Dynamic surface control for a class of nonlinear systems

Abstract

A new method is proposed for designing controllers with arbitrarily small tracking error for uncertain, mismatched nonlinear systems in the strict feedback form. This method is another "synthetic input technique," similar to backstepping and multiple surface control methods, but with an important addition, 1 low pass filters are included in the design where is the relative degree of the output to be controlled. It is shown that these low pass filters allow a design where the model is not differentiated, thus ending the complexity arising due to the "explosion of terms" that has made other methods difficult to implement in practice. The backstepping approach, while suffering from the problem of "explosion of terms" guarantees boundedness of tracking errors globally; however, the proposed approach, while being simpler to implement, can only guarantee boundedness of tracking error semiglobally, when the nonlinearities in the system are non-Lipschitz.

Adaptive Command Filtered Backstepping Trajectory Tracking Control of Hexarotor UAV

“…Position subsystem is given by (7) and (8). Let d x  and d y  be the desired speed in x and y direction, respectively.…”

“…For instance, in the inspection of the transmission lines using the hexarotor UAV, in order to facilitate the camera carried by the UAV focusing on the components of the transmission lines, the attitude angles and angular rate of the hexarotor UAV cannot change too much. Third, the problem of the control saturation is not considered [8,9]. Especially the last defect, it may lead to serious problems in the actual control systems.…”

Performance enhanced design of chaos controller for the mechanical centrifugal flywheel governor system via adaptive dynamic surface control

“…If the chaos controller is designed as (23) and (31) with tracking differentiator (9) and adaptive laws (24) and (32), by selecting the appropriate parameters such as c 1 , c 2 , c 3 , r 11 , r 12 , r 21 , r 22 a 2 , a 3 , γ 2 , γ 3 , m 2 , m 3 , then all signals of the mechanical centrifugal flywheel governor system are uniformly ultimately bounded and the tracking error remains close to zero. Furthermore, the output constraint is never transgressed in the process.…”

“…To solve this issue, by introducing a first-order filter at each recursive step of backstepping, the dynamic surface control is proposed to avoid the differentiation items on the virtual function. [22][23][24] Despite the elimination of backstepping's drawback on these paper, the precision of the first-order filters is less than satisfactory. High-order sliding mode differentiator is employed to generalize the use of the main properties of standard sliding mode and cancel the item that the relative degree is equal to one.…”

Multiple Sliding Surface Control for Systems in Nonlinear Block Controllable Form

“…In Swaroop, Hedrick, Yip, and Gerdes, (2000), the use of a low-pass filter was discussed to smooth the signal produced by Eq. (14).…”