer.This paper describes an implementation of procedures, libraries, and separation of duties to improve security in programming. This implementation helps to limit scope, reveal programmer intent and fix accountability. It assumes and supports such improved programming technologies as top-down design, structured programming, psuedo-code documentation, use of librarians, inspections, and “walk-throughs”.While the implementation described here will contribute to security, it is not sufficient. Management will wish to consider the application of many other measures.     

Global stabilization of feedforward systems with exponentially unstable Jacobian linearization

The global stabilization of a class of feedforward systems having an exponentially unstable Jacobian linearization is achieved by a high-gain feedback saturated at a low level. The control law forces the derivatives of the state variables to small values along the closed-loop trajectories. This “slow control” design is illustrated with a benchmark example and its limitations are emphasized.     

Network flow control under capacity constraints: A case study

In this paper, we demonstrate how tools from nonlinear system theory can play an important role in tackling “hard nonlinearities” and “unknown disturbances” in network flow control problems. Specifically, a nonlinear control law is presented for a communication network buffer management model under physical constraints. Explicit conditions are identified under which the problem of asymptotic regulation of a class of networks against unknown inter-node traffic is solvable, in the presence of control input and state saturation. The conditions include a Lipschitz-type condition and a “PE” condition. Under these conditions, we achieve either asymptotic or practical regulation for a single-node system. We also propose a decentralized, discontinuous control law to achieve (global) asymptotic regulation of large-scale networks. Our main result on controlling large-scale networks is based on an interesting extension of the well-known Young's inequality for the case with saturation nonlinearities. We present computer simulations to illustrate the effectiveness of the proposed flow control schemes.     

On the pole location of a system designed by robust stability-degree assignment

In this paper, we examine the pole location of the feedback system composed of the nominal plant and the H_∞ central controller designed by the robust stability-degree assignment. Namely, the exact pole location at γ=∞ and the behavior near the infimum of γ are clarified where γ is the upper bound of the H_∞ norm constraint. The original design goal is to stabilize the plant against additive perturbations with the regional pole placement condition Re s<−α, and the design problem is reduced to the one-block H_∞ control problem.     

B2B e-commerce supply chain integration and performance: A contingency fit perspective on the role of environment

Drawing upon contingency theory “fit” research in the IT and supply chain management literature, we applied the “fit” concept to the relationship between B2B e-commerce supply chain integration and performance. The results demonstrated that the effect of B2B supply chain integration on financial, market, and operational performance decreased as product turbulence and demand unpredictability jointly increased. Managerial implications include the conditions under which IT investments yield performance improvement and the need for firms to actively manage demand uncertainty.     

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.