A Modified Robotic Manipulator Controller Based on Bernstein-Kantorovich-Stancu Operator

Abstract

With the development of intelligent manufacturing and mechatronics, robotic manipulators are used more widely. There are complex noises and external disturbances in many application cases that affect the control accuracy of the manipulator servo system. On the basis of previous research, this paper improves the manipulator controller, introduces the Bernstein–Kantorovich–Stancu (BKS) operator, and proposes a modified robotic manipulator controller to improve the error tracking accuracy of the manipulator controller when observing complex disturbances and noises. In addition, in order to solve the problem that the coupling between the external disturbances of each axis of the manipulator leads to a large amount of computation when observing disturbances, an improved full-order observer is designed, which simplifies the parameters of the controller combined with the BKS operator and reduces the complexity of the algorithm. Through a theoretical analysis and a simulation test, it was verified that the proposed manipulator controller could effectively suppress external disturbance and noise, and the application of the BKS operator in the manipulator servo system control is feasible and effective.

Cascade Synthesis of Observers of Mixed Variables for Flexible Joint Manipulators Tracking Systems under Parametric and External Disturbances

“…Using (20) and (22), we obtain the inequalities for the choice of high gains l ij . This choice is based on the estimates of solutions of the closed-loop system (15), (17), and (18) in the linear zones on the intervals [0; t 1 ], [t 2i−2 ; t 2i−1 ], i = 2, 3, 4, and must ensure the fulfillment of inequalities ( 21) and ( 23):…”

“…It follows from inequalities ( 21)-( 23) and (27), in that the evaluation signals of mixed variables v i (t) ≈ e i+1 (t), i = 1, 2, 3 contain less error than the evaluation signals z i (t) ≈ e i (t), i = 2, 3, 4. Therefore, let us use the following estimates v 3 (t) ≈ e 4 (t), v 4 (t) ≈ e 5 (t), t ≥ T. Next, we will implement the control law (9) in a closed-loop system (1) with measurements x 1 (t), g(t) and the observer-differentiator ( 14) and (17) in the following form…”

“…However, for t > T 0 , they can be made arbitrarily small in modulo by increasing the high gains l j (37). Signals (38) with the reference actions g(t) enter the second circuit (observer ( 14)) and are used to form corrective actions (17):…”

“…The total dynamic order of a two-loop observer ( 14), (17), and ( 30), ( 34) is 5n. In a closed-loop system (1) with measurements x 3 (t), x 4 (t), g(t) and dynamic feedback, the control law (9) will be implemented in the form…”

“…In the second experiment, we assumed that only tracking error e 1 (t) measurements are available, and the parameters of the plant (40) are not exactly known. In particular, parameters a 21 , a 45 are in the range a 21 = a 21,0 + ∆a 21 , a 45 = a 45,0 + ∆a 45 , where a 21,0 = 27, a 45,0 = 29.5 are the nominal values, |∆a 21 (t)| ≤ 0.78, |∆a 45 (t)| ≤ 0.5; f 1 (t) = 0.05, f 2 (t) = 0.025t is the sawtooth function with principal period 2 s. To obtain estimates of mixed variables e 4 (t) and e 5 (t) (8) required for the control law (29), we implemented the observer of mixed variables ( 14), (17), and (18). Based on the given estimation accuracy |e 4 (t) − v 3 (t)| ≤ α 3 = 0.01 and |e 5 (t) − v 4 (t)| ≤ α 4 = 3, and using inequalities ( 24), (25), and (28), we selected the following gains:…”