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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 severa...
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Context 1
... q 1 , q 2 , q 3 , q 4 = 50 , 0 . 1 , 500 , 1 , R = 1 , we obtain the feedback gains as k = [ − 7 . 0711 , − 9 . 6708 , − 27 . 0228 , − 2 . 8418] T . The initial states of the 2 WMR are as x = [0 , 0 , 0 . 1 , 0] T . The simulation results are shown in Fig. 3. The wheel reaches the desired setpoint smoothly with a small overshoot, the pendulum angular stays around zero. Next, the linear controller is applied to the 2 WMR system in presence of the frictions, τ f = 0 . 2 θ ̇ + 0 . 3sgn( θ ̇ ) and f r = 0 . 5 x ̇ + sgn( x ̇ ) . The simulation results are shown in Fig. 4. It is found that the pendulum and the wheel keep vibrating around the desired positions, which are not satisfactory responses and indicates the limited robustness of the linear controller. We consider the joint friction exists in the system and τ f = 0 . 2 θ ̇ + 0 . 3sgn( θ ̇ ) , which is a matched uncertainty. ISMC is applied with s = [0 , 0 , 0 , 1] , ρ = 0 . 1 + 0 . 2 | x 4 | + 0 . 3 , and the nominal linear controller κ uses the same feedback gains as in the pervious subsection. We set θ r = 0 and γ c = 0 since f r = 0 and φ = 0 . The simulation results are shown in Fig. 5. The 2 WMR reaches the desired setpoint smoothly and the pendulum is balanced at θ e = 0 . The 2 WMR responses are almost the same as in Fig. 4 despite the system is in presence of the joint friction τ f , which demonstrates the effectiveness of ISMC in rejecting matched uncertainties. It is noted that control signal shows switching behavior, which can be explained as the following. In the ideal sliding mode, we have σ = 0 . To make the system states stay on the switching surface, an infinite switching frequency is needed, which is impossible to achieve in any digital implementation. Due to the finite sampling frequency in implementations, the “chattering” phenomenon occurs. Remark 3: In this paper, the DC motor is controlled by a discontinuous pulse width modulation (PWM) signal. The characteristic of the PWM control is its switching (on–off) op- eration mode, which is achieved by electronic power switchers. Therefore, the implementation of the switching type control signal is not a problem. Furthermore, it may even be more advantageous to employ the ISMC than other continuous controllers because the ISMC naturally generates a discontinues control signal while other continuous controllers are designed to generate continuous signals which however are forced to become discontinuous in real implementation [31], [32]. Two type of unmatched uncertainties exist in the system, one is due to the external disturbance and the other is due to the uncertain system parameters. First, we consider the 2 WMR system with the ground friction f r = 0 . 5 x ̇ + sgn( x ̇ ) and the joint friction τ f = 0 . 2 θ ̇ + 0 . 3sgn( θ ̇ ) . ISMC is applied with ρ = 0 . 1 + 0 . 2 | x 4 | + 0 . 3 + br/ ( b + ar )(0 . 5 | x 2 | + 1) and the nominal controller in (33). Other control parameters are chosen the same as in the preceding simulation. The simulation results are shown in Fig. 6. The 2 WMR reaches the desired setpoint at t = 20 s and the pendulum is finally balanced at the upright position, i.e., θ = 0 , which indicates that the proposed ISMC is also robust to unmatched unknown friction. At the time interval 3 ∼ 15 s, the 2 WMR reaches a steady state that the 2 WMR travels with the constant speed 0.1 m/s, the pendulum is balanced at θ = 0 . 041 rad and the tracking error of the wheel position exists. The results are consistent with the analysis in Section II-D. When f r = 0 , the equilibrium of the pendulum is not the upright position, but related with the size of the ground friction. Since the ground friction is unknown to the designer, θ r = 0 is used in the controller design, which yields e 3 = θ − θ r = 0 and e 1 = 0 . Although the ground friction brings a tracking error of the wheel position during the traveling, the system performance is still satisfactory. When the 2 WMR stops at the desired setpoint at t = 20 s, the ground friction disappears, so does the tracking error of the wheel position. Next, the 2 WMR system with parameter uncertainties is considered. The actual values of the uncertain parameters are as [ m p , l, φ ] = [2 . 0 kg , 0 . 18 m , π/ 15 rad ] , which are assumed to be unknown to the designer. Estimated values of the uncertain parameters, [ m ˆ p , ˆ l, φ ˆ ] = [1 . 6 kg , 0 . 13 m , 0 rad ] , are used in sliding surface and controller designs. The frictions are also considered to exist in the system. ISMC is applied with θ r = 0 and the nominal controller is designed as in (33). First, γ c = 0 is applied. ISMC shows the robustness to the parameter uncertainties. The pendulum balances at a new equilibrium position θ = 0 . 