2-sliding mode control for nonlinear plants with parametric and dynamic uncertainties

Abstract

A problem of sliding mode control design for a SISO nonlinear system with unmodeled actuator of the 2 nd order is considered. A design methodology based on nonlinear dynamic sliding manifold (NDSM) is proposed to attenuate the chattering phenomenon affecting sliding-mode-controlled plants in presence of unmodeled dynamics. The controller utilizes the pass filter characteristics of the physical-actuating device to provide a smoothing effect on the discontinuous control signal. The methodology proposed allows for maintaining the sliding mode on the surface designed without actuator dynamics being taken into account. This goal is achieved via auxiliary dynamic sliding manifold design, the 2-sliding mode on the auxiliary NDSM provides for finite-time-convergence of the sliding surface quantity to zero. The proposed controller design is based on the relative degrees of the plant and the unmodeled actuator dynamics and the ranges of the uncertainties of the plant and actuator.

Finite-Time Stability and High Relative Degrees in Sliding-Mode Control

“…Any r-sliding homogeneous controller can be complemented by an (r − 1)th order differentiator [2,7,27,29,57] producing an output-feedback controller. In order to preserve the demonstrated exactness, finite-time stability and the corresponding asymptotic properties, the natural way is to calculateσ ,... ,σ (r−1) in real time by means of a robust finite-time convergent exact homogeneous differentiator [31,32].…”

Effect of sliding mode observers in the homing guidance loop

“…where the missile acceleration a M is assumed known, while the uncertain target acceleration a T is replaced by SMC control u [5] u ¼ r sign( J)…”

Missile Interceptor Guidance and Control Using Second Order Sliding Modes

“…It can be done using the first order exact differentiator (see Levant 1998Levant , 2003, or the first order robust-to noise differentiator based on nonlinear dynamic sliding manifold (NDSM) (see Krupp, Shkolnikov, & Shtessel, 2000), where NDSM is developed to incorporate a low-pass nonlinear filter in the observer structure producing a robust to noise differentiator. A robust differentiator of a given signal, ) (t x , polluted with noise, has the form …”

“…In order to avoid differentiation of q e control (31) can be also designed based on NDSM (see Krupp, Shkolnikov, & Shtessel, 2000) as follows: . Thus, using only output feedback q e , the control voltage (32) to the actuator (20) provides for the output q e convergence to zero in a finite time.…”

“…A smooth asymptotic second order sliding mode control algorithm (SOSM) (see Shtessel, Shkolnikov, and Brown, 2003) is reassessed and is proved to be SOSM control. Next, the guidance algorithm based on a smooth SOSM control and SOSM controller/autopilot based on nonlinear dynamic sliding manifold (see Krupp, Shkolnikov, & Shtessel, 2000) are used for designing an integrated guidance-flight-control system. The main idea developed in this work is to enforce the suitable closed-loop missile-target engagement kinematics using the input voltage signal to the actuator as control.…”