Алгоритми стабілізації та позиціонування двоколісного експериментального балансуючого зразка

• Дата: 2025
• Автори: Kulik, Anatoliy, Dergachov, Konstantin, Pasichnik, Sergey
• Формат: Стаття
• Мова: Ukrainian
• Опубліковано: V.M. Glushkov Institute of Cybernetics of NAS of Ukraine 2025
• Теми: двоколісний експериментальний балансуючий зразок; об’єкт керування; математичні моделі; передавальна функція; простір станів; синтез; зважений модуль похибки
• Онлайн доступ: https://jais.net.ua/index.php/files/article/view/421
• Назва журналу: Problems of Control and Informatics

Peculiarities of objects movement with the structural instability studying by means of physical analogs is a widely used approach for such objects control systems designing. The work considered holding-balance two-wheeled experimental sample (TWES) studying. The motion of the TWES is divided into two components — short-period rotational movement of the body around vertical position and translational long-period TWES mass center movement on the horizontal surface. To control the local movements of the object, a vertical position stabilization circuit and a horizontal motion positioning circuit have been synthesized. The synthesis was carried out using the principle of control by state and mathematical models of TWES in the form of differential equations in the form of Cauchy and object’s transfer functions by controlling and disturbing influences. Based on the transfer functions, differential equations of the object state were obtained in the canonical form of controllability, which satisfied controllability and observability criteria. The components of the state vector are identified using a Luenberger observer, which is a full-order filter. In order to ensure a compromise between the requirements for the stability and quality of the TWES movement processes, the coefficients of corrective feedback by state and the coefficients of observers of stabilization and positioning circuits were calculated using optimal quality estimates and standard transient characteristics. The integral of the weighted error modulus was taken as the optimal criterion, which allows to reduce the influence of significant initial values of deviations on the quality of transient processes in object motion local control loops. The values of the correcting coefficients and observer coefficients depend on the choice of the natural frequency of oscillations of the closed system. By modeling the joint operation of the stabilization and positioning circuits, it was determined that stable response of the control system to step input influence is possible at values of the natural oscillation frequency exceeding 65 rad/s for stabilization circuit feedback coefficients. The natural oscillation frequency for the observer calculation has been chosen twice as large. The obtained results indicate the fundamental possibility of controlling the state of the holding-balance TWES movement and could be useful in the control systems designing for unstable objects.