Manuel A. Duarte

Combined direct and indirect approach to adaptive control

An approach to adaptive control is introduced using a combination of both direct and indirect methods. On the basis of estimates of the plant parameters and the current values of the control parameters, closed-loop estimation errors epsilon /sub theta /(t) and epsilon /sub k/(t) are defined. These in turn are used in the adaptive laws for updating both identification and control parameters. The global uniform stability of the overall system is shown by constructing a Lyapunov function. Only the control of a first-order plant is treated in detail, to get across the principal concepts involved. In particular, the dynamic adjustment of the control parameters based on the estimates of the plant parameters is introduced as an indirect method and is the precursor of the combined method. >

A comparative experimental study of five multivariable control strategies applied to a grinding plant

Abstract This paper deals with the implementation of five multivariable adaptive, as well as classical, control strategies in an industrial grinding plant. The extended horizon, pole-placement, model reference, direct Nyquist Array and sequential loop closing algorithms were studied and implemented at CODELCO-Andinas copper grinding plant, with each of them delivering good performance. The 2×2 system chosen to be controlled has the percentage of solids (percentage of +65 mesh) fed to the hydrocyclones and the level of the sump as output variables, and the water flow added to the sump and the pump speed as input variables. The adaptive extended horizon algorithm performs the best, although all five strategies considerably improve the actual operation of the plant which consists of only one control loop. After a comparison amongst the control strategies, a brief economic impact analysis is performed to support the claim that multivariable control algorithms substantially improve the operation of the grinding plant, maintaining the percentage of solids (percentage over mesh 65) around a pre-specified value (optimal for practical purposes); thus obtaining interesting economic benefits.

Control of grinding plants using predictive multivariable neural control

This work investigates the use of a recently developed direct neural network (NN) multivariable predictive controller applied to a grinding plant. The NN controller is trained so that an estimation of the control error several steps ahead is minimized, which are given by a properly designed NN called predictor. An NN, which identifies the plant, is used to backpropagate the control error at present instant of time, as well as at various steps ahead. A linear, as well as a phenomenological (nonlinear), model of CODELCO-ANDINA grinding plant are used to simulate the proposed control strategy. The linear model was built from empirical data obtained from a real grinding plant around an operating point. The phenomenological model is based on a mass balance and power consumption of the mills containing 17 particle size intervals. Several tests are performed, driving the process to an operation point, and then, controlling it by training the NN controller on line. Finally, a comparison with other control strategies already applied at a simulation level is presented. These include classical and adaptive multivariable control algorithms. All the results presented in the paper are based on simulations.

Grinding operation optimization of the CODELCO-Andina concentrator plant

Abstract This paper presents results following the application of a sub-optimal control scheme, both through simulation and in situ, from the operation of Section C of the CODELCO-Andina copper concentrator plant. The algorithm permits the determination of the necessary control action at each instant of time in order to maximize a defined plant performance index. The main objective of the algorithm is to maximize the mineral tonnage processed by the section, subject to it not exceeding a predetermined value establishes! for the operation conditions of the mills, while at the same time maintaining constant the mass fraction over 65 mesh (212 [microns]) in the overflow of the hydrocyclones, at a value within the operational requirements of the flotation stage. The performance index is defined in terms of; the percentage of pulp solids fed to the hydrocyclones of each line of ball mills, penalty functions to prevent electric power to the ball mills ,falling below the lower limit (so as not to enter the overload region), the tonnage processed in the section, and, since water is a scarce resource, a term considering the water added to each sump is also included. The scheme is first studied and adjusted in a simulator of a concentrator plant similar to that used in the industrial application. For plant implementation, a PC software program, denoted CONMOL, is developed in TurboPascal for Windows. This software allows plant applications to be carried out through a communications interface. Finally, the results of two tests performed on Section C of the CODELCO-Andina copper concentrator plant are shown where the control is applied over 3 and 5.5 hours respectively.

Error models with parameter constraints

This work treats the analysis of two adaptive systems described by error models. The desired but unknown parameters of each adaptive system are, however, not independent. In general, only linear constraints upon these parameters are considered, although a constant but unknown scalar that introduces some non-linearities is acceptable within the given constraint. The necessity of this analysis frequently arises, in the areas of both adaptive control and parameter estimation. It is shown that, if the relationship between ideal parameters is linear, it is then possible to find coupled adaptive laws such that the overall adaptive system is globally stable for each type of known error model. Simulations show that the parameter estimation is generally much closer using coupled adaptive laws than those not incorporating the information contained within the constraint.

Multivariable control of grinding plants: a comparative simulation study.

In this paper five multivariable adaptive and classical control strategies have been studied and implemented in a simulator of the copper grinding plant of CODELCO-Andina. The strategies presented were compared and, according to theory, exhibit good behavior. The extended horizon, pole-placement and model reference multivariable adaptive control strategies were formulated in discrete-time and use a model of the plant whose parameters are updated on line using the recursive least squares method along with UD factorization of the covariance matrix and variable forgetting factor. The direct Nyquist array and sequential loop closing techniques were also studied and simulated. The two-by-two multivariable system chosen to represent the grinding plant has the percentage of solids (density) of the pulp fed to the hydrocyclones (which is highly correlated with the percentage of +65 mesh in the overflow of hydrocyclones) and the sump level as output (controlled) variables. The water flow added to the sump and the speed of the pump are its input (manipulated) variables. All the algorithms tested by simulation exhibited good performance and were able to control the grinding plant in a stable fashion. Adaptive algorithms showed better performance than classical techniques, with the extended horizon and pole-placement algorithms proving to be the best. The fact that adaptive algorithms continuously adjust their parameters renders such controllers superior to those based on fixed parameters.

Discrete-time combined model reference adaptive control

SUMMARY The discrete-time version of continuous-time combined model reference adaptive control (CMRAC) is presented in this paper. A global stability proof of the overall adaptive scheme is given using arguments similar to those used in discrete-time direct model reference adaptive control (DMRAC) but properly modified to account for the di⁄erent structure of CMRAC with respect to DMRAC. ( 1997 by John Wiley & Sons, Ltd.

Indirect model reference adaptive control with dynamic adjustment of parameters

SUMMARY The paper discusses in detail a new method for indirect model reference adaptive control (MRAC) of linear time-invariant continuous-time plants with unknown parameters. The method involves not only dynamic adjustment of plant parameter estimates but also those of the controller parameters. Hence the overall system can be described by a set of non-linear differential equations as in the case of direct control. Many of the difficulties encountered in the conventional indirect approach, where an algebraic equation is solved to determine the control parameters, are consequently bypassed in this method. The proof of stability of the equilibrium state of the overall system is found to be different from that used in direct control. Using Lyapunov’s theory, it is first shown that the parameter errors between the parameter estimates of the identifier and the true parameters of the plant, as well as those between the actual parameters of the controller and their desired values, are bounded. Following this, using growth rates of signals in the adaptive loop as well as order arguments, it is shown that the error equations are globally uniformly stable and that the tracking (control) error tends to zero asymptotically. This in turn establishes the fact that both direct and indirect model reference adaptive schemes require the same amount of prior information to achieve stable adaptive control.