(748e) Adaptive Control of System with Unknown Inputs with Application to Chemical Reaction Control

We present an approach to control a system composed of a deterministic nonlinear system plus an uncertain parts modeled as a time-varying parameter vector, also called unknown input or disturbance. These inputs may represent unknown reaction rates, heat or mass transfer rates. The adaptive controller is composed of two parts: a passivity-based input observer to estimate the uncertain, time-varying parameter and a passivity-based controller that updates its control decision based on the observer estimates and on-line measurements.

The main assumptions and the measurement vector has at least the same dimension as the unknown parameter vector, along with an observability condition ^[1], and that the input or disturbance is uniformly continuous ^[3].

The unknown input observer treats the estimation problem as a control problem. In this approach, the observer constructs the error between the observations and the output produced from the observer, and uses Lyapunov method to construct parameter adaptation law that will ensure both measurement and parameter tracking. The estimated parameters are used in a passivity-based back-stepping controller ^[2]. The back-stepping was necessary since we need to augment original dynamics with a first order filter to ensure the existence of a solution to both control and parameter estimation problems. Asymptotic control stability and tuning intuition of the observer and controller are presented based on control stability and trade-off between estimation convergence rate and amplification of measurements noise ^[3]. We show that the controller can be written in a PID with a filter.

The practical problem is motivated by the fact that reaction kinetics and other dynamic mechanisms usually have large uncertainty, and it can affect the effectiveness of model-based controller. The unknown input observer can be used to estimate the reaction rates, heat and mass transfer rates if their mechanisms are not clear. The passivity-based control follows naturally and uses estimates in the feedforward term to update control decisions.

[1] Moreno, Jaime A., and Denis Dochain. "Global observability and detectability analysis of uncertain reaction systems and observer design." International Journal of Control 81.7 (2008): 1062-1070.

[2] Zhao, Zixi, et al. "Passivity-based Backstepping Control of a Semi-batch Reactor." IFAC-PapersOnLine 50.1 (2017): 13741-13746.

[3] Levant, Arie. Robust exact differentiation via sliding mode technique. Automatica 34(3): 379-384 (1998).