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Sliding mode control of vehicle hydraulic travelling system based on exponential convergent disturbance observer

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Abstract

This paper takes the motor drive travelling system of vehicles as research object. Addressing the disturbance derived from complex pavement and nonlinearity of system during walking and combined the characteristics of the mathematical model of hydraulic travelling system, a disturbance observer based on exponential convergent is designed on the conditions of the vehicle drives at low speed. It can estimate disturbances online and feedforward compensate to the control system. Then a sliding mode control strategy is used to motor speed control system. The simulation model of valve controlled motor system is carried out through MATLAB/Simulink platform. Compared of the result between the proportion integral differential (PID), sliding mode control (SMC) and sliding mode control (SMC) + disturbance observer (DOB), the oscillation and overshoot of step response on SMC are decreased obviously. When the slow time-varying torque disturbance is added on to evaluate the effects of disturbance observer induced on the SMC, the disturbance value can estimate precisely and deduce influence of motor speed. It improves the SMC + DOB control accuracy and made the vehicle travel on the complex pavement more smoothly.

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Abbreviations

\(J_{{\text{m}}}\) :

Inertia of motor and external loads (Kg•m2)

\(\omega_{{\text{m}}}\) :

Motor speed (angular velocity) (r/min)

\(B_{{\text{m}}}\) :

Damping coefficient (N•m•s/rad)

\(T_{{\text{L}}}\) :

External load torque (N•m)

\(d\) :

Disturbance which is contains of torque disturbance, un-modeled friction force and nonlinearity(N•m)

\(D_{{\text{m}}}\) :

Displacement of motor (mL/r)

\(\Delta p\) :

Pressure difference between inlet and outlet of motor (MPa)

\(F_{{\text{G}}}\) :

The gravity of the vehicle acting on the drive wheel (N)

\(\theta\) :

Road gradient (°)

\(F_{{\text{r}}}\) :

Frictional resistance (N)

\(\mu\) :

Rolling frictional resistance coefficient

\(Q_{{\text{m}}}\) :

Flow of motor (L/min)

\(C_{{\text{t}}}\) :

Leakage coefficient [m5/(N•s)]

k :

The number of control cycle

s :

Sliding mode manifold

\(\eta\) :

Switching gain of sliding mode control

V:

Lyapunov function

\(V_{{\text{t}}}\) :

The volume of one chamber (m3)

\(\beta_{{\text{e}}}\) :

Bulk modulus (GPa)

\(k_{{\text{q}}}\) :

The gain coefficient between the Qm and km

\(k_{{\text{m}}}\) :

Control signal of proportional multi-way valve

\(\tilde{d}\) :

The estimation of d

\(K\) :

The gain of observer

z :

The assistant vector

\(\tilde{d}\) :

The difference between \(\tilde{d}\) and d

\(K_{{\text{p}}}\) :

Proportional parameter

\(K_{{\text{i}}}\) :

Integration parameter

\(K_{{\text{d}}}\) :

Differential parameter

e :

Motor speed error (r/min)

u :

The control input

u 0 :

Control input value of proportional valve on the last cycle

k 0 :

Sliding mode control parameter

\(\Delta\) :

Boundary value

l :

Gain parameter

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Authors and Affiliations

  1. Beijing Institute of Space Launch Technology, Beijing, 100076, People’s Republic of China

    Liuyu He, Xinyue Wu & Li Zhou

  2. School of Automation Science and Electrical Engineering, Beihang University, Beijing, 100083, People’s Republic of China

    Yunhua Li

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  1. Liuyu He
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  2. Xinyue Wu
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  3. Li Zhou
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  4. Yunhua Li
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Correspondence to Liuyu He.

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He, L., Wu, X., Zhou, L. et al. Sliding mode control of vehicle hydraulic travelling system based on exponential convergent disturbance observer. Int J Intell Robot Appl 7, 708–719 (2023). https://doi.org/10.1007/s41315-023-00290-2

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  • DOI: https://doi.org/10.1007/s41315-023-00290-2

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