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A high-order disturbance observer based sliding mode velocity control of mobile wheeled inverted pendulum systems
Abstract
In this paper, a novel disturbance observer (DO) for the Mobile Wheeled Inverted Pendulum (MWIP) system is proposed. A choice method of optimal gain matrices is also proposed for a given robust gain, which can improve the estimation precision of the DO. Combining the proposed DO and Sliding Mode Control (SMC), a new sliding mode velocity control method is designed for the MWIP system. The convergency of the DO is proved by Lyapunov theorem. And the stability of the closed-loop system is achieved through the appropriate selection of sliding surface coefficients. The effectiveness of all proposed methods is verified by simulation results for the MWIP system.
... To overcome those challenges, various observers are designed to observe unknown parameters [4][5], and disturbances [6][7][8]. Observer design for nonlinear systems is an essential topic in control engineering, and there are many attempts to design efficient and accurate observers in the literature [9][10][11][12][13][14]. ...
... Theorem 2: Consider the kinematics, and the overall dynamics of ACV mentioned in Equation (4), and Assumptions 1 and 2 are fulfilled. Considering the proposed observer mentioned in Equation (9), and using the learning laws mentioned in Equation (11), the nonsingular terminal sliding mode controller with the sliding surface candidate mentioned in Equation (12), and the control inputs mentioned in Equation (13), asymptotically stabilize the system and all closed-loop signals are bounded. ...
... Using the control inputs mentioned in Equations (13), and some mathematical manipulations applied to Equation (18), Equation (20) leads to the following equation. ...
... The problem of feedback control and stabilization of the wheeled inverted pendulum (WIP) is a nontrivial one due to the model's nonlinearities and underactuation. 1,2 Actually, one can use only two control inputs (wheels' torques) so as to control a system of more degrees of freedom. This control problem is of interest for the area of robotics because such a type of two-wheeled vehicles can be used for the transportation of humans and loads without the space and maneuvering limitations exhibited by four-wheel vehicles. ...
... The main parameters of the model are: u r and u l are the torques of the right and left wheel, respectively, m b and m w are the masses of the body of the vehicle and of each one of its wheels, respectively, I bl which is the moment of inertia of the pendulum around the y axis, I bz which is the moment of inertia of the pendulum around the z axis, I bx which is the moment of inertia of the wheel around its axis, I wa and I wd are the moments of inertia of the wheel around its axis and diameter, respectively, l which is the distance between the center of the wheels' axis and the center of gravity of the pendulum, r which is the radius of the wheel, 2b which is the length of the wheels' axis, D b which is the viscous resistance of the driving system, and D w which is the viscous resistance of the ground. 1,2 In particular, the main parameters of the dynamic model of the WIP are defined as follows: ...
... Downloaded from https://www.cambridge.org/core. IP address: 94.66.220.250, on 16 Apr 2019 at 09:14:46, subject to the Cambridge Core terms of use, available atAfter intermediate computations, the dynamic model of the pendulum is written also in the affinein-the-input form:1,2 ⎛ ...
The article proposes a nonlinear optimal control method for the model of the wheeled inverted pendulum (WIP). This is a difficult control and robotics problem due to the system’s strong nonlinearities and due to its underactuation. First, the dynamic model of the WIP undergoes approximate linearization around a temporary operating point which is recomputed at each time step of the control method. The linearization procedure makes use of Taylor series expansion and of the computation of the associated Jacobian matrices. For the linearized model of the wheeled pendulum, an optimal ( H -infinity) feedback controller is developed. The controller’s gain is computed through the repetitive solution of an algebraic Riccati equation at each iteration of the control algorithm. The global asymptotic stability properties of the control method are proven through Lyapunov analysis. Finally, by using the H -infinity Kalman Filter as a robust state estimator, the implementation of a state estimation-based control scheme becomes also possible.
... The effectiveness of the FLC and output feedback controller was proved using the RIP system. For the mobile wheeled RIP system, a new disturbance observer was designed in Ri et al. 24 Optimal gain vectors were also calculated for a better estimate of disturbance observer. ...
... The nonlinear control law (24) drives the energy E of the pendulum toward E r and thus pushes the RIP toward its vertical reference position. The magnitude of the control signal can be large, so to operate and apply the voltage to RIP under safe limits, the following saturation limit is applied on (24). ...
