In this letter, we propose a contraction-based variable gain nonlinear control scheme for the laser-beam stabilizing (LBS) servo-system, which guarantees that the closed-loop system is convergent. With the variable gain acting on the velocity error, the well known waterbed effect of the low-frequency/bandwidth trade-off can be overcome. Moreover, the contraction-based framework allows us to extend the linear control performance metrics for analyzing the closed-loop nonlinear system behavior. The closed-loop system's performance is evaluated in numerical simulations under input disturbances and/or white noise measurements and its efficacy is compared to that using PID and LQG controllers.

A CAD approach permitting us an easily frequency response simulation of LTI systems implemented with analog electronic-devices, is introduced. This technique uses the features of symbolic analysis in order to get more insight into the behavior of the circuit. An important thing is that a reasonable amount of computer effort is saved through modeling several analog circuits using nullors. Most important is that using nullors, a pure nodal-analysis method is established in order t o improve the computation of transfer functions. In the paper, it is also demonstrated the suitability and appropriateness of the proposed simulation technique to be used in education.

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