Abstract
In this paper, two controllers with a compound disturbance observer are proposed for a two-wheeled inverted robot (TWIR) with model uncertainty and unknown input disturbance. First, an equivalent linear model of the TWIR with uncertainty and input disturbance is proposed using the Taylor series expansion for the nonlinear model of the TWIR at an equilibrium point, in which the nonlinear part of the Taylor series and the model uncertainty are combined with unknown input disturbance as compound input disturbance. Then, the compound input disturbance is estimated by using the Newton method and reference model. As the estimated compound disturbance is used to compensate for the compound disturbance, the equivalent linear system becomes closely definite without compound input disturbance. Finally, two controllers are proposed using the equivalent linear system. Stability analysis of the proposed control methods is also given. To illustrate the proposed methods, some simulations for the TWIR are performed and compared with the existing methods. The main contribution of this work includes the following: (i) simple controllers based on compound input disturbance observer for trajectory tracking and balancing of TWIRs with unknown input disturbance and model uncertainty are proposed; (ii) the stability of proposed closed-loop control systems is proved; (iii) our proposed methods are simulated and compared with the existing methods.
Highlights
two-wheeled inverted robot (TWIR) were widely studied in the literature and applied as vehicles in practice [1, 2]. eir nature is an unstable, underactuated, and nonlinear system, so it is very difficult to control them. ere have been many controllers designed for TWIRs such as backstepping [3, 4], sliding mode control [5,6,7], nonlinear control [8,9,10,11], PID control [12, 13], PD controller with iterative learning [14], fractional PID [15], fuzzy control [16, 17], model predictive control [18], and nonlinear disturbance observer-based control [19]
In [5], sliding mode controllers were applied to dealt with model uncertainty, and experimental data based friction compensation models were built for a TWIR, so this is an disadvantage in design
A combination of two PD controllers and a time-delayed controller for fast movement of TWMR was proposed in [12], where the first PD controller was designed for the pitch angle, the other PD controller was applied for the orientation, and the time-delayed controller was synthesised for the position
Summary
TWIRs were widely studied in the literature and applied as vehicles in practice [1, 2]. eir nature is an unstable, underactuated, and nonlinear system, so it is very difficult to control them. ere have been many controllers designed for TWIRs such as backstepping [3, 4], sliding mode control [5,6,7], nonlinear control [8,9,10,11], PID control [12, 13], PD controller with iterative learning [14], fractional PID [15], fuzzy control [16, 17], model predictive control [18], and nonlinear disturbance observer-based control [19]. In [6], adaptive sliding mode control in combination with direct fuzzy control was applied for balancing and trajectory tracking of the TWIR; no disturbance was considered. Four interval type 2 fuzzy logic inference system-based controllers [17] were designed using the Takagi–Sugeno model for the TWIR with uncertainty and disturbance, but the controller is dependent on solving linear matrix inequalities. Our main contributions are to (a) convert the nonlinear model of TWIRs into an equivalent linear model, in which the uncertainty of nonlinear model and the unknown input disturbance are lumped as compound input disturbance, (b) prove the stability of the proposed TWIR control system, and (c) compare the proposed method with other existing methods through numerical simulations.
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