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.     

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.     

Control and design problems in material processing—how can process systems engineers contribute to material processing?

‘Process control and systems engineering’ is not just a subject of study for controlling and designing ‘a plant’ and/or ‘a unit operation’. It also deals with any control and design problems related to physical and chemical phenomena occurring in short time-scale and at nano, meso as well as micro-scale levels. In materials processing, controlling the material structure is of primary importance for realizing high material performance and functions. The phenomena determining the material structure often involve phase separation and/or occur on the surface of the materials, at small level and in short time-scale. To control these phenomena, the current feedback design schemes, where controlled variables are measured by ‘externally equipped sensors’ and fed back to a ‘externally designed controller’, are no longer effective due to the shortness of time and smallness of spatial scales of the objects. Making reference to two novel polymer-processing processes, a micro-cellular polymeric foaming process and surface coating injection-molding process, we discuss how process control and process systems engineers can contribute to controlling the structure of materials.     

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.     

A feedforward–feedback glucose control strategy for type 1 diabetes mellitus

As the “artificial pancreas” becomes closer to reality, automated insulin delivery based on real-time glucose measurements becomes feasible for people with diabetes. This paper is concerned with the development of novel feedforward–feedback control strategies for real-time glucose control and type 1 diabetes. Improved post-meal responses can be achieved by a pre-prandial snack or bolus, or by reducing the glucose setpoint prior to the meal. Several feedforward–feedback control strategies provide attractive alternatives to the standard meal insulin bolus and are evaluated in simulations using a physiological model.     

Role of multiplicity in reactive distillation control system design

The impact of steady-state multiplicities on the control of a simulated industrial scale methyl acetate reactive distillation (RD) column is studied. At a fixed reflux rate, output multiplicity, with multiple output values for the same reboiler duty, causes the column to drift to an undesirable steady-state under open loop operation. The same is avoided for a fixed reflux ratio policy. Input multiplicity, where multiple input values give the same output, leads to “wrong” control action under feedback control severely compromising control system robustness. A new metric, rangeability, is defined to quantify the severity of input multiplicity in a steady-state input–output (IO) relation. Rangeability is used in conjunction with conventional sensitivity analysis for the design of robust control structures for the RD column. Results for the two synthesized control structures show that controlling the most sensitive reactive tray temperature results in poor robustness due to low rangeability causing “wrong” control action for large disturbances. Controlling a reactive tray temperature with acceptable sensitivity but larger rangeability gives better robustness. It is also shown that controlling the difference in the temperature of two suitably chosen reactive trays further improves robustness of both the structures as input multiplicity is avoided. The article brings out the importance of IO relations for control system design and understanding the complex dynamic behavior of RD systems.     

Optimal Time Substitution in a Control Process

Control for the current state of a process by observation is investigated. The aim functional is defined by the ratio of integrals of integrands dependent on control functions. By this functional, control is interpreted as a time substitution control. Optimal control functions for certain classes of control functions and a method for computing them are determined. Relay control functions and related functions are shown to be optimal.__________Translated from Avtomatika i Telemekhanika, No. 8, 2005, pp. 64–83.Original Russian Text Copyright © 2005 by Kharlamov.This work was supported by the Program “Control for Mechanical Systems” no. 19 of the Presidium of the Russian Academy of Sciences and National School Grant, no. 2258.2003.1.     

On global stabilization of Burgers’ equation by boundary control

Although often referred to as a one-dimensional “cartoon” of Navier–Stokes equation because it does not exhibit turbulence, the Burgers equation is a natural first step towards developing methods for control of flows. Recent references include Burns and Kang [Nonlinear Dynamics 2 (1991) 235–262], Choi et al. [J. Fluid Mech. 253 (1993) 509–543], Ito and Kang [SIAM J. Control Optim. 32 (1994) 831–854], Ito and Yan [J. Math. Anal. Appl. 227 (1998) 271–299], Byrnes et al. [J. Dynam. Control Systems 4 (1998) 457–519] and Van Ly et al. [Numer. Funct. Anal. Optim. 18 (1997) 143–188]. While these papers have achieved tremendous progress in local stabilization and global analysis of attractors, the problem of global asymptotic stabilization has remained open. This problem is non-trivial because for large initial conditions the quadratic (convective) term – which is negligible in a linear/local analysis – dominates the dynamics. We derive nonlinear boundary control laws that achieve global asymptotic stability. We consider both the viscous and the inviscid Burgers’ equation, using both Neumann and Dirichlet boundary control. We also study the case where the viscosity parameter is uncertain, as well as the case of stochastic Burgers’ equation. For some of the control laws that would require the measurement in the interior of the domain, we develop the observer-based versions.     

