Stable Model Predictive Control for Integrating Systems with Optimizing Targets

This paper concern the development of a stable model predictive controller (MPC) to be integrated with real time optimization (RTO) in the control structure of a process system with stable and integrating outputs. The real time process optimizer produces Optimal targets for the system inputs and for Outputs that Should be dynamically implemented by the MPC controller. This paper is based oil a previous work (Comput. Chem. Eng. 2005, 29, 1089) where a nominally stable MPC was proposed for systems with the conventional control approach where only the outputs have set points. This work is also based oil the work of Gonzalez et at. (J. Process Control 2009, 19, 110) where the zone control of stable systems is studied. The new control for is obtained by defining ail extended control objective that includes input targets and zone controller the outputs. Additional decision variables are also defined to increase the set of feasible solutions to the control problem. The hard constraints resulting from the cancellation of the integrating modes Lit the end of the control horizon are softened,, and the resulting control problem is made feasible to a large class of unknown disturbances and changes of the optimizing targets. The methods are illustrated with the simulated application of the proposed,approaches to a distillation column of the oil refining industry.

Control charts for individual observations of a bivariate Poisson process

In this paper, three single-control charts are proposed to monitor individual observations of a bivariate Poisson process. The specified false-alarm risk, their control limits, and ARLs were determined to compare their performances for different types and sizes of shifts. In most of the cases, the single charts presented better performance rather than two separate control charts ( one for each quality characteristic). A numerical example illustrates the proposed control charts.

Diagnostic errors and repetitive sequential classifications in on-line process control by attributes

The procedure of on-line process control by attributes, known as Taguchi`s on-line process control, consists of inspecting the mth item (a single item) at every m produced items and deciding, at each inspection, whether the fraction of conforming items was reduced or not. If the inspected item is nonconforming, the production is stopped for adjustment. As the inspection system can be subject to diagnosis errors, one develops a probabilistic model that classifies repeatedly the examined item until a conforming or b non-conforming classification is observed. The first event that occurs (a conforming classifications or b non-conforming classifications) determines the final classification of the examined item. Proprieties of an ergodic Markov chain were used to get the expression of average cost of the system of control, which can be optimized by three parameters: the sampling interval of the inspections (m); the number of repeated conforming classifications (a); and the number of repeated non-conforming classifications (b). The optimum design is compared with two alternative approaches: the first one consists of a simple preventive policy. The production system is adjusted at every n produced items (no inspection is performed). The second classifies the examined item repeatedly r (fixed) times and considers it conforming if most classification results are conforming. Results indicate that the current proposal performs better than the procedure that fixes the number of repeated classifications and classifies the examined item as conforming if most classifications were conforming. On the other hand, the preventive policy can be averagely the most economical alternative rather than those ones that require inspection depending on the degree of errors and costs. A numerical example illustrates the proposed procedure. (C) 2009 Elsevier B. V. All rights reserved.

Effects of the preventive and corrective adjustments in economical designs for online process control for attributes with misclassification errors

The procedure for online process control by attributes consists of inspecting a single item at every m produced items. It is decided on the basis of the inspection result whether the process is in-control (the conforming fraction is stable) or out-of-control (the conforming fraction is decreased, for example). Most articles about online process control have cited the stoppage of the production process for an adjustment when the inspected item is non-conforming (then the production is restarted in-control, here denominated as corrective adjustment). Moreover, the articles related to this subject do not present semi-economical designs (which may yield high quantities of non-conforming items), as they do not include a policy of preventive adjustments (in such case no item is inspected), which can be more economical, mainly if the inspected item can be misclassified. In this article, the possibility of preventive or corrective adjustments in the process is decided at every m produced item. If a preventive adjustment is decided upon, then no item is inspected. On the contrary, the m-th item is inspected; if it conforms, the production goes on, otherwise, an adjustment takes place and the process restarts in-control. This approach is economically feasible for some practical situations and the parameters of the proposed procedure are determined minimizing an average cost function subject to some statistical restrictions (for example, to assure a minimal levelfixed in advanceof conforming items in the production process). Numerical examples illustrate the proposal.

Distributed power control algorithm for multiple access systems based on Verhulst model

In this paper the continuous Verhulst dynamic model is used to synthesize a new distributed power control algorithm (DPCA) for use in direct sequence code division multiple access (DS-CDMA) systems. The Verhulst model was initially designed to describe the population growth of biological species under food and physical space restrictions. The discretization of the corresponding differential equation is accomplished via the Euler numeric integration (ENI) method. Analytical convergence conditions for the proposed DPCA are also established. Several properties of the proposed recursive algorithm, such as Euclidean distance from optimum vector after convergence, convergence speed, normalized mean squared error (NSE), average power consumption per user, performance under dynamics channels, and implementation complexity aspects, are analyzed through simulations. The simulation results are compared with two other DPCAs: the classic algorithm derived by Foschini and Miljanic and the sigmoidal of Uykan and Koivo. Under estimated errors conditions, the proposed DPCA exhibits smaller discrepancy from the optimum power vector solution and better convergence (under fixed and adaptive convergence factor) than the classic and sigmoidal DPCAs. (C) 2010 Elsevier GmbH. All rights reserved.