26 rad. However, the tracking performance of the 2 WMR is not satisfactory. The tracking error of the wheel position in steady state is e 1 ,s | γ c =0 = − 0 . 9259 m. Next, γ c = − 6 . 5471 is computed according to (35) and used in (33). The simulation results for the two cases, with and without the compensation term γ c , are shown in Fig. 7. By adding the compensation term to the control input, the 2 WMR tracks the planned trajectory better and reaches the desired setpoint without steady-state error. The simulation results are consistent with the theoretical analysis in Sections II-D and III-D. V. I MPLEMENTATION AND E XPERIMENT R ESULTS In simulations, an ideal model of the 2 WMR is used. To stabilize the 2 WMR system in absence of uncertainties, the feedback gains for the nominal linear controller can be chosen in a wide range as long as A 0 − g 0 k T is Hurwitz. However, considering the existence of mismatch between the real-time system model and the mathematical model (1) and (2), the feedback gains obtained from simulations may not function well on the real-time platform, thus need to be adjusted through experimental testings on the 2 WMR prototype. For implementation, first, we consider a simple regulation task that is to balance the robot at the original position on a flat surface, i.e., x r = 0 , v r = 0 , and φ = 0 . Since there exists backlash in the driving mechanism of the 2 WMR [10], strong vibrations are observed by applying the linear controller with the feedback gains obtained from simulations. To reduce the vibrations, the feedback gains are adjusted to k = [ − 10 , − 0 . 5 , − 35 , − 3] T . ISMC is applied with the projection vector as s = [0 , 0 , 0 , 0 . 05] and the feedback gains for the nominal linear controller as k = [ − 10 , − 0 . 5 , − 35 , − 3] T . For comparison, the linear controller alone is also applied to the 2 WMR. Fig. 8 shows the experimental results for the 2 WMR under the ISMC and the linear controller. When the linear controller is applied, the 2 WMR is stabilized at the first few seconds, however, becomes unstable in 10 seconds. By applying the ISMC, the 2 WMR is consistently stabilized. The wheels stay around the original place and the pendulum is balanced around θ = 0 , which verifies the effectiveness of the ISMC in handling system uncertainties. A testing is conducted to check the robustness of the ISMC with respect to an exceptional disturbance. The experiment results are shown in Fig. 9. At t = 18 s, we push the 2 WMR to the right about 0.15 m. The 2 WMR is finally stabilized around the original position and the transit responses show small oscillations. For comparison, several other existing methods, including the fuzzy traveling and position controller (FTPC) proposed in [7], and the sliding-mode controller proposed in [19], [20], are used to control the 2 WMRs. The experimental results for the 2 WMR system under the FTPC [7] and SMC [19], [20] can be found in [10] (Figs. 11 and 12). By comparing the results, it is evident that the ISMC proposed in this work provides a better performance than the existing methods [7], [19], [20] when controlling the 2 WMR. Next, the robot is placed on an inclined surface and the slope angle φ is unknown. ISMC is applied with θ r = 0 and the nominal linear controller is designed as in (33). For the first trial, we set γ c = 0 . The pendulum is balanced around θ e = 0 . 1 rad, however, steady-state error of the wheel position exists, and e 1 ,s | γ c =0 = − 0 . 35 m. For the second trial, we use γ c = − 3 . 5 , which is computed according to (35). Experiment results for the two cases, with and without the compensation term, are shown in Fig. 10. The steady-state error for the wheel position is eliminated under ISMC with the compensation term, which is consistent with the theoretical analysis and simulation results. First, we consider the mobile robot travels on a flat surface, i.e., φ = 0 . The planned trajectory for the wheeled mobile robot is the same as we used for simulation. ISMC is applied with θ r = 0 , γ c = 0 . All other controller parameters are chosen the same as for the regulation task. Experiment results are shown in Fig. 11. The 2 WMR reached the desired setpoint and stays there afterward. ISMC shows the effectiveness for setpoint control of the 2 WMR system. However, it is observed that the trajectory of the wheels x 1 is not smooth enough. When the real position of the 2 WMR x 1 surpasses the given reference x r , the 2 WMR would stop for a while or travel backwards, which are not the desired motions. Considering our objective for the 2 WMR is traveling forward to arrive the desired position, ...
