Nieliniowe sterowanie predykcyjne ramion manipulatorów

pol Artykuł w języku polskim DOI: 10.14313/PAR_248/47

wyślij Piotr Tatjewski Politechnika Warszawska, Nowowiejska 15/19, 00-665 Warszawa

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Streszczenie

Przedmiotem artykułu są algorytmy sterowania predykcyjnego (typu MPC – Model Predictive Control) ramion manipulatorów sztywnych. Zastosowano MPC z modelem w przestrzeni stanów i wykorzystano najnowszą technikę tłumienia zakłóceń i błędów modelowania, pozwalającą uniknąć dynamicznego modelowania zakłóceń lub uciekania się do dodatkowych technik ich eliminowania, takich jak SMC. Rozważane są przede wszystkim najbardziej efektywne obliczeniowo algorytmy MPC-NPL (NPL – Nonlinear Prediction and Linearization), w dwóch wersjach: z optymalizacją QP (Quadratic Programming) z ograniczeniami i z jawną optymalizacją bez ograniczeń i spełnieniem ograniczeń nierównościowych a posteriori. Dla wszystkich rozważanych algorytmów przeprowadzono kompleksową analizę symulacyjną sterowania manipulatorem z napędem bezpośrednim, przy dwóch rodzajach zakłócenia: zewnętrznym i parametrycznym. Wyniki porównano z uzyskanymi dla znanego algorytmu CTC-PID (CTC – Computer Torque Control), uzyskując lepszą jakość regulacji algorytmami MPC. Zbadano wpływ długości okresu próbkowania i obliczeniowego opóźnienia sterowania na jakość regulacji, co jest istotne dla algorytmów z szybkim próbkowaniem opartych na modelach.

Słowa kluczowe

opóźnienie sterowania, sterowanie manipulatorów, sterowanie nieliniowe, sterowanie predykcyjne, szybkie próbkowanie

Nonlinear Predictive Control of Manipulator Arms

Abstract

The subject of the article are predictive control algorithms (of MPC type – Model Predictive Control) for rigid manipulator arms. MPC with a state-space model and with the latest disturbance and modeling error suppression technique was applied, which avoids dynamic disturbance modeling or resorting to additional disturbance cancellation techniques, such as SMC. First of all, the most computationally efficient MPC-NPL (Nonlinear Prediction and Linearization) algorithms are considered, in two versions: the first with constrained QP (Quadratic Programming) optimization and the second with explicit (analytical) optimization without constraints and satisfying a posteriori inequality constraints. For all considered algorithms, a comprehensive simulation analysis was carried out for a direct drive manipulator, with two kinds of disturbances: external and parametric. The obtained results were compared with those for the well-known CTC-PID algorithm (CTC – Computer Torque Control), showing better control quality with MPC algorithms. In addition, the influence of the length of the sampling period and of the computational delay on control quality was investigated, which is important for model-based algorithms with fast sampling.

Keywords

contrlo delay, fast sampling, manipulator control, model predictive control, nonlinear control system

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