Robust tuning of dead-time compensators for processes with anintegrator and long dead-time

Presents a simple criterion for tuning a dead time compensator for plants with an integrator and long dead time. The criterion is based on the definition of a closed-loop performance and considers that the model of the process is not precisely known. Using an estimation of the dead time and velocity gain of the plant, the proposed control law has only one tuning parameter that determines the closed-loop performance and robustness. By tuning this parameter it is possible to attain some robust performance specifications. In order to compare the proposed criterion with previous algorithms proposed in the literature, a comparative analysis of robustness is presented. Some simulation examples demonstrate the good properties of the proposed compensator     

2DOF discrete dead-time compensators for stable and integrative processes with dead-time

This paper presents an analysis of 2DOF discrete dead-time compensators for stable and integrative processes. The proposed structure can be tuned taking into account the performance and robustness of the closed-loop. Also a novel procedure to choose the sampling period is presented considering the robustness and the disturbance rejection response of the closed-loop system. In order to illustrate the results, some simulation examples and experimental results are shown.     

A unified approach to design dead-time compensators for stable andintegrative processes with dead-time

Proposes a unified 2 degrees of freedom robust dead-time compensator, for both stable and integrative plants. Using the performance and robustness as closed loop specifications simple and effective tuning rules are derived for the proposed controller. A comparative analysis with some structures of dead-time compensators that have been proposed in literature is presented. The analysis is made using the two most typical models of processes with delay that are found in the process industry. The comparative analysis shows that for the cases studied the proposed controller gives better or at least the same performance as the others. It is also shown that the tuning of this structure is simple because the tuning parameters have the usual physical meaning. Some simulation and experimental results illustrate the good performance of the controller     

Interactive tool for analysis of time-delay systems with dead-time compensators

The problem of controlling delayed systems has been widely studied in the control community. The Smith predictor (SP) scheme was the most famous and efficient technique to cope with this problem. Afterwards, robustness problems and those related to the control of integrating and unstable delayed processes were resolved. This work presents an interactive tool for studying and understanding the different alternatives available for controlling systems with large delays. Interactive tools have provided excellent support for the control community during recent years. In this sense, the tool developed here helps to compare easily the performance of PID controllers and SP approaches for processes with delay, as well as other control structures used to solve different problems that the original SP has when integrator and unstable models are employed. Robustness problems due to presence of model uncertainties can also be analyzed. Furthermore, some real industrial processes are also described as motivation in the study of the problems presented in the paper. The tool incorporates a set of typical transfer functions based on these real industrial processes.     

On the order of stable compensators

By means of two typical examples it is shown that in general the minimal order of a stabilizing stable compensator may not be bounded in terms of the plant order. Such bounds can only be given in the special case of plants with at most one right half plane zero. Implications for the simultaneous stabilization problem are elucidated.     

On the order of simultaneously stabilizing compensators

In this paper, simultaneous strong stabilization problem is considered, and it is shown that there is no upper bound for the minimal order of a simultaneously strongly stabilizing compensator, in terms of the plant orders. A similar problem was also considered by Smith et al. (1986), where it was shown that such a bound does not exist for the strong stabilization problem of a single plant. But the examples given in the article were forcing an approximate unstable pole-zero cancellation or forcing the distance between two distinct unstable zeros to go to zero. In this paper it is shown that: 1) if approximate unstable pole-zero cancellation does not occur, and the distances between distinct unstable zeros are bounded below by a positive constant, then it is possible to find an upper bound for the minimal order of a strongly stabilizing compensator, and 2) for the simultaneous strong stabilization problem (even for the two plant case), such a bound cannot be found     

Optimal dead-time compensator design for stable and integrating processes with time delay

Recently, a modified Smith predictor with a prefilter has been proposed for first-order stable and integrating processes with time delay. The paper is a further investigation on the empirical method. In this paper, an optimal design procedure is developed for the scheme. With respect to the proposed controller and corresponding processes with time delay, the closed-loop time domain responses are estimated quantitatively. The robustness of the closed-loop system is analyzed. Finally, a simple tuning rule is proposed, which allows to tune the controller for desired time domain properties such as overshoot and rise time, or frequency domain criteria such as stability margin and bandwidth.     

On the design of stabilizing compensators via semi-infiniteoptimization

The authors derive a modified Nyquist stability test which makes possible the use of semi-infinite optimization for the design of stabilizing compensators. The test provide a simple necessary and sufficient condition of exponential stability and is computationally well-conditioned. Computational aspects of the derived stability test are discussed and a design example is given     

On the explicit dead-time compensation for robust model predictive control

Computational simplicity is one of the most important aspects to take into account in robust model predictive control (MPC). In dead-time processes, it is common to use an augmented state-space representation in order to apply robust MPC strategies but, this procedure may affect computational aspects. In this paper, explicit dead-time compensation will be used to avoid augmented representation. This technique will be analyzed in terms of robust stability and constraint satisfaction for discrete-time linear systems. The results of this discussion will be applied to a robust tube-based MPC strategy which is able to guarantee robust stability and constraint satisfaction of a dead-time system by considering a prediction model without dead-time. Moreover, taking advantage of the proposed scheme, the robust MPC will be particularized for first-order plus dead-time models which simplifies significantly controller synthesis. The proposed dead-time compensation method will be applied to different robust MPC strategies in two case studies: (i) a simulated quadruple-tank system, and (ii) an experimental scaled laboratory heater process.     

