Applying the Simple Adaptive Control to a Design using a B controller.

Darren Loo, Amine Houimdi, David Bensoussan

École de technologie supérieure, Montréal, QC, H3C1K3, CA

(e-mail: david.bensoussan@etsmtl.ca, darren.loo.1@ens.etsmtl.ca, ahouimdi@gmail.com).

One of the underlying guiding principles of Simple adaptive Control (SAC) is that the smoothness of trajectory allows for a better alignment to the desired trajectory [1]. To that effect, it is proposed to design a controller  so that it performs a desired path which is practical.

Our aim will be to define the desired path as the closed loop obtained by a new control method (B controller) [2] based on sensitivity considerations. This controller can be applied to unstable invertible plants. The compensator leads to an open loop transfer function J(s) = J₁(s) J₂(s)J₃(s) which acts on three frequency ranges: J₁(s) achieves low sensitivity with high gain at low frequencies; J₃(s) ensures that J(s) is strictly proper; J₂(s) is a set of phase circuits that allows to tune in the time response without affecting stability and robustness. Theoretical and experimental results [3] have shown that while using practical gains, the B controller keeps excellent stability margins and leads to a time response that presents no overshoot, with rise time equal to settling time.

At first, we will propose an adaptive architecture in which the desired architecture is defined by  J(s).[I + J(s)]^-1 . We then apply the SAC method to this scheme and compare the performance results to those which were previously obtained on an Autopilot design [4,5].

In light of the said comparison, we will discuss possible avenues of research in adaptive control architectures.