Yoram Halevi

Integrated Communication and Control Systems: Part II—Design Considerations

Asynchronous time-division multiplexed networks, used in Integrated Communication and Control Systems (ICCS), introduce time-varying and possibly stochastic delays in the feedback control loops. The objective of this on-going research is to develop a comprehensive methodology for the analysis and design of the above class of delayed control systems. In the first part [1] of this two-part paper, we developed a discrete-time, finite-dimensional, time-varying model of the delayed control system; necessary and sufficient conditions for system stability have been established for periodically varying delays. This second part elucidates the significance of the above model relative to the system dynamic performance as well as addresses major criteria for and outlines alternative analytical approaches to ICCS design. Pertinent concepts are illustrated by simulation.

Automatic tuning of decentralized PID controllers for TITO processes

This paper presents a new algorithm for automatic tuning of decentralized PID control for two-input two-output (TITO) plants that fully extends the single-loop relay auto-tuner to the multiloop case. The tuning procedure consists of two stages. In the first, the desired critical point, which consists of the critical gains of the two loops and a critical frequency, is identified. Unlike SISO plants, there are infinitely many such points, and knowledge of the desired one is essential to the tuning procedure. The auto-tuner identifies the desired critical point with almost no a priori information on the process. During the identification phase, all controllers are replaced by relays, thus generating limit cycles with the same period in both loops. It is shown that each limit cycle corresponds to a single critical point of the process. By varying the relay parameters, different critical points can be determined. The auto-tuner contains a procedure that converges rapidly to the desired critical point while maintaining the amplitudes of the process variables as well as of the manipulated variables within prespecified ranges. In the second stage, the data of the desired critical point and possibly of other critical points is used to tune the PID controller by the Ziegler-Nichols rule or its modifications. This paper focuses on the first stage. The steady-state process gains, which are required for the appropriate choice of the desired critical point, are determined by the auto-tuner in closed-loop fashion simultaneously with the identification of the critical points. The identification of the process gains is achieved at no extra plant time. On the basis of a large number of simulated cases, the proposed auto-tuner seems to be efficient and robust. This paper discusses the underlying principles of the auto-tuner and its properties and capabilities demonstrated via examples. The algorithm is not limited to TITO cases, and can be extended to any number of loops.

Paper: On the design and properties of multivariable dead time compensators

The design problem of multivariable dead time compensators for MIMO systems with multiple dead times is considered. Analytical design aids which take into account the stability and sensitivity properties of these systems are presented. Conditions for practical stability, estimates on allowable tolerances in process models and methods for determining controller gains are derived. Based upon sufficient conditions, these methods lead to conservative gains. The extent of conservation is related to the amount of computational effort involved in each method and to the available plant information. It is shown that the type of dead time compensator treated here cannot be applied to unstable processes. Diagonal dominance theory is used to derive some of the results. Illustrative examples demonstrate the main results.

The optimal reduced-order estimator for systems with singular measurement noise

The optimal reduced-order estimator is completely characterized by necessary conditions, resulting from the optimal projection equations. The solution consists of one Riccati equation and two Lyapunov equations coupled by two projections. Explicit expressions for all of the estimator parameters are given. The relation between the reduced-order singular estimator and the full-order optimal singular estimator (which is of reduced order itself) is investigated. It is shown that under certain conditions the optimal estimator is recovered from the reduced-order estimator. >

Control of Flexible Structures Governed by the Wave Equation Using Infinite Dimensional Transfer Functions

A method of noncollocated controller design for flexible structures, governed by the wave equation, is proposed. First an exact, infinite dimension, transfer function is derived and its properties are investigated. A key element in that part is the existence of time delays due to the wave motion. The controller design consists of two stages. The first one is an inner collocated rate loop. It is shown that there exists a controller that leads to a finite dimensional plus delay inner closed loop, which is the equivalent plant for the outer loop. In the second stage an outer noncollocated position loop is closed. It has the structure of an observer-predictor control scheme to compensate for the response delay. The resulting overall transfer function is second order with arbitrarily assigned dynamics, plus delay.

Stable LQG controllers

The optimal LQG controller is known to stabilize the closed loop if certain mild conditions are satisfied. The controller itself, however, may be unstable. The paper presents a method of selecting the weighting and covariance matrices such that the optimal controller is internally asymptotically stable. The method is very easy to apply and for stable open-loop system involves the solution of a single Lyapunov equation. >

A general and exact method for determining limit cycles in decentralized relay systems

An exact method for evaluating the periods and stability of limit cycles in decentralized relay systems is presented. The method can cope with relays having dead zones and hystereses. The underlying idea is to convert the continuous decentralized relay system under a limit cycle to an equivalent fictitious sampled-data system with synchronous samplers. Consequently, regular sampled-data tools can be applied in a straightforward manner to derive closed-form necessary conditions as well as stability conditions and other properties of such systems. This paper extends and generalises recent results obtained by the authors.

Nonlinear Modeling and Control of a Unicycle

A unicycle system is composed of a unicycle and a rider. This system is inherently unstable, but together with a skilled rider can be autonomously controlled and stabilized. A dynamical investigation, a control design and a numerical solution of a nonlinear unicycle autonomous model are presented. The use of a nonlinear model for the control design is shown in this paper to be of great importance. A three-rigid-body physical model was selected for the dynamical study of the system. In a linearized model important physical characteristics of the unicycle system disappear (e.g. interactions between the longitudinal and lateral systems are being neglected), and therefore it is not recommended to be used for the control design. A nonlinear control law, which replaces the rider in stabilizing the model, was derived in the present work, using a nonlinear unicycle model. A simulation study shows good performance of this controller. Time spectral element methods are developed and used for integrating the nonlinear equations of motion. The approach employs the time discontinuous Galerkin method which leads to A-stable high order accurate time integration schemes.

Model updating via weighted reference basis with connectivity constraints

Abstract The paper considers the problem of updating an analytical model from experimental data using the reference basis approach. In the general framework of the reference basis method, certain quantities, e.g., natural frequencies or modeshapes, are considered to be completely accurate and the others are updated by solving a constrained optimization problem. However, the underlying structure, known as connectivity, existing in the model is not preserved, and the method is not suited for parametric updating. In this paper, a method for introducing connectivity constraints into reference basis, while maintaining its advantages, is presented. It brings the reference basis method closer to a broad class of updating methods that use parametric updating. The notions of “connectivity cost” and “parameterization cost” are defined and used to obtain the best model for a given parameterization and to compare the outcomes of different parameterizations.

A new interpretation of the fault-detection filter Part 2. The optimal detection filter

Park and Rizzoni (1993) obtained closed-form expressions for detection filters; i.e. the structure of all detection filters for a given fault direction was defined. An important consequence of these results is that they permit the formation of the optimal detection filter problem, for optimization with respect to process and measurement noises. The necessary conditions for the existence of the optimal detection filter are obtained, and a numerical solution technique is shown to be feasible by virtue of the uniqueness of the detection filter gains. From an optimization point of view the problem can be regarded as optimal estimation with some structural constraints on the observer gain. This problem is solved for both the continuous-time and the discrete-time cases.