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.     

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.     

Bond graph modelling of a photovoltaic system feeding an induction motor-pump

Water pumping using induction motors has become one of the most feasible photovoltaic (PV) applications. A bond graph model to enable testing the PV system performance by computer simulation was developed. The PV-powered water pumping system investigated in this paper consists mainly of a PV generator, DC–DC and DC–AC converters, and induction motor-pump. The DC–DC converter control strategy is based on pulse width modulation (PWM). However, the oriented field control is used for the induction machine control. Computer simulations were carried out for maximum power point tracking (MPPT).     

Comparative evaluation of nonlinear model predictive and flatness-based two-degree-of-freedom control design in view of industrial application

Two advanced nonlinear model-based control design methods – nonlinear model predictive control (NMPC) and a two-degree-of-freedom control-scheme with flatness-based feedforward control design and decentralised PI-controllers (FB-2DOF) – are compared in view of industrial application. The comparative evaluation is carried out on a setpoint-transition of the Klatt–Engell reactor model. Based on an analysis of simulation scenarios, the controllers are compared with respect to controller performance, robustness criteria, and implementation issues. Thereby, the choice of the control task and the comparison methodology are oriented on industrial practice.In the considered comparative evaluation, NMPC exhibits performance advantages when it comes to time-efficient setpoint-transitions in the nominal case, in which FB-2DOF control design is restricted by the existing input constraints. In return, robustness of stability of the FB-2DOF controller is determined only by the feedback controll part; it is therefore independent from the setpoint-transition performance – determined by the feedforward controll part – whereas the NMPC suffers from degradation of robustness properties if it is tuned for time-efficiency only. NMPC allows direct incorporation of process models and constraints, but, as it employs computationally expensive online optimisation, has to be connected to the digital control system (DCS) via some standard interface. The FB-2DOF controller in contrast can be directly implemented in a DCS, whereby the feedforward-part can be realised as an extension of an already existing feedback-part.     

Neural network based switching control of AC–AC converter with DC–AC inverter for voltage sags, harmonics and EMI reduction using hybrid filter topology

A neural network based AC–AC voltage restorer is designed for voltage sags and PWM type active power filter with compound trap passive filter as a new hybrid filter are simultaneously used for voltage harmonics compensation and electromagnetic interference (EMI) reduction. First objective is to apply the neural network based switching control technique for the AC–AC voltage restorer to reduce time delays during the switching conditions and switching losses. The aim of the IGBTs used in the AC–AC voltage restorer is to test and to find the best switching frequency–power combination in the steps of the simulation. Thus, the proposed AC–AC voltage restorer has important advantages such as fast switching response, simplicity and more intelligent structure, better output waveform. The transient condition of the AC–AC voltage restorer is improved via the neural network based control technique. The second objective is the proposed strategy for elimination of voltage harmonics using PWM type DC–AC inverter part of the system as an active power filter. The last objective of the system is EMI reduction with using hybrid filter and voltage restorer together. Three problems which are voltage sags, harmonics and EMI are solved with the proposed system simultaneously.     

Some aspects of the design of local process-control systems

Some aspects of the software for one class of industrial process control systems are considered. A system of algorithmic algebras is proposed, adapting the structured program design method to this particular class of control systems.Translated from Kibernetika, No. 6, pp. 80–82, November–December, 1989.     

Robust nonlinear feedback–feedforward control of a coupled kinetic Monte Carlo–finite difference simulation

Robust nonlinear feedforward–feedback controllers are designed for a multiscale system that dynamically couples kinetic Monte Carlo (KMC) and finite difference (FD) simulation codes. The coupled codes simulate the copper electrodeposition process for manufacturing on-chip copper interconnects in electronic devices. The control objective is to regulate the current density subject to the condition that the steady-state fluctuation of the overpotential remains bounded within ±0.01 V. The controller designs incorporate a low-order stochastic model that captures the input–output behavior of the coupled KMC–FD code. The controllers achieve the objectives and the closed-loop responses implemented on the low-order model and the coupled KMC–FD code match well within stochastic variations. The nonlinear feedforward control reduces the rise time of the controller response while the feedback control ensures robustness in the presence of model uncertainty.     

Control of distributed-parameter systems under uncertainty

The maximum principle and a necessary condition of optimality are derived for a particular control problem.Translated from Kibernetika i Sistemnyi Analiz, No. 6, pp. 165–167, November–December, 1991.     