On the extraction of dead-time controllers and estimators from delay-free parametrizations

An approach to control design for dead-time (DT) systems is proposed. The underlying idea is to treat the DT element not as a part of the generalized plant, but rather as a (causality) constraint imposed upon the controller (estimator). This enables one to use well-understood parametrizations of all delay free controllers in the DT design. In particular, DT controllers can be extracted from such delay-free parametrizations. In the paper, the extraction procedures are developed in both H/sup 2/ and H/sup /spl infin// settings. It is shown that the proposed approach yields simple solution procedures and new transparent and intuitively appealing structures for the resulting controllers and estimators.     

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.     

On the convergence properties of adaptive pole-placementcontrollers with antiwindup compensators

To avoid the windup problem in adaptive pole-placement controllers in the presence of a saturating input, an antiwindup compensator based on a generalization to the conditioning technique is introduced to the controller. This modification to the controller also provides a unified approach to investigate the asymptotic properties of the adaptive controllers with a class of antiwindup compensators, at least, when applied to stable processes     

On the dead-time compensation from L/sup 1/ perspectives

It is known that both H/sup 2/ and H/sup /spl infin// optimization problems for dead-time systems are solved by controllers having the so-called modified Smith predictor (dead-time compensator) structure. This note shows that this is also true for the L/sup 1/ control problem. More precisely, it is demonstrated that the use of the modified Smith predictor enables one to reduce the standard L/sup 1/ problem for systems with a single loop delay to an equivalent delay-free problem. The (sub)optimal solution therefore always contains the modified Smith predictor.     

On the practical stability of optimal stochastic control systems with dead-time

The practical stability of optimal stochastic control systems for processes having dead-times is considered. Previously obtained necessary conditions for practical stability of such systems are generalized using Pontryagin's theorem on the roots of two-variable polynomials. The conditions are expressed in terms of the relations between the orders of the process, the process model and the disturbance model.     

On the order of stable compensators for a class of time-delay system

The stabilization using a stable compensator does not introduce additional unstable zeros into the closed-loop transfer function beyond those of the original plant, so it is a desirable compensator, the price is that the compensator‘s order will go up. This note considered the order of stable compensators for a class of time-delay systems. First, it is shown that for single-loop plants with at most one real fight-half plane zero, a special upper bound for the minimal order of a strongly stabilizing compensator can be obtained in terms of the plant order; Second, it is shown that approximate unstable pole-zero cancellation does not occur,and the distances between distinct unstable zeroes are bounded below by a positive constant, then it is possible to find an upper bound for the minimal order of a strongly stabilizing compensator.     

On the design of finite-dimensional stabilizing compensators forinfinite-dimensional feedback-systems via semiinfinite optimization

The computational stability criterion presented by E. Polak and T.L. Wuu (see ibid., vol.34, p.196-200, Feb. 1989) is extended to a form that can be used in the design of finite-dimensional stabilizing compensators for a class of feedback systems with infinite-dimensional plants. Since, in this case, the characteristic function is not a polynomial, there is no simple way to define a normalizing polynomial. Hence, approximation theory has to be used. The new stability test guarantees not only input-output stability, but also internal stability of the feedback system. Furthermore, since the numerical implementation of the test does not depend on the use of a reduced plant model, the test does not lead to spillover effects. Because the compensator is parametrized in the state-space form, the order of the compensator can be assigned by the designer     

An approach to compute and design the delay margin of a large‐scale matrix delay equation

A methodology to compute and design the delay margin (DM) of large‐scale linear time‐invariant systems is presented. Different from existing work, this methodology is scalable; does not impose restrictions on the system to be able to invoke simultaneous triangularization or simultaneous diagonalization; and sheds light on how the finite number of delay‐free system eigenvalues can be effectively utilized to compute or design the DM.     

On the design of optimal constrained dynamic compensators for linear constant systems

The design of linear time-invariant dynamic compensators of fixed dimensionalitys, which are to be used for the regulation of annth-order linear time-invariant plant, is dealt with. A modified quadratic cost criterion is employed in which a quadratic penalty on the system state as well as all compensator gains is used; the effects of the initial state are averaged out. The optimal compensator gains are specified by a set of simultaneous nonlinear matrix algebraic equations. The numerical solution of these equations would specify the gain matrices of the dynamic compensator. The proposed method may prove useful in the design of low-orderscompensators for high-ordernplants that have fewroutputs, so that the dimension of the compensator is less than that obtained through the use of the associated Kalman-Bucy filternor the Luenberger observern - r.     

On the computation of proper,feedforward internally stabilizing and pole-placing compensators

By combining two important results from the ‘polynomial’ and ‘fractional representation’ approaches we derive a state-space formula for the direct computation of a proper, feedforward, internally stabilizing, and pole-placing compensator C(s).