Galerkin Method and Weighting Functions Applied to Nonlinear H(infinity) Control with Output Feedback

This paper considers two aspects of the nonlinear H(infinity) control problem: the use of weighting functions for performance and robustness improvement, as in the linear case, and the development of a successive Galerkin approximation method for the solution of the Hamilton-Jacobi-Isaacs equation that arises in the output-feedback case. Design of nonlinear H(infinity) controllers obtained by the well-established Taylor approximation and by the proposed Galerkin approximation method applied to a magnetic levitation system are presented for comparison purposes.

On the convergence of successive Galerkin approximation for nonlinear output feedback H(infinity) control

Although the formulation of the nonlinear theory of H(infinity) control has been well developed, solving the Hamilton-Jacobi-Isaacs equation remains a challenge and is the major bottleneck for practical application of the theory. Several numerical methods have been proposed for its solution. In this paper, results on convergence and stability for a successive Galerkin approximation approach for nonlinear H(infinity) control via output feedback are presented. An example is presented illustrating the application of the algorithm.

Using bifurcations in the determination of lock-in ranges for third-order phase-locked loops

Transmission and switching in digital telecommunication networks require distribution of precise time signals among the nodes. Commercial systems usually adopt a master-slave (MS) clock distribution strategy building slave nodes with phase-locked loop (PLL) circuits. PLLs are responsible for synchronizing their local oscillations with signals from master nodes, providing reliable clocks in all nodes. The dynamics of a PLL is described by an ordinary nonlinear differential equation, with order one plus the order of its internal linear low-pass filter. Second-order loops are commonly used because their synchronous state is asymptotically stable and the lock-in range and design parameters are expressed by a linear equivalent system [Gardner FM. Phaselock techniques. New York: John Wiley & Sons: 1979]. In spite of being simple and robust, second-order PLLs frequently present double-frequency terms in PD output and it is very difficult to adapt a first-order filter in order to cut off these components [Piqueira JRC, Monteiro LHA. Considering second-harmonic terms in the operation of the phase detector for second order phase-locked loop. IEEE Trans Circuits Syst [2003;50(6):805-9; Piqueira JRC, Monteiro LHA. All-pole phase-locked loops: calculating lock-in range by using Evan`s root-locus. Int J Control 2006;79(7):822-9]. Consequently, higher-order filters are used, resulting in nonlinear loops with order greater than 2. Such systems, due to high order and nonlinear terms, depending on parameters combinations, can present some undesirable behaviors, resulting from bifurcations, as error oscillation and chaos, decreasing synchronization ranges. In this work, we consider a second-order Sallen-Key loop filter [van Valkenburg ME. Analog filter design. New York: Holt, Rinehart & Winston; 1982] implying a third order PLL The resulting lock-in range of the third-order PLL is determined by two bifurcation conditions: a saddle-node and a Hopf. (C) 2008 Elsevier B.V. All rights reserved.

On the basic reproduction number and the topological properties of the contact network: An epidemiological study in mainly locally connected cellular automata

We study the spreading of contagious diseases in a population of constant size using susceptible-infective-recovered (SIR) models described in terms of ordinary differential equations (ODEs) and probabilistic cellular automata (PCA). In the PCA model, each individual (represented by a cell in the lattice) is mainly locally connected to others. We investigate how the topological properties of the random network representing contacts among individuals influence the transient behavior and the permanent regime of the epidemiological system described by ODE and PCA. Our main conclusions are: (1) the basic reproduction number (commonly called R(0)) related to a disease propagation in a population cannot be uniquely determined from some features of transient behavior of the infective group; (2) R(0) cannot be associated to a unique combination of clustering coefficient and average shortest path length characterizing the contact network. We discuss how these results can embarrass the specification of control strategies for combating disease propagations. (C) 2009 Elsevier B.V. All rights reserved.

Comparison of friction models applied to a control valve

Eight different models to represent the effect of friction in control valves are presented: four models based on physical principles and four empirical ones. The physical models, both static and dynamic, have the same structure. The models are implemented in Simulink/Matlab (R) and compared, using different friction coefficients and input signals. Three of the models were able to reproduce the stick-slip phenomenon and passed all the tests, which were applied following ISA standards. (C) 2008 Elsevier Ltd. All rights reserved.