Context 2
... q 1 , q 2 , q 3 , q 4 = 50 , 0 . 1 , 500 , 1 , R = 1 , we obtain the feedback gains as k = [ − 7 . 0711 , − 9 . 6708 , − 27 . 0228 , − 2 . 8418] T . The initial states of the 2 WMR are as x = [0 , 0 , 0 . 1 , 0] T . The simulation results are shown in Fig. 3. The wheel reaches the desired setpoint smoothly with a small overshoot, the pendulum angular stays around zero. Next, the linear controller is applied to the 2 WMR system in presence of the frictions, τ f = 0 . 2 θ ̇ + 0 . 3sgn( θ ̇ ) and f r = 0 . 5 x ̇ + sgn( x ̇ ) . The simulation results are shown in Fig. 4. It is found that the pendulum and the wheel keep vibrating around the desired positions, which are not satisfactory responses and indicates the limited robustness of the linear controller. We consider the joint friction exists in the system and τ f = 0 . 2 θ ̇ + 0 . 3sgn( θ ̇ ) , which is a matched uncertainty. ISMC is applied with s = [0 , 0 , 0 , 1] , ρ = 0 . 1 + 0 . 2 | x 4 | + 0 . 3 , and the nominal linear controller κ uses the same feedback gains as in the pervious subsection. We set θ r = 0 and γ c = 0 since f r = 0 and φ = 0 . The simulation results are shown in Fig. 5. The 2 WMR reaches the desired setpoint smoothly and the pendulum is balanced at θ e = 0 . The 2 WMR responses are almost the same as in Fig. 4 despite the system is in presence of the joint friction τ f , which demonstrates the effectiveness of ISMC in rejecting matched uncertainties. It is noted that control signal shows switching behavior, which can be explained as the following. In the ideal sliding mode, we have σ = 0 . To make the system states stay on the switching surface, an infinite switching frequency is needed, which is impossible to achieve in any digital implementation. Due to the finite sampling frequency in implementations, the “chattering” phenomenon occurs. Remark 3: In this paper, the DC motor is controlled by a discontinuous pulse width modulation (PWM) signal. The characteristic of the PWM control is its switching (on–off) op- eration mode, which is achieved by electronic power switchers. Therefore, the implementation of the switching type control signal is not a problem. Furthermore, it may even be more advantageous to employ the ISMC than other continuous controllers because the ISMC naturally generates a discontinues control signal while other continuous controllers are designed to generate continuous signals which however are forced to become discontinuous in real implementation [31], [32]. Two type of unmatched uncertainties exist in the system, one is due to the external disturbance and the other is due to the uncertain system parameters. First, we consider the 2 WMR system with the ground friction f r = 0 . 5 x ̇ + sgn( x ̇ ) and the joint friction τ f = 0 . 2 θ ̇ + 0 . 3sgn( θ ̇ ) . ISMC is applied with ρ = 0 . 1 + 0 . 2 | x 4 | + 0 . 3 + br/ ( b + ar )(0 . 5 | x 2 | + 1) and the nominal controller in (33). Other control parameters are chosen the same as in the preceding simulation. The simulation results are shown in Fig. 6. The 2 WMR reaches the desired setpoint at t = 20 s and the pendulum is finally balanced at the upright position, i.e., θ = 0 , which indicates that the proposed ISMC is also robust to unmatched unknown friction. At the time interval 3 ∼ 15 s, the 2 WMR reaches a steady state that the 2 WMR travels with the constant speed 0.1 m/s, the pendulum is balanced at θ = 0 . 041 rad and the tracking error of the wheel position exists. The results are consistent with the analysis in Section II-D. When f r = 0 , the equilibrium of the pendulum is not the upright position, but related with the size of the ground friction. Since the ground friction is unknown to the designer, θ r = 0 is used in the controller design, which yields e 3 = θ − θ r = 0 and e 1 = 0 . Although the ground friction brings a tracking error of the wheel position during the traveling, the system performance is still satisfactory. When the 2 WMR stops at the desired setpoint at t = 20 s, the ground friction disappears, so does the tracking error of the wheel position. Next, the 2 WMR system with parameter uncertainties is considered. The actual values of the uncertain parameters are as [ m p , l, φ ] = [2 . 0 kg , 0 . 18 m , π/ 15 rad ] , which are assumed to be unknown to the designer. Estimated values of the uncertain parameters, [ m ˆ p , ˆ l, φ ˆ ] = [1 . 6 kg , 0 . 13 m , 0 rad ] , are used in sliding surface and controller designs. The frictions are also considered to exist in the system. ISMC is applied with θ r = 0 and the nominal controller is designed as in (33). First, γ c = 0 is applied. ISMC shows the robustness to the parameter uncertainties. The pendulum balances at a new equilibrium position θ = 0 . 