Optimization of automatic control systems for DC electric drives using nonlinear correction devices

Abstract

Purpose of the work. The purpose of this work is to study a nonlinear correction device for an automatic control system for a DC electric drive, which provides an approach to the optimal operating mode according to the criterion of speed and accuracy, while simultaneously determining the stability conditions and limits of the system's performance.

Research methods. The work uses mathematical modeling, the theory of optimal control based on the minimax principle, the harmonic linearization method for stability analysis, as well as numerical methods to determine the optimal parameters of the phase-leading link. Structural diagrams of DC electric drives and models with relay characteristics were used, which made it possible to study the influence of nonlinear correction on the dynamic properties of the system.

Results. In the process of research, a structural diagram of a DC electric drive with a nonlinear regulator, including a phase-leading link and relay elements, was constructed. A method for approximating the optimal control law using the minimax principle is proposed, which ensures minimization of deviations from the optimal regime in a wide range of input amplitudes. Dependencies between the parameters of the phase-leading link and the magnitude of the system error deviation are established, which made it possible to formulate criteria for selecting its time constants. Analytical expressions for estimating the signal switching moment are obtained, the normalized relations between the amplitude and the switching time are constructed, which determine the quality of the control process. It is shown that the proposed nonlinear corrector allows to reduce the time of the transient process and reduce the error magnitude without a significant increase in overshoot. The analysis of the system stability using the harmonic linearization method made it possible to determine the critical values of the gain coefficients and self-oscillation frequencies. It is established that the presence of a nonlinear corrector significantly affects the dynamic characteristics and at the same time narrows the limits of stability. The constructed graphs of the critical gain and self-oscillation frequency depending on the nonlinear link parameter allowed us to determine clearly the areas of stable and unstable operation of the DC electric drive. Thus, the results confirm that the use of a nonlinear correction device provides an increase in the system speed and a decrease in the error, but requires consideration of  a compromise between the quality of regulation and the margin of stability.

Scientific novelty. The work substantiates a new approach to the synthesis of DC electric drive control systems based on nonlinear dynamic correction. The application of the minimax principle for approximating the optimal control law is proposed and its effectiveness in a wide range of input influences is shown. For the first time, a comprehensive analysis of the relationship between the parameters of the nonlinear link and the system stability limits is carried out.

Practical value. The results of the work can be used in the design of electric drives operating in modes with high requirements for speed and regulation accuracy. The proposed approaches contribute to the creation of more effective control algorithms that take into account the trade-off between speed, accuracy, and system stability.