A simulation study of non-linear disturbance observer-based sliding mode control for inverted pendulum with mismatched disturbances

Objective: This study proposes the application of optimized Sliding Mode Control (SMC) with Nonlinear Disturbance Observer (NDO) for the Inverted pendulum, which is subjected to mismatched disturbances. Methods/Statistical Analysis: Sliding Mode Control (SMC) with Nonlinear Disturbance Observer (NDO) solves the main problem of chattering present in traditional sliding mode controllers while retaining the nominal performance even with mismatched disturbances. Chattering defines the presence of finite frequency and finite amplitude oscillations in the control input. Genetic Algorithm is used for searching the optimal controller parameters, which includes switching function coefficient, switching gain and observer gain. Findings: Simulation results shows the advantages of NDO based SMC and proves that NDOSMC can observe the mismatched disturbances very effectively. The conventional SMC method is also used in the control design the Inverted pendulum for comparison studies. The two main issues to be tackled in conventional Sliding Mode Control (SMC) are convergence time and chattering. Chattering and convergence time can be reduced in SMC by getting the optimal values of controller parameters using intelligent optimization techniques such as Genetic Algorithm (GA). In the present study convergence time and chattering of the controlled system are considered as the performance index of objective function. Application/Improvements: This study can further be extended for Multi-Input Multi-Output (MIMO) systems subjected to mismatched disturbances and parametric uncertainties.

Variable structure control with sliding mode, which is commonly known as sliding mode control (SMC), is a nonlinear control strategy that is well known for its robust characteristics (Utkin, 1977). The main feature of SMC is that it can switch the control law very fast to drive the system states from any initial state onto a user-specified sliding surface, and to maintain the states on the surface for all subsequent time (Utkin, 1977), (Phuah et al., 2005 a). The conventional SMC has two disadvantages (Ertugrul & Kaynak, 2000), (Slotine & Sastry, 1983), which are the chattering phenomenon (Slotine & Sastry, 1983), (Young et al., 1999) and the difficulty in calculating the equivalent control law of SMC that requires a thorough knowledge of the parameters and dynamics of the nominal controlled plant (Ertugrul & Kaynak, 2000), (Slotine & Sastry, 1983), (Hussain & Ho, 2004). Many methods of SMC using neural networks (NN) have been proposed (Phuah et al., 2005 a), (Ertugrul & Kaynak, 2000), (Hussain & Ho, 2004), (Phuah et al., 2005 b), (Yasser et al., 2007), (Topalov et al., 2007). In this paper, sliding mode controls using NN are proposed to deal with the problem of eliminating the chattering effect and the difficulty in calculating the equivalent control law of SMC that requires a thorough knowledge of the parameters and dynamics of the nominal controlled plant. The first method of this method applies a method using a simplified form of the distance function proposed in (Phuah et al., 2005 a), (Phuah et al., 2005 b). Furthermore, the simplified distance function of our method uses a sliding surface in the space of the output error and its derivations, as proposed in (Yasser et al., 2006 a), (Yasser et al., 2006 c), instead of the space of the states error to construct a corrective control input. Thus, no observer is required in the proposed method. Moreover, we also propose the application of an NN to construct the equivalent control input of SMC. The weights of the NN are adjusted using a backpropagation algorithm as in (Yasser et al., 2006 b). Hence, a thorough knowledge of the parameters and dynamics of the nominal controlled plant is not required for calculating the equivalent control law. Finally, a stability analysis is carried out, and the effectiveness of this first control method is confirmed through computer simulations. This first method has been previously discussed in (Yasser et al., 2007). The second method of this paper applies an NN to produce the gain of the corrective control of SMC. Furthermore, the output of the switching function the corrective control of SMC is applied for the learning and training of the NN. There is no equivalent control of SMC is used in this second method. As in the first method, this second method applies a method using a sliding surface in the space of the output error and its derivations, as proposed in

In this paper, sliding mode controller (SMC) and integral sliding mode controller (ISMC) are designed for a variable speed wind turbine. The main objective of the controller is to optimize the energy captured from the wind at below rated power. To overcome the steady state error, the ISMC is introduced. However, in the presence of large uncertainties, ISMC control approach produces oscillatory phenomenon due to the higher needed gain. To eliminate the tradeoffs between the ISMC tracking performance and the high gain at the control input, we have introduced a new method based on the modification of the output tracking error through the use of the exponential function in order to eliminate the reaching phase. The stability of the proposed ISMC is analyzed by Lyapunov theory and the control action didn't show any chattering. The simulation results of ISMC are presented and the control performance is compared with conventional SMC.