26 rad. However, the tracking performance of the 2 WMR is not satisfactory. The tracking error of the wheel position in steady state is e 1 ,s | γ c =0 = − 0 . 9259 m. Next, γ c = − 6 . 5471 is computed according to (35) and used in (33). The simulation results for the two cases, with and without the compensation term γ c , are shown in Fig. 7. By adding the compensation term to the control input, the 2 WMR tracks the planned trajectory better and reaches the desired setpoint without steady-state error. The simulation results are consistent with the theoretical analysis in Sections II-D and III-D. V. I MPLEMENTATION AND E XPERIMENT R ESULTS In simulations, an ideal model of the 2 WMR is used. To stabilize the 2 WMR system in absence of uncertainties, the feedback gains for the nominal linear controller can be chosen in a wide range as long as A 0 − g 0 k T is Hurwitz. However, considering the existence of mismatch between the real-time system model and the mathematical model (1) and (2), the feedback gains obtained from simulations may not function well on the real-time platform, thus need to be adjusted through experimental testings on the 2 WMR prototype. For implementation, first, we consider a simple regulation task that is to balance the robot at the original position on a flat surface, i.e., x r = 0 , v r = 0 , and φ = 0 . Since there exists backlash in the driving mechanism of the 2 WMR [10], strong vibrations are observed by applying the linear controller with the feedback gains obtained from simulations. To reduce the vibrations, the feedback gains are adjusted to k = [ − 10 , − 0 . 5 , − 35 , − 3] T . ISMC is applied with the projection vector as s = [0 , 0 , 0 , 0 . 05] and the feedback gains for the nominal linear controller as k = [ − 10 , − 0 . 5 , − 35 , − 3] T . For comparison, the linear controller alone is also applied to the 2 WMR. Fig. 8 shows the experimental results for the 2 WMR under the ISMC and the linear controller. When the linear controller is applied, the 2 WMR is stabilized at the first few seconds, however, becomes unstable in 10 seconds. By applying the ISMC, the 2 WMR is consistently stabilized. The wheels stay around the original place and the pendulum is balanced around θ = 0 , which verifies the effectiveness of the ISMC in handling system uncertainties. A testing is conducted to check the robustness of the ISMC with respect to an exceptional disturbance. The experiment results are shown in Fig. 9. At t = 18 s, we push the 2 WMR to the right about 0.15 m. The 2 WMR is finally stabilized around the original position and the transit responses show small oscillations. For comparison, several other existing methods, including the fuzzy traveling and position controller (FTPC) proposed in [7], and the sliding-mode controller proposed in [19], [20], are used to control the 2 WMRs. The experimental results for the 2 WMR system under the FTPC [7] and SMC [19], [20] can be found in [10] (Figs. 11 and 12). By comparing the results, it is evident that the ISMC proposed in this work provides a better performance than the existing methods [7], [19], [20] when controlling the 2 WMR. Next, the robot is placed on an inclined surface and the slope angle φ is unknown. ISMC is applied with θ r = 0 and the nominal linear controller is designed as in (33). For the first trial, we set γ c = 0 . The pendulum is balanced around θ e = 0 . 1 rad, however, steady-state error of the wheel position exists, and e 1 ,s | γ c =0 = − 0 . 35 m. For the second trial, we use γ c = − 3 . 5 , which is computed according to (35). Experiment results for the two cases, with and without the compensation term, are shown in Fig. 10. The steady-state error for the wheel position is eliminated under ISMC with the compensation term, which is consistent with the theoretical analysis and simulation results. First, we consider the mobile robot travels on a flat surface, i.e., φ = 0 . The planned trajectory for the wheeled mobile robot is the same as we used for simulation. ISMC is applied with θ r = 0 , γ c = 0 . All other controller parameters are chosen the same as for the regulation task. Experiment results are shown in Fig. 11. The 2 WMR reached the desired setpoint and stays there afterward. ISMC shows the effectiveness for setpoint control of the 2 WMR system. However, it is observed that the trajectory of the wheels x 1 is not smooth enough. When the real position of the 2 WMR x 1 surpasses the given reference x r , the 2 WMR would stop for a while or travel backwards, which are not the desired motions. Considering our objective for the 2 WMR is traveling forward to arrive the desired position, ...
