TRAJECTORY TRACKING CONTROL OF A TWO WHEELED SELF-BALANCING ROBOT BY USING SLIDING MODE CONTROL

A two-wheeled self-balancing robot based on the inverted pendulum model which is built as a platform to look into the use of a Kalman filter for sensor fusion. As the robot is inherently unstable, it is necessary to implement a control system to keep the system in balanced. This paper examines the stability and evaluates the performance of a PID controller in the self-balancing robot. The main challenging issues are when an external force is applied and reducing vibration in order to improve the stability of the robot. It mainly focuses on the dynamic modeling and PID controller design to reduce the problem. Besides the simulation of the transfer function, poles and zeros, Kalman filter are the cause which determines the performance of the self-balancing robot.

A two-wheeled self-balancing robot that works on the principle of inverted pendulum theory is most commonly used in control systems as an exemplar for comparing various control and optimization algorithms. This nonlinear dynamic system has gained much interest among researchers and engineers and the main aim is to stabilize this system with minimum deviation about any desired axis. As this system is affected by external disturbances and measured parametric errors, the need for the implementation of controllers has become crucial. Hardware and software implementation form the basis of the system design. The proposed work aims at the implementation of a PID controller for the successful working of the two-wheeled self-balancing robot driven by stepper motors. The closed-loop controller’s parameters have been optimized by using pole placement method. Besides, the response of the system under the fuzzy controller, created using Mamdani fuzzy interface engine in Simulink, has been illustrated.

For two-wheeled self-balancing robot nonlinear model uncertainties and other characteristics, the design of fuzzy immune PD controller and a simulation study. The simulation results show that the control system than the conventional fuzzy PD controller with a small overshoot, adjust the time is short, anti-interference ability, etc., applicable to the mathematical model and the parameter change is difficult to determine two-wheeled self-balancing robot control system.

In order to maintain upright stability, two-wheel self-balancing robots belong to a type of underactuated, intrinsically unstable systems that need constant feedback control. The design, modelling, and practical implementation of a two-wheel self-balancing robot employing a proportional-derivative (PD) control approach are presented in this study. An inverted pendulum supported by two driven wheels serves as the model for the robot. An inertial measuring device made up of an accelerometer and gyroscope provides real-time orientation feedback. To fuse sensor data and reduce noise and drift, a complementary filter is used. LabVIEW is used to build the control algorithm on an NI myRIO platform, where the PD controller produces pulse-width-modulated motor commands. According to experimental data, the PD controller can achieve stable balancing with low oscillations and a quick transient response when the gain is tuned appropriately. The paper demonstrates that classical PD control provides a dependable and computationally effective solution for self-balancing robotic platforms, making it appropriate for real-time embedded control, prototype-level, and instructional applications.

There has been ongoing experiments on a two-wheeled self-balancing robot for several years, and it is almost similar to the model of an inverted pendulum on a cart. The presented paper describes the model, design, working and simulation of a two-wheeled self-balancing robot. Properties of the system under study are extremely non-linear. Moreover, there is a great deal of instability in the controller of proposed system. To improve the stability of mobile robots, this paper introduces fractional order PID (FOPID) or PI <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">λ</sup> D <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">μ</sup> controller for a non-linear and high-order system and compares it with the conventional PID. FOPID controller is designed specifically to adjust the parameters of the system more accurately according to desired specifications. The factorrs of the considered controller are optimized using both Nelder-Mead (N-M) technique and Particle Swarm Optimization (PSO) technique. The results obtained by N-M technique are compared with those of PSO technique. N-M tuned FOPID controller significantly improves the quality of controller in contrast to PSO technique. Simulation results also indicate that Nelder-Mead tuned FOPID is a better and more stable controller as compared to classical PID or PSO tuned FOPID, for a non-linear system like a two-wheeled self-balancing robot.