In this paper, a proportional-integral sliding mode control (PISMC) method is presented to achieve the attitude and position control of an unmanned helicopter system for autonomous hovering. The PISMC includes the advantages of both conventional sliding mode control (SMC) and integral sliding mode control (ISMC). The proposed PISMC algorithm is capable of stabilized attitude and position control for unmanned helicopter autonomous hovering, and it offers a performance improvement over the conventional SMC and ISMC algorithms as well. The system performance is quantified and an experimental unmanned helicopter system is developed to access the performance of the PISMC. Both simulations and actual flight tests are conducted to verify the PISMC attitude and position control. The simulation results show that the PISMC tracking error is smaller and that PISMC converges faster than SMC does. The flight test results prove that the proposed PISMC is effective in the attitude and position control of unmanned helicopter autonomous hovering.

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.

This paper proposes an integral sliding mode control with a novel model-based iterative feedforward compensating the hysteresis to finish high-precision positioning control of the piezoactuated stage. The Bouc-Wen model is established to design a novel iterative feedforward control (IFC) method. The IFC reduces the effects of inherent hysteresis on the positioning precision of the piezo-actuated stage. The positioning error of the IFC is inevitable because of the model uncertainty. Subsequently, an integral sliding mode control algorithm is implemented to further decrease the tracking error and enhance the anti-disturbance capability of the IFC. To reduce the chattering of the proposed controller, a boundary layer method based on Fal-function is designed. The stability of the integral sliding mode control is analyzed via Lyapunov stability theory. The feasibility of the proposed controller is certified by a series of simulation results. Compared with the IFC and conventional sliding mode control (CSMC) method, the proposed controller has higher performance in terms of the positioning precision of piezo-actuated stages.

This article is motivated by the control issues of the translational oscillator with rotational actuator system in the existence of uncertain disturbances. A nonlinear disturbance observer and a global sliding mode control method are proposed for the disturbance estimation and stabilization of the translational oscillator with rotational actuator system. Compared with the existing control methods, uncertain disturbances are estimated by the proposed nonlinear disturbance observer. In addition, the sliding mode control method is continuous and global robustness with respect to disturbances. Specifically, to facilitate the controller design, the dynamics of the translational oscillator with rotational actuator system are rearranged as the cascade form first. Then, a virtual signal is constructed and corresponding error dynamics are derived. Subsequently, a nonlinear disturbance observer and a continuous global sliding mode control method are proposed for the disturbance rejection and stabilization of the translational oscillator with rotational actuator system. Finally, simulation results are provided to verify the effectiveness and robustness of the proposed controller.

This paper concerns the finite time tracking control problem for the longitudinal model of an airbreathing hypersonic vehicle (AHV) with actuator faults and external disturbances. First, the dynamics of system outputs V and h are given by calculating the differentials. Next, combining external disturbances and actuator additive faults as lumped disturbances, a nonlinear disturbance observer (NDOB) is designed to estimate them. Then, two integral sliding mode manifolds are designed based on tracking errors. Finally, combining NDOB and integral sliding mode control (SMC) techniques, a composite fault tolerant controller is constructed for the longitudinal model of an AHV. This control approach can make the velocity and altitude track the reference signals in finite time and reduce chattering phenomenon caused by SMC. Simulation results are given to show the effectiveness of the proposed control method.