Citations
... Mechanical joints in robot manipulators are driven by motor currents [1][2][3]. The path tracking control of mobile robots is realized by adjusting wheel velocities [4][5][6][7]. Gyroscopic precession can be integrated into one-wheeled robots for steering control [8]. Flight dynamics in unmanned aerial vehicles (UAVs) can be stabilized through attitude adjustment [9][10][11][12]. ...
... For the convenience of distinguishing, they are denoted as the α-system and β-system. For cascaded systems [1][2][3][4][5][6][7][8][9][10][11][12], the nonlinearity of the α-system n α usually contains a dynamic coupling term that coordinates the behavior of the actuated and unactuated subsystems. Hence, n α can be modeled as the combination of a known dynamic coupling term and a residual term, i.e., ...
... where u αr is the desired value of u α , and y r is the desired value of y. This assumption is summarized from real systems [1][2][3][4][5][6][7][8][9][10][11][12]. ...
Control design for the nonlinear cascaded system is challenging due to its complicated system dynamics and system uncertainty, both of which can be considered some kind of system nonlinearity. In this paper, we propose a novel nonlinearity approximation scheme with a simplified structure, where the system nonlinearity is approximated by a steady component and an alternating component using only local tracking errors. The nonlinearity of each subsystem is estimated independently. On this basis, a model-free adaptive control for a class of nonlinear cascaded systems is proposed. A squared-error correction procedure is introduced to regulate the weight coefficients of the approximation components, which makes the whole adaptive system stable even with the unmodeled uncertainties. The effectiveness of the proposed controller is validated on a flexible joint system through numerical simulations and experiments. Simulation and experimental results show that the proposed controller can achieve better control performance than the radial basis function network control. Due to its simplicity and robustness, this method is suitable for engineering applications.
... Studies on controlling WMR to follow desired trajectories have extensively focused on techniques including sliding mode control [7]- [9], optimal control [10], [11], backstepping control [12], fuzzy logic control [13], [14], and neural network control [15], [16]. However, most controllers assume ideal conditions without disturbances or uncertainties, which can lead to instability in real-world deployments. ...
A wheeled mobile robot (WMR) is a nonlinear nonholonomic system with many applications in industry. However, uncertainties such as wheel slippage can degrade its tracking performance. This paper proposes a H∞ robust adaptive kinematic controller to improve the tracking of desired trajectories in the presence of wheel slippage disturbances. A differential game formulation is developed between the controller and the slippage disturbance. The controller approximates the solution to the associated Hamilton–Jacobi–Isaacs (HJI) equation online using a critic neural network and iterative least squares tuning. This provides adaptive estimates of the optimal control and disturbance signals. The controller is then simulated on a WMR model incorporating longitudinal and lateral wheel slippages. Tracking performance is evaluated for challenging curved trajectories like rotated-8 and butterfly shapes under slippage to test the system's robustness. The results illustrate the accuracy and responsiveness of the control approach in minimizing slippage effects and tracking errors for the nonlinear kinematic system.
... As long as the sliding surface is reached, the system will become immune from the matched uncertainties and input disturbances. To remove the reaching phase, an integral SMC was developed by using the integral sliding manifold, including an integral term, which can enable the system states to reach and remain on the sliding manifold from the beginning [4][5][6]. Although towards a wide variety of actual systems, the relevant uncertainties and disturbances can be assumed to be matched in the design of control systems, there are also many physical systems, such as permanent magnet synchronous motors [7], underactuated aerial vehicles and robotic systems [8] directly affected by unmatched disturbances. ...