Postural control during kneeling

Postural control was studied when the subject was kneeling with erect trunk in a quiet posture and compared to that obtained during quiet standing. The analysis was based on the center of pressure motion in the sagittal plane (CPx), both in the time and in the frequency domains. One could assume that postural control during kneeling would be poorer than in standing because it is a less natural posture. This could cause a higher CPx variability. The power spectral density (PSD) of the CPx obtained from the experimental data in the kneeling position (KN) showed a significant decrease at frequencies below 0.3 Hz compared to upright (UP) (P < 0.01), which indicates less sway in KN. Conversely, there was an increase in fast postural oscillations (above 0.7 Hz) during KN compared to UP (P < 0.05). The root mean square (RMS) of the CPx was higher for UP (P < 0.01) while the mean velocity (MV) was higher during KN (P < 0.05). Lack of vision had a significant effect on the PSD and the parameters estimated from the CPx in both positions. We also sought to verify whether the changes in the PSD of the CPx found between the UP and KN positions were exclusively due to biomechanical factors (e.g., lowered center of gravity), or also reflected changes in the neural processes involved in the control of balance. To reach this goal, besides the experimental approach, a simple feedback model (a PID neural system, with added neural noise and controlling an inverted pendulum) was used to simulate postural sway in both conditions (in KN the pendulum was shortened, the mass and the moment of inertia were decreased). A parameter optimization method was used to fit the CPx power spectrum given by the model to that obtained experimentally. The results indicated that the changed anthropometric parameters in KN would indeed cause a large decrease in the power spectrum at low frequencies. However, the model fitting also showed that there were considerable changes also in the neural subsystem when the subject went from standing to kneeling. There was a lowering of the proportional and derivative gains and an increase in the neural noise power. Additional increases in the neural noise power were found also when the subject closed his eyes.

Flatness-based control of a single qubit gate

This work considers the open-loop control problem of steering a two-level quantum system from any initial to any final condition. The model of this system evolves on the state space X = SU(2), having two inputs that correspond to the complex amplitude of a resonant laser field. A symmetry preserving flat output is constructed using a fully geometric construction and quaternion computations. Simulation results of this flatness-based open-loop control are provided.

Singular Perturbation for the Discounted Continuous Control of Piecewise Deterministic Markov Processes

This paper deals with the expected discounted continuous control of piecewise deterministic Markov processes (PDMP`s) using a singular perturbation approach for dealing with rapidly oscillating parameters. The state space of the PDMP is written as the product of a finite set and a subset of the Euclidean space a""e (n) . The discrete part of the state, called the regime, characterizes the mode of operation of the physical system under consideration, and is supposed to have a fast (associated to a small parameter epsilon > 0) and a slow behavior. By using a similar approach as developed in Yin and Zhang (Continuous-Time Markov Chains and Applications: A Singular Perturbation Approach, Applications of Mathematics, vol. 37, Springer, New York, 1998, Chaps. 1 and 3) the idea in this paper is to reduce the number of regimes by considering an averaged model in which the regimes within the same class are aggregated through the quasi-stationary distribution so that the different states in this class are replaced by a single one. The main goal is to show that the value function of the control problem for the system driven by the perturbed Markov chain converges to the value function of this limit control problem as epsilon goes to zero. This convergence is obtained by, roughly speaking, showing that the infimum and supremum limits of the value functions satisfy two optimality inequalities as epsilon goes to zero. This enables us to show the result by invoking a uniqueness argument, without needing any kind of Lipschitz continuity condition.

A new technique to control brushless motor for blood pump application

This article presents a back-electromotive force (BEMF)-based technique of detection for sensorless brushless direct current motor (BLDCM) drivers. The BLDCM has been chosen as the energy converter in rotary or pulsatile blood pumps that use electrical motors for pumping. However, in order to operate properly, the BLDCM driver needs to know the shaft position. Usually, that information is obtained through a set of Hall sensors assembled close to the rotor and connected to the electronic controller by wires. Sometimes, a large distance between the motor and controller makes the system susceptible to interference on the sensor signal because of winding current switching. Thus, the goal of the sensorless technique presented in this study is to avoid this problem. First, the operation of BLDCM was evaluated on the electronic simulator PSpice. Then, a BEMF detector circuitry was assembled in our laboratories. For the tests, a sensor-dependent system was assembled where the direct comparison between the Hall sensors signals and the detected signals was performed. The obtained results showed that the output sensorless detector signals are very similar to the Hall signals at speeds of more than 2500 rpm. Therefore, the sensorless technique is recommended as a responsible or redundant system to be used in rotary blood pumps.

Dynamic positioning systems: An experimental analysis of sliding mode control

Vessel dynamic positioning (DP) systems are based on conventional PID-type controllers and an extended Kalman filter. However, they present a difficult tuning procedure, and the closed-loop performance varies with environmental or loading conditions since the dynamics of the vessel are eminently nonlinear. Gain scheduling is normally used to address the nonlinearity of the system. To overcome these problems, a sliding mode control was evaluated. This controller is robust to variations in environmental and loading conditions, it maintains performance and stability for a large range of conditions, and presents an easy tuning methodology. The performance of the controller was evaluated numerically and experimentally in order to address its effectiveness. The results are compared with those obtained from conventional PID controller. (c) 2010 Elsevier Ltd. All rights reserved.