Towards an ultra-local model control of two-tank-system

Abstract

This paper deals with the design of an ultralocal model control. The proposed approach is based on the estimation of the ultra-local model parameters using least squares resolution technique instead of numerical derivation technique. The closed-loop control is implemented through an adaptive PI in order to reject the influences of the disturbance and noise output signais. Its main advantages are: its simplicity and its robustness with respect to the parameter uncertainties of system. In this paper, it is processed to test the efficiency of the parameter estimation method compared with the performance of numerical derivation technique. The method is applied to the water level control of a two-tank-system. Numerical simulations show that the generated desired trajectory is followed in an efficient way even with severe operating conditions.

Performances comparison between ultra-local model control, integral sliding mode control and PID control for a coupled tanks system

“…From the two previous relations (35) and 40, we can generate a linear system of equations in the following matrix form:…”

“…The loop is closed thanks to an adaptive PID (a-PID) controller, which provides the feedforward compensation and is easily tuned. This control approach have already been successfully applied in several case-studies for different fields (1), (11), (12), (18), (19), (22), (27), (35), (36). The algebraic derivation method developed in (7) is restricted by the estimation of a single parameter, and the second parameter is considered constant and imposed by the practitioner.…”

Design of adaptive PID controllers based on adaptive Smith predictor for ultra-local model control

“…The time delays have been also taken into account by the ultra-local model control, recently introduced by M. Fliess and C. Join with the free-model control notion which does not require any mathematical modeling (7), (8), (9), (10), (11), (18), (35), (36), (37). The unknown dynamics is approximated on a very small time interval by an ultra-local model which is continuously updated based on the online algebraic identification techniques (14), (15), (31).…”

An algebraic control approach based on the estimation of an ultra-local Bro¨ıda model

“…For this reason, the industrial world is not willing to employ most techniques based on a precise mathematical modeling in spite of considerable advances in the last years. This unfortunate situation is overcome thanks to the ultra-local model control which is recently introduced by M. Fliess and C. Join [6], [7], [8], [28], [29]. The concept of this approach is based on an elementary continuously updated local modeling via the unique knowledge of the input-output behavior.…”