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SUMMARYIn this paper, a boundary controller with disturbance observer is proposed for the vibration suppression of an axially moving belt system. The model of the belt system is described by a nonhomogeneous partial differential equation and a set of ordinary differential equations with consideration of the highacceleration/deceleration and unknown spatiotemporally varying distributed disturbance. Applying the finite-dimensional backstepping control and Lyapunov's direct method, a boundary controller is developed to stabilize the belt system at the small neighborhood of its equilibrium position and a disturbance observer is introduced to attenuate the effect of unknown external disturbance. The S-curve acceleration/deceleration method is adopted to plan the speed of the belt. With the proposed control scheme, the spillover instability problems are avoided, the uniform boundedness and the stability of the closed-loop belt system can be achieved. Simulations are provided to illustrate the effectiveness of the proposed control scheme. Copyright

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This paper develops a linearization-based adaptive control technique for control of the nonlinear NASA Generic Transport Model with large parametric and structural uncertainties caused by damage. It presents new studies of linearization of the nonlinear aircraft dynamics in the presence of damage. A state-feedback multivariable model reference adaptive control scheme is developed for the linearized aircraft model with damage to ensure stability and asymptotic output tracking for aircraft in the presence of damage. The invariance characteristic of system infinityzero structures of the nonlinear and linear system models is investigated. This work shows how a linearization-based model reference adaptive control scheme using state feedback can be applied to a nonlinear aircraft dynamic system with damage, and the control system simulation of the Generic Transport Model demonstrates some desired performance of such a control system in the neighborhood of the chosen operating point. Nomenclature A; B; C, f 0 = linearized aircraft system parameters and dynamics offset d e , d r , d a , = elevator, rudder, and aileron deflections, deg d tl , d tr = left and right engine throttles Gs, m s = linearized system transfer matrix and its modified left interactor matrix I x , I y , I z = moments of inertia about body axes I xy , I xz , I yz = cross-products of inertia about body axes K p , i = high-frequency gain matrix and its leading principal minors ( 1 ; . . . ; M ) K 1 t, K 2 t, k 3 t = adaptively updated controller parameters L, M, N = body-axis moments m = mass of the aircraft p b , q b , r b = body-axis components of angular velocity, rad=s T L , T R = engine thrusts on left and right sides ut = d e ; d r ; d a ; d tl ; d tr T , aircraft system controlinput signal u b , v b , w b= body-axis velocity components of origin of body-axis frame, ft=s W m s, y m t, rt = reference system transfer matrix, output signal, and reference input signal X, Y, Z = body-axis aerodynamic forces xt, yt = u b ; w b ; q b ; ; v b ; r b ; p b ; ; T , ; T , aircraft state and output signals x 0 ; u 0 = operating point for linearization xt, yt, ut = linearized aircraft system state, output, and control-input signalsx b , y b , z b = coordinates of the center of gravity in the body frame , , = roll, pitch, and yaw angles, rad

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