Rotary Inverted Pendulum (RIP) mimics the behavior of many practical control systems like crane mechanism, segway, unicycle robot, traction control in vehicles, rocket stabilization, and launching. RIP is a fourth-order nonlinear open-loop unstable dynamical system and is widely used for testing the effectiveness of the newly developed control algorithms. In this paper, a Hybrid Control Scheme (HCS) based on energy balance and fuzzy logic controllers is proposed to implement the swing up and stabilization control of RIP. In the proposed control scheme, the fuzzy logic-based state feedback gains are dynamically tuned in real-time by minimizing the absolute error between the desired and actual states to get robust control performance. The proposed HCS is also compared with the conventional Linear Quadratic Controller (LQR) for this application. The comparative results show that the proposed fuzzy logic-based hybrid control scheme gives the optimal control performance in terms of achieving satisfactory transient, steady-state, and robust responses from a given RIP system, as compared to the conventional LQR based control scheme. The proposed control scheme is also relatively less complex with a low computational cost and provides desired response characteristics as compared to the existing ones in the literature.
... To estimate the unknown disturbance of the self-balancing mobile robot, the nonlinear disturbance observer is designed as [41], [42] ...
... Consider (28), (36) and (42). Differentiating V yieldṡ ...
In this paper, a robust tracking control scheme based on nonlinear disturbance observer is developed for the self-balancing mobile robot with external unknown disturbances. A desired velocity control law is firstly designed using the Lyapunov analysis method and the arctan function. To improve the tracking control performance, a nonlinear disturbance observer is developed to estimate the unknown disturbance of the self-balancing mobile robot. Using the output of the designed disturbance observer, the robust tracking control scheme is presented employing the sliding mode method for the selfbalancing mobile robot. Numerical simulation results further demonstrate the effectiveness of the proposed robust tracking control scheme for the self-balancing mobile robot subject to external unknown disturbances.
In this paper, an adaptive tracking control scheme is investigated for a medium scale unmanned autonomous helicopter (UAH) with unknown external disturbances and system uncertainties to achieve improvement on the flight performance. The neural networks (NNs) are employed to compensate the system uncertainties. The second-order disturbance observers are introduced to restrain the compound disturbances which are combined with the NN approximation errors and the external disturbances. Accordingly, the tracking control law is designed for the UAH. The closed-loop stability of the whole UAH system is proved by using Lyapunov function method. Simulation results show that the proposed control scheme can effectively solve the tracking control problems of UAH, and has strong robustness for the external disturbances and system uncertainties.
A terminal sliding mode controller with nonlinear disturbance observer is investigated to control mobile wheeled inverted pendulum system. In order to eliminate the main drawback of the sliding mode control, “chattering” phenomenon, and for compensation of the model uncertainties and external disturbance, we designed a nonlinear disturbance observer of the mobile wheeled inverted pendulum system. Based on the nonlinear disturbance observer, a terminal sliding mode controller is also proposed. The stability of the closed-loop mobile wheeled inverted pendulum system is proved by Lyapunov theorem. Simulation results show that the terminal sliding mode controller with nonlinear disturbance observer can eliminate the “chattering” phenomenon, improve the control precision, and suppress the effects of external disturbance and model uncertainties effectively.
In this study, a dynamic surface controller based on a nonlinear disturbance observer is investigated to control mobile wheeled inverted pendulum system. By using a coordinate transformation, the underactuated system is presented as a semi-strict feedback form which is convenient for controller design. A dynamic surface controller together with a nonlinear disturbance observer is designed to stabilize the underactuated plant. The proposed dynamic surface controller with a nonlinear disturbance observer can compensate the external disturbances and the model uncertainties to improve the system performance significantly. The stability of the closed-loop mobile wheeled inverted pendulum system is proved by Lyapunov theorem. Simulation results show that the dynamic surface controller with a nonlinear disturbance observer can suppress the effects of external disturbances and model uncertainties effectively.
