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Applying the Simple Adaptive Control to a Design using a B controller
Azeddine Ghodbane, Maher Hammami, David Bensoussan

Last modified: 2023-06-29


Applying the Simple Adaptive Control to a Design using a B controller.
Azeddine Ghodbane, Maher Hammami, David Bensoussan
École de technologie supérieure, Montréal, QC, H3C1K3, CA
(e-mail: azeddine.ghodbane@etsmtl.ca, maher.hammami02@gmail.com,david.bensoussan@etsmtl.ca).

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.

1. Barkana, I., Robustness and perfect tracking in simple adaptive control. International J. Adaptive. Control and Signal Processing, .2016;30:1118-1151
2. Bensoussan D. (2015) Robust and ultrafast response compensator for unstable invertible plants. Automatica 60, pp. 43-47
3. Sun Y. Bensoussan D., Hammami M, Wang T., and Houimdi A., Robust and Ultrafast Response Compensator Applied to a Levitation System, European Control Conference ECC15, Linz, Austria, July 15-17, 2015.
4. Cohen, K., and Bossert, D. E., “Fuzzy Logic Non-Minimum Phase Autopilot Design,” AIAA Paper 2003-5550, Aug. 2003.
5. Barkana, I., Classical and simple adaptive control design for a non-minimum phase autopilot. Journal of Guidance, Control and Dynamics 28(4), 631–638 (2005).