The work considers the peculiarities of the way the follow-up system based on the piezoelectric engine functions. The system consists of a piezoelectric engine of the reverse rotation, presented as two independent piezoelectric engines of rectified rotation with the common arbor and separate power supply units; a feedback sensor, a comparator unit, a reverse control unit; a step-length control unit and a clock frequency generator.
It has been defined that unlike the control system with single value nonlinearity, for which Popov criterion is applied to research the stability of the equilibrium, the stability of the control system of the piezoelectric engine with hysteresis nonlinearity and numerous equilibrium positions is evaluated applying the stability criterion of Yakubovitch. To analyze the stability of the control units of the piezoelectric engine with hysteresis nonlinearity, a generalization is used, under which control unit system links are transformed into a hysteresis link of the nonlinear part and links of the linear part of the control unit.
The functional chart of the control unit of the deformation of the piezoelectric transducer is analyzed. The research has been done on the absolute stability of the control unit of the deformation of the piezoelectric transducer for nano- and micro displacements under deterministic impacts based on criterion of Yakubovitch.
Amplitude-phase-frequency characteristics have been built on the complex plane for two kinds of curved lines, for which the conditions of stability are met but the conditions of absolute stability of the control unit of the deformation of the piezoelectric transducer are not met. It is defined that the frequency criterion of the absolute stability is simple and convenient for the synthesis of the compensating devices of the control unit of the deformation of the piezoelectric transducer for nano- and micro displacements. It has been noted that the frequency criterion of the absolute stability of numerous equilibrium positions in a nonlinear system with one hysteresis nonlinearity of the piezoelectric transducer is true both for the systems with deterministic and random processes, as well as both for lumped parameters and distributed constants.
Analytic formulae have been obtained for the synthesis of the follow-up control system based on the piezoelectric engine with the ability to change from step running to continuous operation and back.
Key words: follow-up system; automatic control unit; piezoelectric engine; absolute stability; stability criterion of Yakubovitch; compensating device.
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