This paper focuses on a neural adaptive H∞ sliding-mode control scheme for a class of uncertain nonlinear systems subject to external disturbances by the aid of adaptive dynamic programming (ADP). First, by combining the neural network (NN) approximation method with a nonlinear disturbance observer, an enhanced observer framework is developed for estimating the system uncertainties and observing the external disturbances simultaneously. Then, based on the reliable estimations provided by the enhanced observer, an adaptive sliding-mode controller is meticulously designed, which can effectively counteract the effects of the system uncertainties and the separated matched disturbances, even in the absence of prior knowledge regarding their upper bounds. While the remaining unmatched disturbances are attenuated by means of H∞ control performance on the sliding surface. Moreover, a single critic network-based ADP algorithm is employed to learn the cost function related to the Hamilton–Jacobi–Isaacs equation, and thus, the H∞ optimal control is obtained. An updated law for the critic NN is proposed not only to make the Nash equilibrium achieved, but also to stabilize the sliding-mode dynamics without the need for an initial stabilizing control. In addition, we analyze the uniform ultimate boundedness stability of the resultant closed-loop system via Lyapunov’s method. Finally, the effectiveness of the proposed scheme is verified through simulations of a single-link robot arm and a power system.
... The role of ( ) o s here is to suppress the jitter amplitude and weaken the state variable fluctuation problem after the system is stabilized, and the suppression effect will be more obvious as the parameter b increases. To further weaken the jitter problem of the stabilized system, the smoothing process is carried out for the symbolic function ( ) sgn s in this paper, which is known as the traditional symbolic function [37], as shown in the following equation. ...
... The role of o(s) here is to suppress the jitter amplitude and weaken the state variable fluctuation problem after the system is stabilized, and the suppression effect will be more obvious as the parameter b increases. To further weaken the jitter problem of the stabilized system, the smoothing process is carried out for the symbolic function sgn(s) in this paper, which is known as the traditional symbolic function [37], as shown in the following equation. ...
A proposed optimized model for the trajectory tracking control of a wheeled inverted pendulum robot (WIPR) system is presented in this study, which addresses the problem of poor trajectory tracking performance in the presence of unknown disturbances due to the nonlinear and underactuated characteristics of the system. First, a kinematic controller was used to track a reference trajectory and generate a control law that specifies the desired forward and rotation speeds of the system. Next, a nonlinear disturbance observer (NDO) was designed to enhance the system’s robustness to external disturbances and improve its tracking performance. Then, the coupled system state variables were decoupled into two subsystems: a forward rotation subsystem and a tilt angle velocity subsystem. An improved hierarchical sliding mode controller was designed to control these subsystems separately. Finally, simulation experiments were conducted to compare the proposed method with a common sliding mode control approach. The simulation results demonstrate that the proposed method achieves better tracking performance in the presence of unknown disturbances.
... However, this technique requires the unmatched disturbance to be sufficiently smooth, and it is effective for special singleinput and single-output (SISO) systems with the nonlinear block controllable form (NBC-form). Castanos et al. developed the ISM design method of minimizing the unmatched perturbations for the nonlinear affine system and applied the method to normal nonlinear affine systems (Castanos and Fridman, 2006;Rubagotti et al., 2011). Xu et al. (2014) adopted this ISM design method in their work and achieved the controlling of the underactuated plant in the presence of both matched and unmatched uncertainties and disturbances. Zhang (2015) proposed an ISM controller design based on the quadratic integral sliding mode (QISM) for SISO systems with unmatched disturbance. ...
In this paper, a novel integral sliding mode (ISM) design was used to deal with the problem of unmatched uncertainty rejection in uncertain linear time-invariant (ULTI) systems. First, a new type of Lyapunov-function integral sliding mode (LFISM) with the ability to suppress unmatched uncertainty and disturbance was introduced. Despite the unmatched uncertainty, the system is robustly stable in ideal sliding mode or ultimate uniform bounded (UUB) stable in non-ideal sliding mode on the proposed LFISM surface. Then, the corresponding sliding mode control (SMC) control was designed based on the augmented system with the added integrator to ensure the reachability of the proposed LFISM, which led to a continuous sliding mode control (CSMC). The proposed method was applied to an academic case and an aircraft attitude control plant, and the comparison simulation results showed that the LFISM has better performance and rejection ability to the unmatched uncertainties.
... The preceding results on the robust compensator design of TWIP can be classified into the extended state observer [14], the nonlinear disturbance observer [15], sliding mode control methods [16,17], as well as the combined synthesis of a disturbance observer and a sliding control [18]. These works prove that it is a challenging problem to determine the disturbance compensation input for underactuated systems because they do not have a one-to-one correspondence between the actuators and the degrees of freedom. ...
