Time Adaptive Control Research Articles

Factorization Techniques in Discrete Time Adaptive Control

Many algorithms recently proposed for discrete time adaptive control use a recursive least-squares type iteration. Typical examples are the modified least-squares and weighted least-squares algorithms. Numerical difficulties arrise with such algorithms when the covariance matrix is directly updated. The paper discusses the square-root and U-D factorization techniques applicable for the covariance matrix or its inverse. These techniques avoid the numerical problems encountered with direct implementation of the recursions. New versions of the factorisation algorithms are presented and analysied in the paper. Implementation details and recommendations for the usage of the newly developed mathematical routines to solve the related problems are given.

Discrete time adaptive control of linear systems with preload nonlinearity

In this note a method is presented for doing discrete time adaptive control of a nonlinear system which is given by a cascade connection of a preload nonlinearity followed by a linear system. It is shown that the algorithm will ensure that the closed loop system is globally convergent with a specific residue and stable for both the deterministic and stochastic cases.

Adaptive Control of Tubular Chemical Reactors

Real time adaptive control for a type of tubular chemical reactors is designed. The system dynamics is considered to be described by a first order partial differential equation system. A verified integral reactor model, taking off the time delay influance is derived. This model is suitable for a multi variable adaptive control system design. The model output is used to generate the control based on the discrete linear time - optimal control strategy (deadbeat servo problem), designed for a replacing second order model. The parameters of the model are estimated using recursive least squares estimation at each sampling period. As an example a one-dimensional control problem of a packed-bed catalytic tubular chemical reactor with lumped and boundary control actions is considered.

Discrete time adaptive control of linear dynamic systems with a two-segment piecewise-linear asymmetric nonlinearity

In this note a method is presented for doing discrete adaptive control of a nonlinear system which is given by a cascade connection of a "two-segment piecewise-linear asymmetric nonlinearity" followed by a linear system. A switching gain sequence is introduced to make the parameter identification time invariant. The algorithm will ensure that the closed-loop system is globally convergent and stable for both the deterministic and stochastic cases.

Some Practical Solutions for the Robustness Problem of Multivariable Adaptive Control

Publisher Summary This chapter presents two successful applications of multivariable discrete time adaptive control of stable and unstable nonminimum phase system. The first application is the multivariable control of a steam generator of a fast breeder reactor that is a stable system with an inverse possibly unstable. The second application deals with the terminal voltage control of the turbo-generator unit that eventually becomes unstable with an inverse having weakly damped oscillatory modes. This characteristic of second application produces the same problems as nonminimum phase systems. However, both the applications are the illustrations of two ways for robustifying control problems. The first example features a very efficient solution for stable damped systems that consists essentially in precancellation of the system poles. The second example describes another solution for eventually unstable system: the extended Smith predictor principle has the interest of giving a basic tool to make work control and is designed on simple linearized system on highly complicated linear or nonlinear real systems.

A Frequency Domain Analysis of Direct Adaptive Pole Placement Algorithms in the Presence of Unmodelled Dynamics

This paper examines a general class of direct adaptive pole placement algorithms in the presence of unmodelled high frequency dynamics. The analysis is broken into three stages. The first stage addresses the robustness of the fixed control structure on which most continuous time adaptive control schemes are based. The second stage looks at the effect of unmodelled dynamics on the estimation model used in equation error formulations of continuous time algorithms. The last stage looks specifically at the identification process.

Continuous time adaptive identification and control algorithms via newly developed adaptive laws

In the first part of this paper, a continuous time adaptive identification algorithm via newly developed adaptive laws is presented. The principle of the algorithm is very simple, nevertheless the convergence property is quite excellent. In the second half part, two continuous time adaptive control algorithms via adaptive laws, as were used for adaptive identification, are presented. A new canonical form for adaptive control is first developed for this purpose. The design procedure for adaptive control systems requires neither positive realness nor augmented error signals and can be applied irrespective of the relative degree of the plant transfer function.

Computational aspects of discrete time adaptive control

Stable model reference adaptive control schemes for discrete time systems can be designed which take into account computational time and limited range of computing machines. An algorithm is developed using Lyapunov second method and properties of strictly positive real functions.

Adaptive Control with Forgetting Factor

This paper considers a discrete time adaptive control algorithm with forgetting factor applicable to minimum phase plants. The tracking and regulation objectives are independently specified. The relevance of the eigenvalues of the gain matrix (Fk) used in the up-dating equation for the adaptive parameters (p^(k)) is shown. It is proved that if the maximum eigenvalue of the inverse of the gain matrix Fk has an upper bound and a non zero lower bound then the global convergence of the control algorithm is insured. The result of the design is a simple control scheme using a linear constant feedforward controller and a non-linear feedback controller. The performances of the control structure in tracking and regulation are evaluated by simulations.

An Integrated Distributed Control Structure for Global Communications

The worldwide communications resources of the Defense Communications System (DCS) are controlled by a multilevel control complex, with distribution of control functions among many control facilities. The control structure is going through substantial changes, driven by considerations of reliability, survivability, crisis management capability, and of course, cost. This paper introduces the control structure, the ongoing and programmed improvements for the control capabilities, and how the Automated Technical Control (ATEC) equipments will form the basis of a distributed, processor based communications control utility. Finally, the unique features of the Real Time Adaptive Control System (RTACS) for the third generation Defense Satellite Communications System (DSCS) will be described, along with the integration of RTACS into the distributed global control structure.

Real time-adaptive control of systems containing inaccessible state variables†

This paper describes an adaptive scheme for controlling a non-linear process which is attractive from the point of view of implementation in a real time mode. Effective process control can be maintained, even when certain of the state variables are inaccessible, without the need for excessive computation. The process is repeatedly identified as a series of quasi-linear systems. The nature of the control is defined by a model, static or dynamic, set a priori. A ‘sub-optimal’ controller is modified by each successive identification.