Salvador Alcántara

H∞ control of fractional linear systems

Abstract In this paper, the standard H ∞ control problem for continuous-time fractional linear time-invariant single-input–single-output systems is solved. The adopted approach consists of extending to the fractional case the procedure followed within the classical solution for the integer case. According to the classical route, we first consider the generalization to fractional systems of the standard Youla parameterization of all the stabilizing controllers. The H ∞ optimal controller is then found among the class of stabilizing controllers, recasting the control problem into a model-matching one. The results obtained naturally extend well-established results to a fractional setting, including both the commensurate and noncommensurate case, thus providing a framework where H ∞ design can be recast along the well-known and fruitful lines of the integer case. A worked-through example is discussed in detail to illustrate the design procedure.

Controller parameters dependence on model information through dimensional analysis

In this article we make use of dimensional analysis in order to investigate the controller parameters dependence on model information (i.e. model parameters). The objective is to relate the influence that each model parameter has on each controller parameter. In order to accomplish this goal the model transfer function is first analyzed using dimensional analysis and characterized by means of of dimensionless numbers. Secondly each controller parameter is related with the model parameters. As a result it is derived the underlaying structure that any homogeneous tuning rule must follow. The general results are particularized for PID control of first order and second order systems. The results can be applied to PID tuning and PID tuning rules comparison.

Identification and adaptive control of delayed unstable systems

In this paper, we develop a multimodel adaptive control strategy to be applied to delay compensation schemes for unstable systems. The strategy is based on intelligent control and the only requirement about the system is that the delay is unknown but bounded. The proposed approach can be used on any delay compensation scheme increasing the robustness of the system with respect to delay uncertainty. In particular, this paper considers the modified Smith Predictor (SP) for unstable and integrating systems with time-delay proposed by S. Majhi and D. P. Atherton. Simulation examples show the usefulness of implementing this strategy when the delay is unknown, showing that the scheme is capable of stabilizing the system with large delay and the good results obtained in the identification of the delay.

General Smith Predictors from an Observer-Controller perspective

The Smith Predictor is a well-known method for designing controllers for plants with I/O delays. Assuming the time delay known, this control configuration compensates the delay within the loop making it possible to design the controller just considering the (rational) delay-free part of the plant.

A 2DOF H ∞ robust tracking design for a special type of observed state feedback controllers

A control configuration for the design of robust controllers in the general context of LTI systems (SISO, MIMO, stable, unstable) is presented. It consists of a two-degree-of-freedom control architecture constituted by a particular observed state feedback controller arising from a right coprime factorization of the plant together with a prefilter block. Before detailing the general design methodology involving the available two degrees of freedom, the feedback part of the scheme is first analyzed by its own in order to establish connections with respect to a conventional state feedback controller with full state observer. A prefilter block is added afterwards and an optimization based design procedure for the resulting two-degree-of-freedom control scheme is suggested. The feedback part is designed in regulator mode to guarantee robust stability and some performance in terms of disturbance rejection whereas the prefilter controller deals with the servo specifications given in terms of a reference model.

Multimodel-based techniques for the identification of the delay in MIMO systems

This paper introduces a novel method to identify each individual delay in Multiple Input Multiple Output linear systems with unknown delays. The solution is based on a multi-model scheme consisting of a set of tentative delay estimations along with a switching mechanism aimed at progressively updating them through time according to a figure of merit. Moreover, the set of tentative delays is proved to converge to the actual delays under certain persistent excitation conditions on the input signals. Another contribution of the paper stems from the fact that the presented method can be regarded as an online implementation of an heuristic optimization method known as Pattern Search, very uncommon in control systems applications. Also, numerical examples showing the feasibility and effectiveness of the proposed method are included.

Smith Predictor based intelligent control of multiple-input-multiple-output systems with unknown delays

One of the main drawbacks of the Smith predictor (SP) for controlling systems affected by external delays is that the resulting performance relies on the accuracy of the knowledge regarding such delays. Thus, as the mismatch between the true value of the delay and the nominal one employed for control purposes increases the closed loop performance deteriorates accordingly. This point is particularly remarkable when dealing with multivariable plants in which strong coupling between the different input-output channels may exist. In this communication an intelligent control scheme aimed at the control of multivariable plants with uncertain external delays is proposed. It arises as the result of combining the basic SP with a supervised multiple model architecture that tackles the delay uncertainty.

Analytical H ∞ design for a Smith-type inverse-response compensator

In this paper a control configuration for inverse-response processes is presented. It results in a Smith-type predictor scheme that aims to put the non-minimum phase dynamics out of the feedback loop. The design is carried out analytically by solving an H∞ weighted optimization problem assuming a second order stable process with one positive zero. The performance of the proposed control configuration is compared by simulation with two different approaches to show its applicability.

Brief paper: Stable genetic adaptive controllers for multivariable systems using a two-degree-of-freedom topology

This paper introduces an adaptive reference tracking controller based on the online genetic estimation of the parameters of the system. The main novelty of the paper relies on the fact that the stability of the genetic adaptive scheme is analytically proved and not simply validated by means of simulation as it is customary in the literature. The resulting set-up is flexible enough to be integrated within a great variety of genetic estimation algorithms, which can in many cases outperform traditional estimation procedures. The goal is achieved by using a certain two-degree-of-freedom (2-DOF) based implementation of the control law in which the reference tracking property is separated from the closed-loop stability. Within this framework, the here-presented procedure for the genetic controller synthesis just affects two time-varying pre-filter blocks that do not compromise the closed-loop stability under weak conditions. In this manner, the power and versatility of genetic algorithms can be safely used to achieve tracking performance disregarding stability, which is delegated to a static feedback controller designed on the basis of robust control theory.

Tuning PI controllers based on ℋ ∞ Weighted Sensitivity

ℋ∞ control theory is usually associated with highorder controllers. In this paper, simple tuning rules (extending the well-known SIMC) for the Proportional-Integral (PI) algorithm are derived analytically based on ℋ∞ Weighted Sensitivity. The presented approach deals with stable, integrating and unstable plants in a unified way, avoiding any notion of coprime factorization. The final tuning involves two adjustable parameters, λ and γ with clear engineering meaning: λ selects the Robustness/Performance compromise, whereas γ allows to balance the Servo/Regulator performance. Based on this, several application scenarios are considered. First, a One-Degree-Of-Freedom (1-DOF) PI controller is assumed. Second, 2-DOF and switched implementations are investigated.