ABSTRACTSegway is a self-balancing motorized two-wheeled vehicle which is able to carry the human body. In the presented paper, a problem of nonholonomic constrained mechanical systems is treated. New methods in nonholonomic mechanics are applied to a problem of a two-wheeled self-balancing robots motion ‘SEGWAY’. This method of the geometrical theory of general nonholonomic constrained systems on fibred manifolds and their jet prolongations, based on so-called Chetaev-type constraint forces, was proposed and developed in the last decade by Krupková and others. The equations of motion of a two-wheeled self-balancing robot are highly nonlinear and rolling without slipping condition can only be expressed by nonholonomic constraint equations. In this paper, the geometrical theory is applied to the above mentioned mechanical problem using the above mentioned Krupková approach. Additionally, the results of numerical solutions of constrained equations of motion derived within the theory are in good agreement with results of (1) [Maddahi, A., Shamekhi, A. H., & Ghaffari, A. (2015). A Lyapunov controller for self-balancing two-wheeled vehicles. Robotica, 33(1), 225–239]. using Lyapunov's feedback control design technique. The existence, continuity, and uniqueness of the solution for the proposed control system are proved utilizing the Filippov's solution (2). And with fuzzy controller proposed by [Qian, Q., Wu, J., & Wang, Z. (2017). A novel configuration of two-wheeled self-balancing robot/Nova konfiguracija samobalansirajuceg robota na dva kotaca (Original scientific paper/Izvorni znastveni clanak). Tehnicki Vjesnik-Technical Gazette, 24(2), 459–465].

Two-wheeled self-balancing robot is a mechanically unstable, nonholonomic constraint robot. This paper has established a dynamics and kinematics for nonholonomic mobile robot. In order to control more effective for self-balancing robot's balance model, has designed fuzzy controller based on the T-S fuzzy model with the parallel distribution compensator (PDC) the structure. It realizes the robot balance and the movement control. Finally, validity and feasibility of the system modeling and the designed controller were confirmed through the actual test results and the simulation results contrast analysis.

In this study, a proposed three phase quasi Z source inverter (QZSI) using Sliding Mode Control (SMC) method is presented. The two impedance source networks have been implemented to increase the nonlinear of system. These control algorithm and proposed topology have been offered to get fast and dynamic response in robust and stable position even though input voltage, references have been changed. According to the proposed model using SMC method, the design of related inverter has been run and observed the behavior of regarding system during simulation. In power electronics systems have included nonlinear loads such as switches, MOSFETs, diodes etc. These cause to negative effects on performance of related systems. On the other hand, generally both Z source (ZS) and quasi Z source (QZS) topologies are preferred, even if buck-boost inverters are designed. SMC method is one of the most popular control types which has provided to dynamic response in robust and stable position against to nonlinear and unstable changes. During the switching process for all parts of system, control method has overcome unintended output and completed control steps based on design structure. Also, the proposed topology has been simulated at MATLAB/SIMULINK.

Sliding mode control (SMC) is a powerful and robust control method. SMC methods have been widely studied in the last three decades from theoretical concepts to industrial applications [1]-[3]. Higher-order sliding mode controllers have recently been addressed to improve the system responses [1]. However, when designing a control for a plant it is sometimes more beneficial to use combined techniques, using SMC in conjunction with other methods such as backstepping, passivity, flatness and even other traditional control design methods including H ∞ , proportional-integral-derivative (PID) and self-tuning. Note that PID control design techniques may also be used for designing the sliding surface. A drawback of the SMC methods may be unwanted chattering resulting from discontinuous control. There are many methods which can be employed to reduce chattering, for example, using a continuous approximation of the discontinuous control, and a combination of continuous and discontinuous sliding mode controllers. Chattering may also be reduced using the higher-order SMC [4] and dynamic sliding mode control [4, 5].

To improve the control performance of linear motors with external perturbations and input saturation, this paper designs an anti-saturation fixed-time integral sliding mode control strategy based on a fixed-time disturbance observer (FxITSMC-FxDO). First, the parameter uncertainties and external disturbances are viewed as composite disturbances. A fixed-time disturbance observer is designed to estimate and compensate for them in real-time, which effectively suppresses chattering by estimating the lumped disturbances. Second, by combined-time theory and integral sliding-modetrol, a fixed-time integral sliding-mode controller is designed to accelerate the convergence speed. Moreover, a non-linear anti-saturation compensator is designed based on the actuator saturation effect parameter to enable the system to exit the saturation region quickly. The fixed-time convergence property of the closed-loop system is proved based on the Lyapunov stability theorem. The experimental results show that the proposed control method effectively improves the control accuracy, response speed, and robustness of linear motors. The step response time of the direct drive permanent magnet linear motor is improved by 16.0% compared to the integral sliding mode control method and 12.5% compared to the finite-time sliding mode control method. In sine target tracking, steady-state accuracy is enhanced by 31.3% over ITSMC and 24.1% over FITSMC-FDO. Furthermore, as the sinusoidal tracking frequency increased from 0.5 to 4 Hz, the proposed control strategy maintained relatively low increases in ITAE and ISE.

