PROJECT TITLE :
Regularized - and DHOBE: An Adaptive Feedforward for a Solenoid Valve
To permit a stable and fast acting hydraulic pressure control on a continuously variable transmission (CVT) for road vehicles, an adaptive feedforward strategy is used. The Dasgupta-Huang outer bounding ellipsoid (DHOBE) and recursive least squares (RLS) with exponential forgetting factor$(rm RLS$-$lambda)$ adaptation algorithms are compared to the non-adaptive feedforward. The experiments show a transparent advantage for the adaptive over the non-adaptive version by compensating for the slow drift of the valve pressure gain during the warm-up amount of the transmission. As a result of of highly correlated input data, the difference algorithms supply deceiving performances with oscillating identified parameters. A regularization procedure is added to each adaptation algorithms, giving the $rrm RLS$-$lambda$ and $rDHOBE$. The regularized algorithms supply considerably better performances and stability than their non-regularized counterparts. As a result of of its implicit parametric uncertainty calculation whereas keeping an equivalent convergence rate, and a lower range of updates, the rDHOBE algorithm is thought to be the best answer for the application. By adapting a easy linear model, the rDHOBE adaptive feedforward succeeds in responding to an abrupt modification of the external pressure setpoint with no added actuation delay whereas keeping the pressure error underneath zero.5 bar.
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