Compensation of unknown multi-harmonic disturbances in nonlinear plants with delayed control

An iterative algorithm of adaptive output control with complete compensation for unknown sinusoidal disturbance

“…In the authors' opinion, the problem solved in this work significantly develops and supplements the approaches published in [1][2][3][4][5][6][7][8][9][10][11] because in contrast to the analogs [6,7] that are the closest ones as to the problem statement, here it is assumed that the relative degree of an object can be higher than unity.…”

“…The suggestion is made of the iterative procedure involving the fact that at every instant of time t i the valueω i obtained by the identification algorithm was substituted into the control algorithm (5). In contrast to the analogs [1][2][3][4][5][6][7][8][9][10][11], the suggested approach makes it possible to counteract the sinusoidal disturbing influence with the unknown amplitude, phase, and frequency, which can be performed under the conditions of the complete parametric indefiniteness of a controllable object and at any relative degree.…”

“…In contrast to [2], in [5] the algorithm of compensation for a disturbing influence is considered for the case of a nonminimum-phase linear object with known parameters, but of any relative degree. In [9,10] this problem was extended to linear objects with known parameters, but with a delay in the control channel. The articles [6,7,11] are devoted to the counteraction of a sinusoidal disturbance under the conditions of the complete parametric indefiniteness of a controllable object.…”

“…At present most of the investigations, which are devoted to the development of the methods of compensation for harmonic disturbances, consider the case when amplitudes, phases, and frequencies are unknown constant parameters (see, for example, [1][2][3][4][5][6][7][8][9][10][11]). Further, variations begin to appear, which are associated with tolerances relative to the object itself, namely, the linearity or nonlinearity of dynamics, the parametric definiteness or its absence, the availability of measurements of all variables of the state or only their portion, etc.…”

Robust hybrid estimation and rejection of multi‐frequency signals

“…When the exosystem, on the other hand, is not perfectly known, the problem becomes much more complicated since it is necessary either to directly adapt the internal model of the exosystem contained in the regulator (see for instance [6,7,8], often considering the case of nonlinear system), or to identify the frequency characteristics of the exogenous signals entering the plant and then either redesign the regulator according to the obtained information or directly cancel the exogenous disturbances using the estimated signal (see for instance [9,10,11,12,13,14,15]). The latter approach is pursued here.…”