... As relevant performances were carried out through the whole-body coordination control in [5][6][7], how to aggressively utilize the gravity of the pendulum is essential to accomplish the balanced agile motions of a TWIP system. In the previous robust control frameworks [14][15][16][17][18] for underactuated TWIPs, it cannot be clearly described how the disturbance estimates along the forward, pitch, and yaw motions are resolved into the compensation input channels. In contrast, the proposed scheme clarifies that the forward and yaw directional disturbances can be compensated through two input channels, and the body disturbances hindering the pitch motion can be indirectly attenuated in terms of a real-time pitch reference input dealing with the pitch directional disturbance estimates. ...
... Related to this issue, the NDOB-combined sliding mode controls employed the so-called dynamic surface in [15], and a novel sliding surface in [18], to achieve an asymptotically stable sliding mode for unmatched disturbances. Additionally, the second sliding controller in [16], the integral-type sliding surface suggested in [17] for TWIP systems, and the second-order sliding control suggested for underactuated systems in [30] belong to this class. However, the chattering problem due to the switching control action is unavoidable when the behavior of the TWIP deviates far from the nominal sliding dynamics, and the complicated parameters and gain structures, which were inevitable to guarantee the Lyapunov stability, would be a great barrier to find an appropriate gain setting for the stable convergence of the inverted pendulum to the equilibrium point. ...
Two-wheeled inverted pendulum (TWIP) vehicles are prone to lose their mobility and postural stability owing to their inherently unstable and underactuated dynamic characteristics, specifically when they encounter abruptly changed slopes or ground friction. Overcoming such environmental disturbances is essential to realize an agile TWIP-based mobile platform. In this paper, we suggest a disturbance compensation method that is compatible with unmanned TWIP systems in terms of the nonlinear-model-based disturbance observer, where the underactuated dynamic model is transformed to a fully actuated form by regarding the gravitational moment of the inverted pendulum as a supplementary pseudo-actuator to counteract the pitch-directional disturbances. Consequently, it enables us to intuitively determine the disturbance compensation input of the two wheels and the pitch reference input accommodating to uncertain terrains in real time. Through simulation and experimental results, the effectiveness of the proposed method is validated.
... Development and control of two wheeled balancing mobile robot or wheeled inverted pendulum is a popular research topic in verifying various control theories over the last decade, the motion control problem of a robot that can self-balancing on wheels has received much attention in both academic and industry worldwide. Two wheeled robot system is not only an intricate multiple-input multiple-output nonlinear system but also a kind of typical non-holonomic system with time-varying dynamics [1]. It is also a complicated coupled dynamic system with non-linear saturation dynamic characteristics [2]. ...
This paper investigates the balancing and tracking control of the mobile robot using a strongly integrated controller. The two independently motorized wheels in this mechatronic system track the target reference and investigate a balancing at the gravity center above the axis of the wheels' rotation where model fluctuations and an external disruption are included in the consideration. In this work, the innovative controller is presented and tested as a coupling controller based on the notions to satisfy considered design objectives. The proposed controller depends on linking several algorithms with each other, where the integrated controller design passes through three phases that are sequential and dependent on each other. The input-output data of TWBMR generated from the closed loop control system is used to develop a neural network model. In this study, the neural networks model can be trained offline and then transferred into a process where adaptive online learning is carried out using Adaptive Network-Based Fuzzy Inference System ANFIS to improve the system performance. The simulation results verify that the considered identification and control strategies can achieve favorable control performance. The ANFIS control design approach does not require an accurate model of the plant. In addition, high-level knowledge of the system is not needed to build a set of rules for a fuzzy controller. ANFIS achieved acceptable tracking accuracy in compared to FLC. Evaluation of navigation and balance abilities for TWMR are tested with different scenarios, the designed controller is investigated to observe the behavior of the robot on various targets, and its effectiveness is validated. The most significant advantages of designed controllers are that it renders the control system insensitive to external disturbances and model uncertainty. Issue (34) September 2022 68 INTRODUCTION Development and control of two wheeled balancing mobile robot or wheeled inverted pendulum is a popular research topic in verifying various control theories over the last decade, the motion control problem of a robot that can self-balancing on wheels has received much attention in both academic and industry worldwide. Two wheeled robot system is not only an intricate multiple-input multiple-output nonlinear system but also a kind of typical non-holonomic system with time-varying dynamics [1]. It is also a complicated coupled dynamic system with non-linear saturation dynamic characteristics [2]. In real movement, TWBMR suffers from uncertain factors, such as load change and road conditions and external interference, this will bring great difficulties to motion control for TWBMR. The control objective of the robot is to perform control motion of the wheels while stabilizing the Intermediate Body (IB) around the upright position [3]. Fuzzy logic control and Adaptive Networks based Fuzzy Inference system is designed and implemented to stabilize the neural network model of TWBMR system [4,5]. The work in this paper can be arranged as follows. In section two, the mathematical model of TWBMR is written, in section three, the system analysis is considered, the neuro model of TWBMR, fuzzy logic controller, and ANFIS is designed in section four, and finally, the conclusion is presented.