Uniting local and global controllers for uncertain nonlinear systems: beyond global inverse optimality

This paper provides a solution to a new problem of global robust control for uncertain nonlinear systems. A new recursive design of stabilizing feedback control is proposed in which inverse optimality is achieved globally through the selection of generalized state-dependent scaling. The inverse optimal control law can always be designed such that its linearization is identical to linear optimal control, i.e. optimal control, for the linearized system with respect to a prescribed quadratic cost functional. Like other backstepping methods, this design is always successful for systems in strict-feedback form. The significance of the result stems from the fact that our controllers achieve desired level of ‘global’ robustness which is prescribed a priori. By uniting locally optimal robust control and global robust control with global inverse optimality, one can obtain global control laws with reasonable robustness without solving Hamilton–Jacobi equations directly.     

Intelligent adaptive control for MIMO uncertain nonlinear systems

This paper investigates an intelligent adaptive control system for multiple-input–multiple-output (MIMO) uncertain nonlinear systems. This control system is comprised of a recurrent-cerebellar-model-articulation-controller (RCMAC) and an auxiliary compensation controller. RCMAC is utilized to approximate a perfect controller, and the parameters of RCMAC are on-line tuned by the derived adaptive laws based on a Lyapunov function. The auxiliary compensation controller is designed to suppress the influence of residual approximation error between the perfect controller and RCMAC. Finally, two MIMO uncertain nonlinear systems, a mass–spring–damper mechanical system and a Chua’s chaotic circuit, are performed to verify the effectiveness of the proposed control scheme. The simulation results confirm that the proposed intelligent adaptive control system can achieve favorable tracking performance with desired robustness.     

Stabilization and H control of symmetric systems: an explicit solution

In this paper we address the H^∞ control analysis, the output feedback stabilization, and the output feedback H^∞ control synthesis problems for state-space symmetric systems. Using a particular solution of the Bounded Real Lemma for an open-loop symmetric system we obtain an explicit expression to compute the H^∞ norm of the system. For the output feedback stabilization problem we obtain an explicit parametrization of all asymptotically stabilizing control gains of state-space symmetric systems. For the H^∞ control synthesis problem we derive an explicit expression for the optimally achievable closed-loop H^∞ norm and the optimal control gains. Extension to robust and positive real control of such systems are also examined. These results are obtained from the linear matrix inequality formulations of the stabilization and the H^∞ control synthesis problems using simple matrix algebraic tools.     

Optimal operation of Petlyuk distillation: steady-state behavior

The “Petlyuk” or “dividing-wall” or “fully thermally coupled” distillation column is an interesting alternative to the conventional cascaded binary columns for separation of multi-component mixtures. However, the industrial use has been limited, and difficulties in operation have been reported as one reason. With three product compositions controlled, the system has two degrees of freedom left for on-line optimization. We show that the steady-state optimal solution surface is quite narrow, and depends strongly on disturbances and design parameters. Thus it seems difficult to achieve the potential energy savings compared to conventional approaches without a good control strategy. We discuss candidate variables which may be used as feedback variables in order to keep the column operation close to optimal in a “self-optimizing” control scheme.     

Robust control of a class of uncertain nonlinear systems

This paper considers the robust control of a class of nonlinear systems with real time-varying parameter uncertainty. Interest is focused on the design of linear dynamic output feedback control and two problems are addressed. The first one is the robust stabilization and the other is the problem of robust performance in an H_∞ sense. A technique is proposed for designing stabilizing controllers for both problems by converting them into ‘scaled’ H_∞ control problems which do not involve parameter uncertainty.     