Traffic problems such as pollution and congestion are becoming more and more serious in urban areas. A potential solution to these problems is to develop narrow vehicles that occupy less space and have lower emissions. There has been increasing interest in underactuated mechanical systems, i.e., mobile wheeled inverted pendulum (MWIP) models, which are widely used in the field of autonomous robotics and intelligent narrow vehicles. A novel narrow vehicle based on an MWIP and a movable seat, called UW-Car, is investigated in this paper. The dynamic model of the underactuated vehicle system running on flat ground is derived by Lagrange's equation of motion. Based on the dynamic model and terminal sliding mode control method, two terminal sliding mode controllers are designed to control velocity and braking of the UW-Car. The first one is used to control the forward speed to a desired value while keeping the body upright and the seat on some fixed position. The second one is a switching sliding mode controller, composed of three terminal sliding mode controllers that quickly brakes the system according to an optimal braking scheme. All the control algorithms are tested in both Matlab simulation and a UW-Car experiment. The simulation and experimental results demonstrate the efficiency of the model and controllers.
In this paper, a phenomenological model of pneumatic muscle is established consisting of a contractile element, spring element, and damping element in parallel. To verify the practicability of pneumatic muscle (PM) modeling, dynamic surface control (DSC) characterized by convenient design and good transient performance is employed for realizing PM tracking control. However, parametric uncertainty is inevitable in PM modeling as friction and unknown external disturbances exist in a PM system. These PM modeling errors and unknown variables can undermine and deteriorate the control performance of PM systems. To solve this problem and improve control accuracy, a novel nonlinear disturbance observer-based dynamic surface control (NDOBDSC) is proposed for trajectory tracking of PM system. Through employing the nonlinear disturbance observer, the stated uncertainties can be estimated online and compensated. The proposed novel control scheme therefore integrates the advantages of DSC, while estimating time-varying uncertainties to achieve compensation of inherent uncertainties. The established control law guarantees that the closed-loop system is semiglobally uniformly and ultimately bounded. Both the simulation studies and practical experiments demonstrate the effectiveness of NDOBDSC, showing that the control performance of NDOBDSC is satisfactory in the presence of modeling errors, friction, changing load, and other uncertainties in the PM system.
This paper presents a novel implementation of an integral sliding-mode controller (ISMC) on a two-wheeled mobile robot (2 WMR). The 2 WMR consists of two wheels in parallel and an inverse pendulum, which is inherently unstable. It is the first time that the sliding-mode control method is employed for real-time control of a 2 WMR platform and several critical issues are addressed. First, the 2 WMR is underactuated, which uses only one actuator to achieve position control of the wheels while balancing the pendulum around the upright position. ISMC is suitable for control of the underactuated 2 WMR, because ISMC has an extra degree of freedom in control when sliding mode is achieved. In this paper, we utilize this extra degree of freedom to implement a linear nominal controller, which is found adequate in stabilizing the sliding manifold in a range around the equilibrium. Second, the 2 WMR system is in presence of both matched and unmatched uncertainties. The implemented ISMC, with an integral sliding surface and a switching term, is able to completely nullify the influence from the matched uncertainties. The implemented linear nominal controller stabilizes the sliding manifold that is subject to unmatched uncertainties. Third, references design are addressed when implementing ISMC on the 2 WMR. The effectiveness of ISMC is verified through intensive simulation and experiment results.
[The 2010 IEEE International Forum on Strategic Technology (IFOST 2010), pp.76-81]. This paper presents a method to design and control a two-wheeled self-balancing robot and it focus on hardware description, signal processing, discrete Kalman filter algorithm, system modelling and PID backstepping controller design. In the system, signals from angle sensors are filtered by a discrete Kalman filter before being fed to the PID backstepping controller. The objectives of the proposed controller are to stabilize the robot while try to keep the motion of robot to track a reference signal. The proposed PID backstepping controller has three control loops, in which the first loop uses a backstepping controller to maintain the robot at equilibrium, the second loop uses a PD controller to control the position of robot and the last uses a PI controller to control the motion direction. Simulations and experimental results show that the proposed control system has good performances in terms of quick response, good balance, stability.
Purpose - The purpose of this paper is to introduce a high load capacity coaxial couple wheeled robot (CCWR) and investigate a simple structure but effective fuzzy equilibrium controller based on (Takagi-Sugeno) T-S for balance control in wide-angle range. Design/methodology/approach - By selecting the robot inclination angle and angular rate as input variables and the DC motors' rotation speed as output variables, a T-S fuzzy controller (FC) is established. Findings - Simplified robot dynamic equilibrium equations are feasible; the robot balance in wide-angle range could be controlled by the T-S FC. Despite the existence of small vibrations near the equilibrium position, the system can return to equilibrium within 3?s, showing strong robustness. Practical implications - The robot can achieve self-balance and pivot around, moreover, it provides a new way for balance control of CCWR in wide-angle range. And at the same time, the robot can achieve its work in semi-autonomous and tele-operated mode. Originality/value - The paper shows that designing the controller based on static analysis is feasible; simple structure T-S fuzzy control way is introduced to balance control for CCWR in a wide angle scale; the development target is to provide a kind of robot platform for testing control algorithms or a personal transporter, and the project is supported by the High Technology Research and Development Program of China.
