Abstract
In this paper, a time-delayed fractional order adaptive sliding mode control algorithm is proposed for a two-wheel self-balancing vehicle system. The closed-loop system is proved based on the Lyapunov-Razumikhin function. The switching function is designed to make the system robust when facing uncertainties and external disturbances. It is designed to avoid monotonically increasing gains and can handle state-dependent uncertainties without a prior bound. The two-wheel self-balancing vehicle used in the experiment consists of a gyroscope MPU-6050 and accelerometer, a motor driving circuit composed of a motor driving chip TB6612FNG, and STM32F103x8B that is selected as the control core. The experimental results show that the time-delayed fractional order adaptive sliding mode control algorithm can make the vehicle achieve autonomous balance and quickly restore its stable state while appropriate disturbance is introduced.
Highlights
E developed criterion gave a solvable solution to obtain the observer gains using convex optimization algorithm
Liu proposed an ESO-based cascade controller for regulating the oxygen excess ratio of the PEMFC air-feed system to its desired value, using the sliding mode technique [4]. e control objective was to avoid oxygen starvation during sudden load changes. e designed cascade controller consists of oxygen excess ratio tracking outer loop and compressor flow rate regulation inner loop. e ESO was used to reconstruct the oxygen excess ratio. e outer control loop using the estimated oxygen excess ratio provided the compressor flow rate reference for the inner loop based on the STA
[8] Within these subsystems, the inclined angle of the vehicle was treated as zero dynamics, the longitudinal acceleration was used as control input, and the sliding mode control technology was used to stabilize the zero dynamic subsystem
Summary
Fractional calculus is the operation of derivatives and integrals extended to the fractional order. Fractional differintegral is one of its most common definitions. For a function x that is defined in [t0, t], the RL fractional integrator is defined as follows [22]: t0. Γ(x) is the gamma function that is defined as follows:. En, the following sliding mode surface function can be constructed: s(t) x_ (t) + cDαx(t),. Taking the derivative of formula (23) yields s_(t) x€(t) + cDα+1x(t). E TDC approximates the system uncertainty by using control input and state information of the immediate past time instant. En, (18) can be written as follows: ξ(t − h) x€(t − h) − τ(t − h).
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