This paper presents a robust adaptive sliding mode control strategy using radial basis function (RBF) neural network for a kind of value controlled asymmetric cylinder electro-hydraulic servo system of an ammunition transfer arm in the presence of uncertain nonlinearity and parameter uncertainty. On the premise of setting the expected trajectory, using RBF neural networks to approximate unknown parameters, by setting appropriate neural network parameters and adaptive terms, the change trend of position parameter was estimated. The stability of close loop system is verified by the Lyapounov theory. Compared with the simulation results of PID control method and expected trajectory, RBF Neural Net sliding mode control method has smaller system tracking error, faster response and better tracking performance.

PurposeThe purpose of this paper is to achieve high-precision sliding mode control without chattering; the control parameters are easy to adjust, and the entire controller is easy to use in engineering practice.Design/methodology/approachUsing double sliding mode surfaces, the gain of the control signal can be adjusted adaptively according to the error signal. A kind of sliding mode controller without chattering is designed and applied to the control of ultrasonic motors.FindingsThe results show that for a position signal with a tracking amplitude of 35 mm, the traditional sliding mode control method has a maximum tracking error of 0.3326 mm under the premise of small chattering; the boundary layer sliding mode control method has a maximum tracking error of 0.3927 mm without chattering, and the maximum tracking error of continuous switching adaptive sliding mode control is 0.1589 mm, and there is no chattering. Under the same control parameters, after adding a load of 0.5 kg, the maximum tracking errors of the traditional sliding mode control method, the boundary layer sliding mode control method and the continuous switching adaptive sliding mode control are 0.4292 mm, 0.5111 mm and 0.1848 mm, respectively.Originality/valueThe proposed method not only switches continuously, but also the amplitude of the switching signal is adaptive, while maintaining the robustness of the conventional sliding mode control method, which has strong engineering application value.

The two-wheeled self-balancing robot (TWSBR) based on an inverted pendulum is an attractive research topic that requires not only maneuvering but also postural balancing control. As TWSBRs have secured platforms with flexible movement and ease of operation, they have been rapidly spreading in everyday life rather than industrial sites. Meanwhile, 3D CAD design and analysis tools enable designers and engineers to realize innovative products while they reduce development time and costs. In this paper, we designed the components of TWSBR in 3D using SOLIDWORKS and assembled a 3D model of TWSBR using function blocks in Simscape. In addition, we derived a linearization model of TWSBR at the upright balancing position and designed an LQR controller for this model. Through the integrated simulation and animation environment in Matlab/Simulink using the 3D model of TWSBR, we presented that the LQR controller can effectively perform upright-balancing and maneuvering control.

One of the unavoidable issues with various real-time control systems is existence of the external disturbances and uncertainties which is usually unavailable. To deal with these disturbances and uncertainties, various robust control methods have been introduced in the literature such as Sliding Mode Control (SMC), adaptive control method and so on. This paper proposes a novel Adaptive Terminal SMC (ATSMC) method to control the hyper-chaotic 4-order system within a finite-time by utilizing only one control input. The dynamical model of the hyper-chaotic 4-order system is subjected to the mismatched external disturbances and uncertainties which are bounded, but these bounds are unavailable. The adaptive concept is employed to approximate the upper bounds of these unknown mismatched external disturbances and uncertainties within a finite-time and their estimations are used in the control input. The robust controller is designed by utilizing Lyapunov stability theory. The key features of the designed controller are robustness against all mismatched uncertainties and external disturbances, and providing stability within a finite-time. Finally, a numerical simulation is performed in Simulink/MATLAB to verify the effectiveness of the designed controller to suppress the chaotic oscillations. The numerical simulation results reveal that the finite-time stability is achieved accurately as soon as the controller is introduced.

The angular velocity of the input link of a mechanism fluctuates due to the inertia of links and the external forces, although it is generally assumed constant in design. The control of the crank angular velocity of a four-bar mechanism driven by a DC motor by moving sliding mode control is considered in this study. A time-varying slope is proposed based on the error state. The mathematical model of the motor-mechanism system is derived using Eksergian’s equation of motion. First, the state space equations are solved numerically for constant motor voltage to show the velocity fluctuations of the crank. Then both the conventional sliding mode control method and the proposed moving sliding mode control method are applied to obviate this unwanted velocity fluctuation. The method is verified by numerical simulations as well as experimental studies. The results of both the sliding mode control and the moving sliding mode control methods are compared. It is shown that a moving sliding surface in the sliding mode control increases the robustness of conventional sliding mode control by decreasing the reaching time. Also, the performance of the moving sliding mode control against parametric variations and external disturbances is experimentally investigated by adding a mass and applying an unexpected force on one of the links of the mechanism.