Cascade Synthesis of Electromechanical Tracking Systems with Respect to Restrictions on State Variables

Kochetkov, Sergey A.; Krasnova, Svetlana A.; Antipov, Aleksey S.

doi:10.1016/j.ifacol.2017.08.1760

Cited by 4 publications

(5 citation statements)

References 10 publications

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“….. χ 1 (t). To satisfy given constraints (18) in the design of corrective actions w we will also, as in [16,17,20,21,38], use non-linear odd sigma-functions σ(x) = −th(−x/2), σ(−x) = −σ(x) in the local feedback. In order to set up the required features, we have introduced two scaling parameters k, m = const > 0 into the sigma function, namely…”

Section: Tracking Differentiator Designmentioning

confidence: 99%

“…Let us redefine system (17) concerning tracking errors e 1 = x 1 − χ 1 and residuals (20). Under (21), we obtain a closed-loop system .…”

Section: Tracking Differentiator Designmentioning

confidence: 99%

“…According to the block principle of control [20,21], we have to ensure that the state variables of the system (22) converge successively from bottom to top in the following neighborhoods of zero:…”

Section: Tracking Differentiator Designmentioning

confidence: 99%

“…This automatically implements the disturbance compensation and residual stabilization mechanisms (25). As can be seen from Equation (20), the variables of the tracking differentiator x 2 , x 3 "track" smooth and bounded sigmoid functions during the stabilization of the residuals e 2 , e 3 , thus ensuring (8). The fulfillment of Equation ( 27) ensures the specified constraints (5), (18).…”

Section: Tracking Differentiator Designmentioning

confidence: 99%

“…We have developed a method that additionally ensures that controlled signals are restricted within specified ranges for tracking non-smooth signals. The main features of the designed algorithms are: (i) the use of S-shaped smooth and bounded sigmoid corrective actions [20,21]; (ii) the procedure of setting its gains considering the velocity and acceleration limitations of a particular UAV. In this way, the generator variables generate a naturally smooth trajectory and provide component-by-component information about its first and second derivatives.…”

Section: Introductionmentioning

confidence: 99%

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Dynamic Models with Sigmoid Corrections to Generation of an Achievable 4D-Trajectory for a UAV and Estimating Wind Disturbances

2023

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For an unmanned aerial vehicle (UAV) of an aircraft type, the problems of planning achievable trajectories as well as robust control under wind disturbances are considered. A computationally simple method for compiling a primary non-smooth 4D trajectory is proposed. Its segments connect the given waypoints and determine the desired average velocity in various sections. Instead of time-consuming methods of analytical smoothing of broken path joints using polynomials, a tracking differentiator with S-shaped smooth and limited sigmoid corrective actions is developed. This virtual dynamic model provides natural smoothing of the primary trajectory considering the design constraints on the velocity, acceleration, and thrust of the UAV. The tracking differentiator variables create an achievable trajectory and are used to synthesize the UAV tracking system. To compensate for the action of wind disturbances on the UAV, a disturbance observer is developed. It is a replica of the equations of the control plant model, which are directly affected by external uncontrolled disturbances. These algorithms also use sigmoid corrections. Unlike standard disturbances observers, this approach does not require the development of a dynamic model of external disturbances and does not assume their smoothness. The effectiveness of the developed algorithms was confirmed by numerical simulation.

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