The Simple Adaptive Control (SAC) algorithm achieves perfect model following and can improve the performance of any linear control design of linear time invariant system [1]. This has been proved and demonstrated in a deterministic context. An introductory analysis of the effect of disturbances, noises, and mild deviations from linearity has not been systematically analyzed, except in preliminary publication [2,3].

The disturbances, noises, and mild deviations from linearity that are considered in this paper are: output encoder and input encoder quantization, actuator’s noise (in hydraulic motor) and disturbance (cogging in electric motor, linear and rotational ball bearing disturbance in piezoelectric motor, linear and rotational gear disturbance), sensors’ noise and nonlinearities and dynamic range (saturation), internal noises (e.g. from power supply), external vibrations, change of moment of inertia (in robots), friction (static, Coulomb, viscous, slip-stick and Stribeck effect), external disturbances (wind effect on a tracking antenna, gravity) and more.

The objective of this paper is to perform thorough analysis of the effect of disturbances, noises, and mild deviations from linearity on the performance of SAC.

The measured tracking error-difference between the command and measured output (includes the measurement noise) and the actual tracking error-difference between the command and actual output (that is not available) are considered.

It is shown that SAC implementation reduces the effect of disturbances, noises and nonlinearities.

A detailed analysis is presented and demonstrated by simulations.