Joseph Bentsman

Direct adaptive control of parabolic systems: algorithm synthesis and convergence and stability analysis

This paper presents a model reference adaptive control of a class of distributed parameter systems described by linear, n-dimensional, parabolic partial differential equations. Unknown parameters appearing in the system equation are either constant or spatially-varying. Distributed sensing and actuation are assumed to be available. Adaptation laws are obtained by the Lyapunov redesign method. It Is shown that the concept of persistency of excitation, which guarantees the parameter error convergence to zero in finite-dimensional adaptive systems, in infinite-dimensional adaptive systems should be investigated in relation to time variable, spatial variable, and also boundary conditions. Unlike the finite-dimensional case, in infinite-dimensional adaptive systems even a constant input is shown to be persistently exciting in the sense that it guarantees the convergence of parameter errors to zero. Averaging theorems for two-time scale systems which involve a finite dimensional slow system and an infinite dimensional fast system are developed. The exponential stability of the adaptive system, which is critical in finite dimensional adaptive control in terms of tolerating disturbances and unmodeled dynamics, is shown by applying averaging. >

Vibrational control of nonlinear systems: Vibrational stabilizability

In this work, the theory of vibrational control for nonlinear systems is developed. The present paper gives criteria for stabilizability of nonlinear systems by linear multiplicative vibrations, by almost periodic forcing and by vector additive vibrations. Illustrative examples are also considered. In a subsequent paper, the problem of vibrational controllability and transient behavior will be addressed.

Nonlinear control oriented boiler modeling-a benchmark problem for controller design

This paper presents the development of a control oriented boiler model carried out on the basis of fundamental physical laws, previous efforts in boiler modeling, known physical constants, plant data, and heuristic adjustments. The resulting fairly accurate model is nonlinear, fourth order, and includes inverse response (shrink and swell effects), time delays, measurement noise models, and a load disturbance component. The model obtained can be directly used for the synthesis of model-based control algorithms as well as setting up a real-time simulator for testing of new boiler control systems and operator training.

Vibrational control of nonlinear time lag systems with bounded delay: averaging theory, stabilizability, and transient behavior

This paper develops the theory of vibrational control of nonlinear time lag systems with arbitrarily large but bounded delay. Averaging theory for fast oscillating, differential delay equations is presented and then applied to vibrational control. Conditions are given which ensure the existence of parametric vibrations that stabilize nonlinear time lag systems. Transient behavior is also discussed. Illustrative examples are given which show 1) the feasibility of the theory to important applications and 2) the differences in the theory presented and the existing known theory for vibrational control of ordinary differential equations. >

Adaptive distributed parameter systems identification with enforceable identifiability conditions and reduced-order spatial differentiation

Presents the synthesis of adaptive identifiers for distributed parameter systems (DPS) with spatially varying parameters described by partial differential equations (PDEs) of parabolic, elliptic, and hyperbolic type. The features of the PDE setting are utilized to obtain the not directly intuitive parameter estimation algorithms that use spatial derivatives of the output data with the order reduced from that of the highest spatial plant derivative. The tunable identifier parameters are passed through the integrator block, which forms their orthogonal expansions. The latter are shown to be pointwise plant parameter estimates. In this regard, the approach of the paper is in the spirit of finite-dimensional observer realization in integrating rather than differentiating the output data, only applied to the spatial rather than temporal domain. The constructively enforceable identifiability conditions, formulated in terms of the sufficiently rich input signals referred to as generators of persistent excitation, are shown to guarantee the existence of a unique zero steady state for the parameter errors. Under such inputs, the tunable parameters in the adaptive identifiers proposed are shown to converge to plant parameters in L/sub 2/ and the orthogonal expansions of these tunable parameters-pointwise.

Vibrational control of nonlinear systems: Vibrational controllability and transient behavior

In the first part of this work [1], the criteria for the existence of stabilizing parametric oscillations have been derived. In the present paper, the problem of choosing the stabilizing vibrations is addressed and the properties of transient behavior of vibrationally controlled nonlinear systems are analyzed.

Application of averaging method for integro-differential equations to model reference adaptive control of parabolic systems

Abstract An averaging theorem for integro-differential equations is applied to the convergence analysis of controller parameters of a model reference adaptive control algorithm for a class of parabolic partial differential equations with constant coefficients. The stability of an adaptive control algorithm is proven as well.

Vibrational control of a class of nonlinear systems by nonlinear multiplicative vibrations

Vibrational control is a nonclassical control principle which proposes a utilization of zero mean parametric excitation of a dynamical system for control purposes. This paper extends nonlinear vibrational control theory developed in [8], [9] to systems controlled by nonlinear multiplicative vibrations. Condition for partial vibrational stabilization with respect to a component of a steady-state vector, the choice of stabilizing vibrations, and the transient motions are discussed for a certain practically important class of nonlinear vibrationally controlled systems. The application of the results is demonstrated on the example of a catalytic reactor, using a combination of numerical and analytical techniques.

Simultaneous gains tuning in boiler/turbine PID-based controller clusters using iterative feedback tuning methodology

Tuning a complex multi-loop PID based control system requires considerable experience. In todays power industry the number of available qualified tuners is dwindling and there is a great need for better tuning tools to maintain and improve the performance of complex multivariable processes. Multi-loop PID tuning is the procedure for the online tuning of a cluster of PID controllers operating in a closed loop with a multivariable process. This paper presents the first application of the simultaneous tuning technique to the multi-input-multi-output (MIMO) PID based nonlinear controller in the power plant control context, with the closed-loop system consisting of a MIMO nonlinear boiler/turbine model and a nonlinear cluster of six PID-type controllers. Although simplified, the dynamics and cross-coupling of the process and the PID cluster are similar to those used in a real power plant. The particular technique selected, iterative feedback tuning (IFT), utilizes the linearized version of the PID cluster for signal conditioning, but the data collection and tuning is carried out on the full nonlinear closed-loop system. Based on the figure of merit for the control system performance, the IFT is shown to deliver performance favorably comparable to that attained through the empirical tuning carried out by an experienced control engineer.

Vibrational control of systems with Arrhenius dynamics

Abstract A nonlinear system with S -shape steady state characteristic is referred to as a system with Arrhenius dynamics. The negative slope part of the S -shape curve represents a set of unstable steady states. Using two examples of Arrhenius systems (catalytic reactor and continuous stirred tank reactor), it is shown that introduction of sufficiently fast oscillations in the parameters of the system generates a new Arrhenius system, the steady state characteristic of which has a smaller negative slope part. Results of analytical investigation as well as numerical simulation are presented. It is shown that vibrational stabilization of Arrhenius systems gives an increase in productivity of the plants.