Trajectory tracking for a quadrotor under wind perturbations: sliding mode control with state-dependent gains

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.

Fixed wing Unmanned Aerial Vehicles (FWUAVs) are widely utilized in both military and civilian sectors due to their ability to perform risky, inaccessible operations. The mathematical model of FWUAVs is complex, incorporating physical laws and coordinate systems with transformation matrices. In addition, controlling FWUAVs is challenging due to their nonlinear and coupled dynamics. This paper focuses on tracking trajectories for fixed wing unmanned aerial vehicles (FWUAVs) using a Robust Fractional Order Sliding Mode Controller (RFOSMC). An RFOSMC, which combines a conventional Sliding Mode Controller (SMC) with flexible fractional calculus, is proposed in this paper. Particle Swarm Optimization (PSO) is used to tune the control gains of RFOSMC. External disturbances and parameter variation are added to evaluate the controller’s performance. Comparative studies have been done with Linear Quadratic Regulator (LQR), Fractional Order PID (FOPID), SMC, and robust FOSMC. RFOSMC performs better than LQR, FOPID, and SMC in tracking accuracy, response speed, and overshoot. In addition, the performance comparison of RFOSMC and conventional SMC has been done based on performance index values of errors (ITAE), and RFOSMC showed a 76.5918% improvement. For a step input, RFOSMC showed the smallest settling time of 0.835s compared with 2.724s for SMC and 4.8573s for FOPID. Open-loop model verification and overall control system of FWUAV are done using MATLAB/Simulink software.

This paper focuses on maintaining the liquid level in tank two in the coupled tank control system with the help of the sliding mode control (SMC). SMC is the potent controller for coupled tank liquid level system under tracking conditions. Sliding mode controller (SMC) is nonlinear control it applies a discontinuous control signal. The main advantages of sliding mode are low sensitivity to plant parameter variations and disturbances. To maintain desired liquid levels in a nonlinear coupled tank is a great challenging task so this problem better handled by SMC. To control this liquid level process a SMC strategy is used we have first order SMC and second order SMC. Regulating this system in less time with proper control signal is not possible in first order SMC due to chattering is obtained which yields unwanted control signal. To fill tank-2 in less time with smooth control signal is possible in higher order SMC. Next, second order SMC is applied and stability is reached fast and no chattering phenomenon. These can be shown in the simulation results with the help of MATLAB. This application report describes how to develop SMC for liquid level control in coupled tank system.

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.

The design of a globally stable second order sliding mode controller for sensorless induction motors is discussed in this paper. The adaptive component of the controller enables to compensate for the variation in time of the rotor resistance value, while the use of a suitably designed sliding mode speed/flux observer avoids the necessity of including speed and flux sensors within the control loop, making this proposal suitable for sensorless applications. The use of a second order sliding mode control approach, realized by regarding the second time derivatives of the stator currents as discontinuous auxiliary control inputs, is effective in limiting the mechanical wear, making this proposal more acceptable in practical applications than those based on conventional sliding mode control.

This work suggests an optimized improved power rate sliding mode control (PRSMC) to control a 4-degrees of freedom (DOF) manipulator in joint space as well as workspace. The proposed sliding mode control (SMC) aims to improve the reaching mode and to employ an optimization method to tune the control parameters that operate the robotic manipulator adaptively. Inverse kinematics is used to obtain the joint desired angles from the end effector desired position, while forward kinematics is used to obtain the real Cartesian position and orientation of the end effector from the real joint angles. The proposed enhancements to the SMC involve the use of the hyperbolic tangent function in the control law to improve the reaching mode. Added to that, particle swarm optimization (PSO) is used to tune the parameters of the improved SMC. Furthermore, the Lyapunov function is utilized to analyze the stability of the closed-loop system. The proposed enhanced sliding mode combined with the optimization method is applied experimentally on a 4-DOF manipulator to prove the feasibility and efficiency of the proposed controller. Finally, the performance of the suggested control scheme is compared with the conventional power rate SMC in order to demonstrate the enhanced performance of the suggested method.