There has been increasing interest in a type of underactuated mechanical systems, mobile-wheeled inverted-pendulum (MWIP) models, which are widely used in the field of autonomous robotics and intelligent vehicles. Robust-velocity-tracking problem of the MWIP systems is investigated in this study. In the velocity-control problem, model uncertainties accompany uncertain equilibriums, which make the controller design become more difficult. Two sliding-mode-control (SMC) methods are proposed for the systems, both of which are capable of handling both parameter uncertainties and external disturbances. The asymptotical stabilities of the corresponding closed-loop systems are achieved through the selection of sliding-surface parameters, which are based on some rules. There is still a steady tracking error when the first SMC controller is used. By assuming a novel sliding surface, the second SMC controller is designed to solve this problem. The effectiveness of the proposed methods is finally confirmed by the numerical simulations.
In this paper, the dynamic model of a wheeled inverted pendulum (e.g., Segway, Quasimoro, and Joe) is analyzed from a controllability and feedback linearizability point of view. First, a dynamic model of this underactuated system is derived with respect to the wheel motor torques as inputs while taking the nonholonomic no-slip constraints into considerations. This model is compared with the previous models derived for similar systems. The strong accessibility condition is checked and the maximum relative degree of the system is found. Based on this result, a partial feedback linearization of the system is obtained and the internal dynamics equations are isolated. The resulting equations are then used to design two novel controllers. The first one is a two-level velocity controller for tracking vehicle orientation and heading speed set-points, while controlling the vehicle pitch (pendulum angle from the vertical) within a specified range. The second controller is also a two-level controller which stabilizes the vehicle's position to the desired point, while again keeping the pitch bounded between specified limits. Simulation results are provided to show the efficacy of the controllers using realistic data.
This work presents a general framework for nonlinear systems subject to disturbances using disturbance observer based control (DOBC) techniques. A two-stage design procedure to improve disturbance attenuation ability of current linear/nonlinear controllers is proposed where the disturbance observer design is separated from the controller design. To facilitate this concept, a nonlinear disturbance observer is developed for disturbances generated by an exogenous system, and global exponential stability is established under certain condition. Furthermore, semiglobal stability condition of the composite controller consisting of a nonlinear controller and the nonlinear disturbance observer is established. The developed method is illustrated by the application to control of a two-link robotic manipulator.
Robotic manipulators are highly nonlinear and coupled systems that are subject to different types of disturbances such as joint frictions, unknown payloads, varying contact points, and unmodeled dynamics. These disturbances, when unaccounted for, adversely affect the performance of the manipulator. Employing a disturbance observer is a common method to reject such disturbances. In addition to disturbance rejection, disturbance observers can be used in force control applications. Recently, research has been done regarding the design of nonlinear disturbance observers (NLDOs) for robotic manipulators. In spite of good results in terms of disturbance tracking, the previously designed nonlinear disturbance observers can merely be used for planar serial manipulators with revolute joints [Chen, W. H., Ballance, D. J., Gawthorp, P. J., O'Reilly, J. (2000). A nonlinear disturbance observer for robotic manipulators. IEEE Transactions on Industrial Electronics, 47 (August (4)), 932–938; Nikoobin, A., Haghighi, R. (2009). Lyapunov-based nonlinear disturbance observer for serial n-link manipulators. Journal of Intelligent & Robotic Systems, 55 (July (2–3)), 135–153]. In this paper, a general systematic approach is proposed to solve the disturbance observer design problem for robotic manipulators without restrictions on the number of degrees-of-freedom (DOFs), the types of joints, or the manipulator configuration. Moreover, this design method does not need the exact dynamic model of the serial robotic manipulator. This method also unifies the previously proposed linear and nonlinear disturbance observers in a general framework. Simulations are presented for a 4-DOF SCARA manipulator to show the effectiveness of the proposed disturbance observer design method. Experimental results using a PHANToM Omni haptic device further illustrate the effectiveness of the design method.