Ashraf Elnaggar

Delay Estimation Using Variable Regression

Systems with unknown delay are very common in industry. Conveyor belts, long pipe-lines or any transportation line are typical sources of system delay where the system input goes to one end of the transportation line (e. g. output valve of a reservoir tank) and the output is measured at the other end of the line (e. g. the level of receiving tank). Traditional online methods of delay estimation do not directly estimate the system delay but rather replace it by a large number of unknown parameters in the system model. In this paper, the unknown delay is directly estimated and no additional parameters are used in the system model. Experimental results are also presented to demonstrate the applicability of the method in adaptive control.

Recursive estimation for system of unknown delay

An algorithm is presented for the recursive estimation of both process parameters and delay when no a priori knowledge of the delay is required. The algorithm is a modification of any standard recursive parameter estimation algorithm and can be applied easily to any of the well-established versions of estimation algorithms (least square, instrumental variables, maximum likelihood, etc.) and their extensions. The algorithm requires minimum additional computations compared to the original algorithms. The delay is explicity estimated, and the parameter vector is of the same length as for the undelayed system. This means clear separation between the system dynamics and delay. Simulation results showing the good performance of the algorithm are presented.<<ETX>>

New method for delay estimation

The authors present an algorithm for delay estimation where no a priori knowledge of the delay or the process parameters is required. The algorithm requires minimum computation and can be easily applied to both offline and online delay estimation. In online delay estimation, the method represents a variable regression estimator that decouples the delay estimation from the parameter estimations. Computer simulation results are presented to demonstrate the efficiency of the method.<<ETX>>

Adaptive GPC based on Laguerre-filters modelling

Abstract A state-space model based on Laguerre filters is proposed to design an adaptive generalized predictive controller (GPC) for stable plants. A sufficient stability condition is derived to study the convergence and stability of the proposed controller in case of a plant-model match. Robustness conditions are also given for the case of plant-model mismatch. The results are applicable to GPC schemes based on moving average models. In the presence of plant-model mismatch, illustrative examples show the robustness of the controller and compare it with other GPC versions.

Stability and convergence analyses of an adaptive GPC based on state-space modeling

A generalized predictive controller (GPC) is derived based on a general state-space model. The equivalence of the predictive control problem to a perturbation problem is revealed. In the case of a small perturbation, the closed-loop poles are calculated with high accuracy. For the case of a general perturbation, an upper bound on the permissible perturbation norm is derived assuming an open-loop stable system. Both the plant-model match and plant-model mismatch cases are analysed. The controller is proven to be robust and an adaptive implementation is motivated. For open-loop stable systems, the convergence and stability of the control scheme are ensured by proper tuning of the control weight and prediction horizon. The results are applicable to a wide range of predictive controllers. The main contribution of this paper is not a new control algorithm, but new techniques to analyse the GPC as well as new stability and convergence results.

Perturbation analysis of GPC with one-step control horizon

Abstract A generalized predictive controller is derived based on a state-space model. The special, but commonly used, case of a one-step control horizon is analyzed. It is shown that the predictive control problem is actually a perturbation problem where there exist easy relations to calculate the closed-loop poles. In case of a plant-model match, the perturbed eigenvalues of a stable system as well as a system having one unstable pole are studied. The results do not necessarily require the infinite prediction horizon or the zero control weighting assumptions. In case of a plant-model mismatch, stability is studied for general plant representations, using operators, as well as for a linear time-invariant representation. It is shown that the generalized predictive controller still yields a mean level controller under some assumptions.

System identification and adaptive control based on a variable regression for systems having unknown delay

An algorithm is presented for the recursive estimation of both process parameters and delay where no a priori knowledge of the delay is required. This algorithm is a modification of any standard recursive parameter estimation algorithm and can be applied easily to any of the well-established versions of estimation algorithms (least squares, instrumental variables, maximum likelihood, etc.) and their extensions. The algorithm requires minimum additional computations to the original algorithm. The delay is explicitly estimated and the parameter vector is of the same length as the undelayed system. This means clear separation between the system dynamics and delay. The proposed algorithm works in open-loop estimation and closed-loop adaptive control.<<ETX>>

Adaptive Control with Direct Delay Estimation

Abstract This paper addresses the challenging problem of controUing systems with unknown delay and offers a new solution by directly estimating the system delay using the Variable Regression Estimator (VRE). Pole-Placement control, Dahlin control and Generalized Predictive Control (GPC) are used with the Variable Regression Estimation and the resulting closed-loop performance enjoys fast adaptation and good regulation with minimum computations. With the VRE direct delay estimation, the GPC tuning parameters can adapt to delay changes in order to provide the same closed-loop performance over the range of delay variation. The VRE-based adaptive controller is successfully applied to an experimental setup with large delay variations.

Stability and convergence analysis of an adaptive GPC based on state space modeling

A generalized predictive controller (GPC) is derived based on a general state-space model. The link between the predictive control problem and the perturbation problem is highlighted. In the case of small perturbation, the closed-loop poles are calculated with high accuracy. For the case of a general perturbation, an upper bound on the permissible perturbation norm is derived assuming an open-loop stable system. Both the plant-model match and plant-model mismatch cases are analyzed. The controller is so robust that an adaptive implementation is motivated. For open-loop stable systems,the convergence and stability of the control scheme are insured by proper tuning of the control weight and prediction horizon. The results are applicable to a wide range of predictive controllers.

A predictive-control implementation using expert systems

An adaptive generalized predictive controller based on Laguerre-filter modeling is commissioned using the expert shell G2. The resulting expert system is used to orchestrate the operation of the controller, to provide an interactive user interface, to adjust the Laguerre-filter model using AI search techniques, and to evaluate the performance of the controller online. Based on the performance evaluation, the tuning parameters of the controller are adjusted online using fuzzy-logic rules. A simulation example demonstrates the operation of the system.<<ETX>>