Zalman J. Palmor

Stabilization of uncertain dynamic systems including state delay

The authors consider a class of time-varying systems with time-varying state delay and uncertain input and parameters. They present sufficient conditions on the open loop to obtain an arbitrary-degree closed-loop stability. They construct a min-max controller from knowledge of the upper bound of the delay. >

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.

Quantitative measures of robustness for systems including delayed perturbations

Asymptotically stable linear systems subject to delayed time-varying and nonlinear perturbations are considered. Razumikhin-type theorems are used to obtain easy-to-compute bounds on the perturbations so that the systems remain stable. Results indicate that if delayed perturbations are included, then the bound is reduced as compared to the one for nondelayed perturbations. However, in certain cases previously obtained bounds for the nondelayed perturbations guarantee stability even when delayed perturbations are in effect. >

An auto-tuner for Smith dead time compensator

An efficient yet simple automatic tuning algorithm is developed for dead-time compensators (DTC) common to industrial process controllers. The auto-tuner is capable of setting eight tuning parameters: two for the primary controller, three for the process model and another three for an additional modification aimed at improving the disturbance rejection properties. The process model used in the algorithm is a first order + dead time which captures the essential dynamics of the majority of loops in the chemical and process industries. The methodology and methods used, however, can be readily extended to higher order and more complicated models. The auto-tuner utilizes two points on the process Nyquist curve acquired through automatically generated controlled limit cycles in closed loop fashion. Least squares is then used to estimate the process model. It is shown that an appropriate selection of the two points as well as the weighting matrix in the least squares leads to a robust estimation. A simple rule b...

Time delay estimation in continuous linear time-invariant systems

The use of a time delay in modeling LTI systems is quite common. However, attempts to estimate these time delays in continuous systems typically resorted to methods which increase the number of parameters in the system, in contradiction to the use of time delay in the model to begin with. We present here an attempt to estimate the time delays directly. The algorithm we present is supported both by analysis and simulations with very encouraging results. >

Control Issues in Systems with Loop Delays

This chapter discusses properties of feedback control systems containing loop delays (dead-time systems) and approaches to controller design for such systems. Consider the feedback system depicted in Fig. 1, where P is a plant, C is a controller, r is a reference signal, d is a disturbance, u is a control signal, and y is an output (measurement) signal. It is assumed throughout that both the measured signal y and the control signal u are delayed by hy and hu units of time, respectively. This is reflected in Fig. 1 by the two delay blocks containing the delay element Dh defined by

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.

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.

A new representation of the parameters of lifted systems

Lifting, i.e., discretization with built-in intersample behavior, is an emerging technique for the analysis and design of sampled-data systems. The applicability of the lifting technique, however, is severely limited owing to difficulties in dealing with the parameters of the lifted systems, which are operators over infinite-dimensional spaces rather than finite-dimensional matrices. In this paper, a new representation for the parameters of the lifted systems is proposed. The technical machinery developed in the paper based on this representation simplifies considerably algebraic manipulation over parameters of the lifted systems, thus extending the scope of applicability of the lifting technique. To illustrate the advantages of the proposed approach, the computational issues in the sampled-data H/sup /spl infin// problem are considered.

Extended limiting forms of optimum observers and LQG regulators

The general problem of optimal estimation in singular observation systems is considered. By generalizing the limiting procedure of Friedland, explicit and closed expressions for the transfer matrices of the optimum observer as well as for the optimal control law in the singular measurement LQG problem are derived. The number of integrators that are required for the implementation of the singular optimum observer is shown, for square systems, to be equal to the number of the systems zeros. The closed form of the optimum observer given here is advantageous as compared with existing procedures. Structural properties of the singular observation problem are discussed, and the role of the zeros of the system in such problems is clarified. The dual results for the case of stochastic ‘cheap’ control are also given.