Synthesis of an Optimal Control for Continuous Markov Processes by Semidefinite Quality Criteria

Optimization of control of continuous Markov processes by semidefinite quality functionals with nonadditive control cost functions is investigated. Equation for the loss function, its parameters for different integrands in the quality criterion, and its interrelation with the Fokker–Planck–Kolmogorov equation for the auxiliary noncontrollable Markov processes are determined. Examples are given.     

Comments on: “Efficient robust constrained model predictive control with a time varying terminal constraint set” by Wan and Kothare

We present an algorithm that modifies the original formulation proposed in Wan and Kothare [Efficient robust constrained model predictive control with a time-varying terminal constraint set, Systems Control Lett. 48 (2003) 375–383]. The modified algorithm can be proved to be robustly stabilizing and preserves all the advantages of the original algorithm, thereby overcoming the limitation pointed out recently by Pluymers et al. [Min–max feedback MPC using a time-varying terminal constraint set and comments on “Efficient robust constrained model predictive control with a time-varying terminal constraint set”, Systems Control Lett. 54 (2005) 1143–1148].     

Design of variable structure control for fuzzy nonlinear systems

In this paper, the variable structure control problem is presented for Takagi–Sugeno fuzzy systems with uncertainties and external disturbances. The sliding surfaces for the T–S fuzzy system are proposed by using a Lyapunov function and a fuzzy Lyapunov function, respectively. And we design the variable structure controllers such that the global T–S fuzzy system confined on the sliding surfaces is asymptotically stable. Two examples are given to illustrate the effectiveness of our proposed methods.     

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.     

Modeling of plasma etching in microelectronics

Computer simulation and experimental results are used to establish the possibility of efficient control of plasma etching rate and nonuniformities.Translated from Kibernetika, No. 5, pp. 27–33, September–October, 1990.     

Some performance measures for computer control units

We consider the representation of various structures of computer control units by automata which preserve the alphabet of the control unit and the functions determining its output and state transitions.Translated from Kibernetika, No. 3, pp. 66–70, May–June, 1989.     

Finite-dimensional regularizers for optimal control problems on solutions of ill-posed variational inequalities

A method is proposed for construction of finite-dimensional regularizers for optimal control on solutions of ill-posed variational inequalities with pseudomonotone operators. It is assumed that all the input data of the problems, including the control sets, are known approximately.Translated from Kibernetika i Sistemnyi Analiz, No. 4, pp. 84–88, July–August, 1991.     

Optimal control of the order of asymptotics for elliptic equations with fast oscillating coefficients. I. Formal constructions

Formal algorithms for complete asymptotic decompositions of solutions to optimal globally bounded control problems for elliptic equations with fast oscillating coefficients are constructed. If the kernel of a differential operator of the initial problem is nonzero, asymptotics of different orders may exist in the control system.Translated from Kibernetika i Sistemnyi Analiz, No. 5, pp. 84–95, September–October 2004.     

Vector control for loss minimization of induction motor using GA–PSO

This paper deals with the GA–PSO (genetic algorithm–particle swarm optimization) based vector control for loss minimization operation of induction motor. It is estimated that more than around 50% of the world electric energy generated is consumed by electric machines such as induction motor, dc motor. So, improving efficiency in electric drives is important and control strategy for minimum energy loss is needed as one of optimal operation strategies. The vector control of induction motor has been widely used to operate in a wide speed range by using flux weakening at rated speed. However, it is still necessary to advance because of coupling is behavior between fluxes in motor. In this paper, vector control approach is suggested for an optimal operation of induction motor using variable acceleration and GA–PSO tuning method through simulation. We can obtain satisfactory results for energy saving control.     

Output–input stability implies feedback stabilization

We study the recently introduced notion of output–input stability, which is a robust variant of the minimum-phase property for general smooth nonlinear control systems. This paper develops the theory of output–input stability in the multi-input, multi-output setting. We show that output–input stability is a combination of two system properties, one related to detectability and the other to left-invertibility. For systems affine in controls, we derive a necessary and sufficient condition for output–input stability, which relies on a global version of the nonlinear structure algorithm. This condition leads naturally to a globally asymptotically stabilizing state feedback strategy for affine output–input stable systems.     

Nonlinear feedback control of multivariable non-minimum-phase processes

A new method of controlling nonlinear processes with a non-minimum-phase delay-free part is presented. Two control laws are derived for stable, multiple-input multiple-output processes. They are obtained by requesting an approximately linear, input–output response and exploiting the connections between model-predictive control and input–output linearization. Conditions under which the closed-loop system is asymptotically stable are given. The application and performance of the control laws are illustrated using numerical simulation of two chemical reactor examples that exhibit non-minimum-phase behavior.