... The design of the switching surface is of most importance because it highly affects the performance of the system. In this regard, SMC approaches including a nonlinear switching surface and a time-varying switching surface have been presented for UMSs (Kurode et al., 2012;Singh and Ha, 2019;Xu et al., 2013). An integral SMC was designed for a wheeled underactuated mobile robot subject to both unmatched and matched uncertainties (Xu et al., 2013). ...
... In this regard, SMC approaches including a nonlinear switching surface and a time-varying switching surface have been presented for UMSs (Kurode et al., 2012;Singh and Ha, 2019;Xu et al., 2013). An integral SMC was designed for a wheeled underactuated mobile robot subject to both unmatched and matched uncertainties (Xu et al., 2013). A nonlinear switching surface was presented to design SMC for a slosh-free motion in a simple pendulum to improve its damping as a class of second-order UMS with unmatched uncertainties (Kurode et al., 2012). ...
This paper investigates a passivity-based hierarchical SM control (PBHSMC) approach to solve the trajectory tracking issue of a special class of UMSs using unmeasured states and in presence of both unmatched and matched perturbations. First, a passivity-based SM observer (PBSMO) is designed for quick estimation of states in the UMS. Then, we develop a nonlinear two-layer switching surface using feedback passivation. The passivation-based approach ensures global asymptotical convergence of tracking error on the switching surface with the discontinuous term. Moreover, we develop an SMC law that can satisfy reaching mode and sliding mode conditions. Finally, to illustrate the performance of theoretical results, the developed control scheme is assessed by numerical simulation of two case studies including flexible-joint manipulator (FJM) and underactuated surface vessel (USV) systems. The simulation results indicate the superiority of the PBSMO-based PBHSMC scheme over the conventional SMO-based HSMC in suppressing unwanted oscillations of link, low tracking error and overshoot, short settling time, smooth and small control efforts, and also more accurate estimation of state variables with less chattering.
... Trajectory tracking control of non-holonomic mobile robots has attracted great attention in recent years, and the applications can be found in broad fields [1][2][3][4][5][6]. Many control strategies have been proposed to tackle the trajectory tracking problem, such as sliding mode control [7][8][9], adaptive control [10][11][12], and backstepping control [13], etc. It is well-known that the physical constraints are often unavoidable for nonholonomic mobile robots, and the constraints are not well-addressed by applying the aforementioned control strategies. ...
... For the real tracking error system (7) and the nominal system (9) with the same inital state and control input. Then, the state deviation p r f (t) −p r f (t) is bounded by ...
... Lemma 4. For the nominal tracking error system (9), if the linear velocity v r of the virtual robot is limited by ...
In this paper, a novel dual-mode robust model predictive control (MPC) approach is proposed for solving the tracking control problem of non-holonomoic mobile robots with additive bounded disturbance. To reduce the negative effect of disturbance and drive the state of real system closer to the one of nominal system , a robust reference signal is introduced into the cost function of MPC. In order to reduced the computation burden caused by online optimization of MPC and further improve the tracking accuracy, a dual-mode control strucuture consisting of the robust MPC and the local nonlinear robust control is developed, in which the local nonlinear robust control law is applied within a specified terminal region. Finally, simulation results on the non-holonomic mobile robot are presented to show the validity of the proposed control approach.
... [26]. As a result, several approaches are recommended in the literature to reduce the chattering effect [27][28][29]; one of them is the ST-SMC technique. ...
This paper deals with the robust current control for three-phase Grid-Connected Inverters (GCI) of distributed generation (DG) systems based on a Super-Twisting Sliding mode controller (ST-SMC) during injecting active and reactive power into the grid. This approach is capable of decreasing the chattering phenomena and improving the system's accuracy. The proposed controller is realized for the inner current controller to guarantee proper regulation, such as short-time response, small steady-state error, and so on. To achieve the appropriate synchronization desired between current injected and grid voltage, a phase locked loop (PLL) based on a synchronous reference frame (SRF) is applied. Finally, simulation results are examined by Powersim (PSIM) software and are compared with those of a conventional controller to validate the proposed controller's effectiveness.
