Adaptive cancelation of matched unknown sinusoidal disturbances for unknown LTI systems by state derivative feedback

Abstract

Solutions already exist for the problem of canceling sinusoidal disturbances by measurement of the state or by measurement of an output for unknown linear and nonlinear systems. In this paper, we design an adaptive controller to cancel matched sinusoidal disturbances forcing a linear time-invariant system with unknown system parameters in controllable canonical form by using only measurement of state-derivatives. Our design is based on three steps, 1) parametrization of the sinusoidal disturbance as the output of a known feedback system with an unknown output vector that depends on both unknown disturbance parameters and unknown plant parameters, 2) design of an adaptive disturbance observer and, 3) design of an adaptive controller. We prove that the equilibrium of the closedloop adaptive system is stable and state of the considered system goes to zero as t → ∞ with perfect disturbance estimation. The effectiveness of the controller is illustrated with a simulation example of a second order system.

Pitch Control Design for Tandem Lifting Body Catamaran by Aft Lifting Body Actuation

“…Proof: The proof of Lemma 2 is given in [33]. Substituting (35) into (4) and representing the system in the reciprocal state space form, we get…”

“…By employing the results in [29] and [33], two adaptive controllers are formulated that includes estimators of the uncertain parameters of the wave model, as well as of the boat pitch moment of inertia and the actuator coefficient for two different cases. In Case 1, we assume the pitch and the pitch rate to be available for control design, whereas only the pitch rate and acceleration measurements are used for feedback in Case 2.…”

Adaptive feedback suppression of unknown periodic components of acoustic noises with time-varying characteristics

“…Several control schemes for noise and vibration reduction have been developed and empirically tested (Bodson, 2005; Patt et al., 2005; Lau et al., 2006; Perez-Arancibia et al., 2009; Pigg and Bodson, 2010; Kim et al., 2011; Landau et al., 2011a,b; Chen and Tomizuka, 2012; Isidori et al., 2012; Aranovskiy and Freidovich, 2013; Marino and Tomei, 2013). Basturk and Krstic (2012) studied the problem of adaptive rejection of unknown periodic components of a disturbance using state derivative feedback. A repetitive control method has been proposed in Houtzager et al.…”