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The paper presented research results of a digital control system for a dynamic plant with pulse-width modulation (PWM) of control impacts. As the control PWM signal is taken the pulse duty cycle, is calculated on each current cycle of the sample from the measured values. A control algorithm is proposed based on a hybrid application of the linear-quadratic optimization procedure and the theory of observers of minimal complexity. To ensure execution that the conditions of Astatism are met, the dynamic model of the plant is supplemented with a discrete integrator. The proposed approach makes it possible to reduce hardware costs and increase the robustness of the control system due to the exclusion of operations for digital–analogue transformations of signals. The proposed algorithm for digital control of a dynamic plant with varying duty cycle values of the PWM signal shows that the PWM model turned out to be linear and practically inertia less, which makes it easy to take into account the modulator model, which significantly simplifies the solution of the problem of synthesizing a control system for a dynamic plant. The possibility of receiving a high-quality modulated control signal allows for significant suppression of signal pulsations and high control accuracy.

The paper proposes a method for the analysis and synthesis of self-oscillations in the form of a finite, predetermined number of terms of the Fourier series in systems reduced to single-loop, with one element having a nonlinear static characteristic of an arbitrary shape and a dynamic part, which is the sum of the products of coordinates and their derivatives. In this case, the nonlinearity is divided into two parts: static and dynamic nonlinearity. The solution to the problem under consideration consists of two parts. First, the parameters of self-oscillations are determined, and then the parameters of the nonlinear dynamic part of the system are synthesized. When implementing this procedure, the calculation time depends on the number of harmonics considered in the first approximation, so it is recommended to choose the minimum number of them in calculations. An algorithm for determining the self-oscillating mode of a control system with elements that have dynamic nonlinearity is proposed. The developed method for calculating self-oscillations is suitable for solving various synthesis problems. The generated system of equations can be used to synthesize the parameters of both linear and nonlinear parts. The advantage is its versatility.

Keywords: silkworm fungus, aqueous solution, bleaching sodium hypochlorite, sodium chloride and hydrogen peroxide, elongation. The linear densities of the twisted yarns, the number of twists and the indicators of semi-circular elongation deformation, ie tensile strength, elongation at break and their composite characteristics were determined (Table 1). In the article \"Application in the production of PAN fibre from an emulsion made of silkworm larvae\" [6] the use of local raw materials in the preparation of emulsions by the above method, possibilities of use in the chemical industry have been studied. According to the variants emulsified in cocoon + mushroom solution, the strength of the woollen yarn increased by 3.3N and the virginity was 2.45 conventional unit. 4.Conclusions Statements from the Introduction and Results sections should not be repeated here.