Adaptive Robust Control for Servo Mechanisms With Partially Unknown States via Dynamic Surface Control Approach

Abstract

In order to achieve high performance control for servo mechanisms with electrical dynamics and unmeasurable states, an observer-based adaptive robust controller (ARC) is developed via dynamic surface control (DSC) technique. To represent electrical dynamics, a third-order model is used to describe the servo mechanism. However, the third-order model brings some difficulties to observer construction and recursive controller design. To solve this problem, we first transform the model into a particular form suitable for observer design, and then construct a parameterized observer to estimate the unmeasurable states. The state estimation is based on the output and its derivatives, which can be acquired by an output differential observer. Subsequently, an observer-based ARC can be developed through DSC technique, with which the problem of "explosion of complexity" caused by backstepping method in the traditional ARC design can be overcome. A stability analysis is given, showing that our control law can guarantee uniformly ultimate boundedness of the solution of the closed-loop system, and make the tracking error arbitrarily small. This scheme is implemented on a precision two-axis turntable. Experimental results are presented to illustrate the effectiveness and the achievable control performance of the proposed scheme.Index Terms-Adaptive robust control (ARC), dynamic surface control (DSC), servo mechanism, state observer, two-axis turntable.

Adaptive Robust Control of Servo Mechanisms With Compensation for Nonlinearly Parameterized Dynamic Friction

“…Then, from (8), it follows that (27) The (25) and (26) imply that, for any , we have . Hence, to make converge to zero, we only need to let .…”

“…The robust control function should be selected to satisfy (18) ( 19) where and is a design parameter. The parameter is updated by (20) where represents the projection operation whose de nition can be seen in [27], the positive de nite matrix represents the adaptation rate, the adaptation function is synthesized as . Since (as is indicated in Assumption 1) and the projection operator is used in the adaptation law to guarantee , we know that there must be certain robust control function satisfying (18) and (19).…”

“…According to our previous work [27], a two-axis turntable servo system (see Fig. 1) is set up as a test-bed.…”

“…From our previous work [27], we know kgm , N/A, Nm. To determine the friction parameters, of ine parameter identication is carried out following the same procedure as in [10].…”

Adaptive Backstepping Control of Dual-Motor Driving Servo Systems with Friction

“…Many kinds of friction models have been proposed to solve the difficulties in modeling and compensation [1] [2], such as Karnopp model, Leuven model, Armstrong model, and Lugre model, proposed by Canudas [3] in 1995, which can describe major features of dynamic friction, taking into account viscous friction, Coulomb friction, static friction and Stribeck effect. The LuGre model is closer to the real friction phenomenon, hence it is widely used [4][5][6][7][8].Based on the LuGre model, many compensation methods were adopted to design the controller.…”