Current sharing of paralleled DC–DC converters using GA-based PID controllers

We demonstrate a concept for pulse-width modulation (PWM) control of a parallel DC–DC buck converter, which eliminates the need for multiple physical connections of gating/PWM signals among the distributed converter modules. The proposed control concept may lead to easier distributed control implementation of parallel DC–DC converters and distributed power systems.For equipment with significant power requirement, the traditional single power supply may not be adequate. Many power supplies with parallel regulation control can be used to solve this problem. This paper proposes a Proportional-Integral-Derivative (PID) controller to control paralleled DC–DC buck converters and current sharing is achieved. A genetic algorithm (GA) is employed to derive optimal or near optimal PID controller gains. Both simulations and experimental results are provided to verify the theoretical analysis through an experimental prototype of paralleled DC–DC buck converters.     

Steering rules for AGV based on primitive function and elementary movement control

The complete structure of an AGV control system is described in the first part of this paper. The AGV control system is hierarchical and consists of five levels. The structure of one level does not depend on the structures of the other levels. This means that the control system depends on the design of the AGV at the lowest level only, at the actuator servo-control level and its coordination in realizing AGV primitive functions.The second part of the paper describes rules applicable to AGV steering. The structure of these rules depends on two groups of factors. The first group is dependent on information groups fed to the AGV processor by the position sensor. The second group of factors represents aims and conditions and AGV steering such as positioning accuracy, positioning time, allowed room for maneuver, the shape of the given trajectory, etc. The AGV steering rules contain sequences of primitive functions. These primitive functions are of such types as “turn left”, “straighten” (correct), “go straight on”, etc. Trajectory, as one of the basic factors, is defined at the level of controlling an elementary movement. The term “to control an elementary movement” means to select a transport road throughout the transport network and to code it using “elementary movement” such as “go straight” (relating to road section), “turn left” (relating to turning at a crossroad) etc.The results of the AGV steering simulation are presented in the third part of the paper. An exact kinematic AGV model used for stimulating control models is also presented.     

Supervisory control of hybrid systems within a behavioural framework

This contribution addresses the synthesis of supervisory control for hybrid systems Σ with discrete external signals. Such systems are in general neither l-complete nor can they be represented by finite state machines. We find an l-complete approximation (abstraction) Σ_l for Σ, represent it by a finite state machine, and investigate the control problem for the approximation. If a solution exists, we synthesize the maximally permissive supervisor for Σ_l. We show that it also solves the control problem for the hybrid system Σ. If no solution exists, approximation accuracy can be increased by computing a k-complete abstraction Σ_k, k>l. This paper is entirely set within the framework on Willems’ behavioural systems theory.     

Predictive pull-based control of an unmanned manufacturing cell, accounting for robot mobility

In order to remove the cell size limitation and to make cellular manufacturing systems more flexible, a manufacturing cell has been equipped with a mobile robot which moves from machine to machine, much like its human counterpart would do. To further acquire a portion of the attributes (intelligence and adaptability of the human worker) lost in robotizing the traditional manned manufacturing cell, a “limited” knowledge-based cell control algorithm is developed. This algorithm maintains standard pull control logic as its underlying basis while utilizing heuristically, knowledge of the ongoing processes and their current status. In this paper, an analysis of this ‘new’ predictive pull-based controller is presented. The simulation results from the predictive pull-based controller are evaluated and compared with the standard pull control logic, first come first serve and shortest distance. A test-bed of an unmanned manufacturing cell with a self-propelled mobile robot was used for experimental verification. Simulation and experimental results show that the degree of improvements gained in the cell performance over the standard pull control method is dependent on the robot’s mobility velocity and how much part inspection/part rejection is performed within the cell. In conclusion, the predictive pull-based algorithm is relatively simple variation of pull control which has the ability of enhancing the “near optimal” pull cell control performance.     

Fuzzy Modeling and Control for Conical Magnetic Bearings Using Linear Matrix Inequality

A general nonlinear model with six degree-of-freedom rotor dynamics and electromagnetic force equations for conical magnetic bearings is developed. For simplicity, a T–S (Takagi–Sugeno) fuzzy model for the nonlinear magnetic bearings assumed no rotor eccentricity is first derived, and a fuzzy control design based on the T–S fuzzy model is then proposed for the high speed and high accuracy control of the complex magnetic bearing systems. The suggested fuzzy control design approach for nonlinear magnetic bearings can be cast into a linear matrix inequality (LMI) problem via robust performance analysis, and the LMI problem can be solved efficiently using the convex optimization techniques. Computer simulations are presented for illustrating the performance of the control strategy considering simultaneous rotor rotation tracking and gap deviations regulation.