The integration of renewable energy sources (RESs) at the edge of the grid plays a contributory role in advancing the transition to a sustainable energy future. However, this transition introduces significant variability, which challenges the maintenance of frequency stability in power systems. To address the impacts of RES variability, various robust control strategies have been developed. This paper compares the performance of different advanced sliding mode control (SMC) approaches, i.e., super twisting (ST) algorithm‐based second order sliding mode control (STSOSMC), second order sliding mode control (SOSMC), double integral sliding mode control (DISMC) and integral sliding mode control (ISMC) with conventional sliding mode control (SMC) for load frequency control with stochastic RESs such as biogas generators (BG) and wind‐based doubly fed induction generators (DFIG). The impact of the advanced sliding mode controllers on the voltage and rotor angle stability of the system is also explored. The efficacy of the controllers is tested under different load disturbances, considering nonlinearities such as communication delay (CD), sensor inaccuracy (SI), governor dead band (GDB), and generation rate constraint (GRC). The results demonstrate that STSOSMC achieves superior frequency regulation with minimal chattering and outperforms other controllers in terms of settling time, overshooting, and undershooting in frequency deviation. The result also demonstrates the effectiveness of STSOSMC in managing the variability and disturbances of RESs. Therefore, it could be considered the most robust control mechanism from the edge of the grid system with high penetration of RESs.

This paper presents the synthesis of a hybrid control applied to a Unicycle Mobile Robot (UMR) based on modified Sliding Mode Control approach (SMC) integrated with Neural State Observer (NSO) and Nonlinear Disturbance Observer (NDO). Furthermore, Lyapunov's direct method is used to ensure the stability of the closed-loop control on the one hand, and the stability of the neural state observer based on the backpropagation algorithm on the other hand. The advantages of the presented hybrid controller for velocity and tracking the trajectory of a mobile robot are revealed by simulation results.

Conventional sliding mode controllers have been successfully applied to control various types systems including the Stewart platform manipulator. But chattering, lack of robustness in the reaching phase and sensitivity to unmatched uncertainty are the basic problems which delayed their practical implementations. To avoid the non robust reaching phase to compensate unmatched uncertainties, integral sliding mode controllers have been proposed but only SISO system examples have been tested. Hence in this paper, MIMO implementation of integral sliding mode controller is tested using a 6 DOF Stewart platform manipulator. The integral sliding mode controller is implemented using MATLAB simulation and the result is compared with PD and conventional sliding mode controller. It was found that the integral sliding mode controller performs better in avoiding uncertainties due to load variation and actuator friction.

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.

Chattering-free higher order sliding mode controller with a high-gain observer for the load following of a pressurized water reactor

This article seeks to achieve high tracking performance of the hybrid automobile electro-coating conveying mechanism with disturbances and uncertainties. An integral sliding mode control scheme is first presented to eliminate the reaching phase in sliding mode control. Then, an adaptive integral sliding mode controller is designed without knowing the disturbance information. Finally, a composite strategy, referred to as nonlinear disturbance observer (NDO)-based adaptive integral sliding model control, is put forward to further reduce the switching gain. By compensating the lumped disturbances via a NDO, the switching gain is only required to be higher than upper bound of the disturbance estimation error which is much smaller than actual disturbance. The results of both numerical simulations and experiments show that the proposed approach has good control performance especially in reducing the switching gain and alleviating the chattering problem.

This article presents an original motion control strategy for robot manipulators based on the coupling of the inverse dynamics method with the so-called second-order sliding mode control approach. Using this method, in principle, all the coupling non-linearities in the dynamical model of the manipulator are compensated, transforming the multi-input non-linear system into a linear and decoupled one. Actually, since the inverse dynamics relies on an identified model, some residual uncertain terms remain and perturb the linear and decoupled system. This motivates the use of a robust control design approach to complete the control scheme. In this article the sliding mode control methodology is adopted. Sliding mode control has many appreciable features, such as design simplicity and robustness versus a wide class of uncertainties and disturbances. Yet conventional sliding mode control seems inappropriate to be applied in robotics since it can generate the so-called chattering effect, which can be destructive for the controlled robot. In this article, this problem is suitably circumvented by designing a second-order sliding mode controller capable of generating a continuous control law making the proposed sliding mode controller actually applicable to industrial robots. To build the inverse dynamics part of the proposed controller, a suitable dynamical model of the system has been formulated, and its parameters have been accurately identified relying on a practical MIMO identification procedure recently devised. The proposed inverse dynamics-based second-order sliding mode controller has been experimentally tested on a COMAU SMART3-S2 industrial manipulator, demonstrating the tracking properties and the good performances of the controlled system.