This paper presents a conventional sliding mode control (SMC) and chattering free improved sliding mode control design strategy for nonlinear systems. In this paper, theoretical and mathematical concept of variable structure control (VSC) system and sliding mode control has been discussed. The modelling of conventional sliding mode controller as well as chattering free improved sliding mode controller for sample nonlinear equation and robotic vehicle located underwater, forming a single direction motion is the main motive of this paper. Chattering in conventional sliding mode controller can be easily removed by using continuous function in place of discontinuous sign function. The Lyapunov stability criterion is used for nonlinear system control giving a simple control algorithm. Simulation result depicts the feasibility and satisfactory performance of chattering free improved sliding mode control as compared to conventional sliding mode control.

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

This study presents simple controllers for trajectory tracking of the kinematic model of an Unmanned Aerial Vehicle (UAV). We consider the effects of wind perturbations on an UAV in flight, and consider the applications of an existing controller with a wind compensation term while the control objective is to track a time-varying trajectory which is given in terms of the inertial coordinate system. Application of the approach to UAVs flying in a string-like formation in the presence of additive wind perturbations is also considered. Numerical and simulation results are demonstrated.

The success of the sliding mode control (SMC) is due to the simplicity of its implementation and its robustness against external disturbances via state space and input output model. In spite of this characteristic, the sliding mode control (SMC) suffers from a main drawback known as the ‘chattering phenomenon’. In order to overcome this problem, a new discrete second order sliding mode control via input output model is proposed in this paper. A stability analysis of the proposed control was then studied. To illustrate the effectiveness of the proposed discrete second order sliding mode control law, a classical discrete sliding mode control and discrete second order sliding mode control were applied to a real discrete second order system via input output model. The experimental results of the proposed discrete sliding mode control law show good performances in terms of the rejection of the external disturbances and the reduction of the chattering phenomenon.

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 combination of standard and second order sliding mode controller are used and investigated for congestion control problem of differentiated Services (Diff-Serv) networks. Robustness against modeling uncertainties and disturbances are major features of sliding mode controller. Chattering phenomenon affects sliding mode congestion control; to overcome this problem, second order sliding mode control (SOSMC) is proposed as a congestion controller but this controller has slower response to SMC. Combination SMC and SOSMC gives better response. There are three types of traffics in Diff-Serv networks; i.e. three types of queues and based on that, the quality of their services are categorized. Each of these types of traffic has its own congestion control mechanisms. Stability of each controller is proved by Lyapunov stability law. To evaluate the capabilities of our proposed robust control strategy, simulation results are provided for both sliding mode controllers and second order slide mode controllers and their corresponding efficiencies are compared.

The main purpose of this paper is to design a robust second order sliding mode controller that can deal with uncertain nonlinear systems. This controller can keep the main advantages of the first order sliding mode controller, such as the ability to make the system asymptotically stable by forcing the error and its derivatives to have a zero value, the simplicity in the operation, and the robustness in the existence of perturbations. In spite of the features that characterize the first order sliding mode controller (1 SMC), it still suffers from the unwanted phenomenon “chattering”, which originates from a discontinuous control part (sign function). In this context, saturation function can be used instead of sign function to reduce this problematic chattering. Different from the saturation function method, the second order sliding mode controller can be used to overcome the chattering; suffered by the first order sliding mode controller and to retain the stability and performance of the system. In this paper, the twisting and the super twisting second-order algorithms of the sliding mode controller were used, and their results were compared with the first order sliding mode controller. So, this subject focused on the chattering problem who suffers from it the 1 SMC and try to reduce it by using the 2 SMC, the uncertain pendulum system was adopted in this work for the purpose of checking the three controllers. The simulations results showed that the second order sliding mode controller has the ability to reduce both the chattering magnitude and the steady state error and achieve an asymptotically stable system. The results were obtained by using MATLAB programming.

The tilt tri-rotor unmanned aerial vehicle (UAV) has three flight modes: the hover mode, the transition mode, and the fixed-wing mode. Controller design in the hover mode is the premise of realizing stable flight of this kind of UAV. Due to the particular structure with odd rotors and strong nonlinearity, the modeling and control of the tilt tri-rotor UAV remain an active and ongoing research topic. To overcome these problems and achieve stable flight control, this paper proposes a sliding mode-based nonlinear control scheme for the hovering flight of a tilt tri-rotor UAV, consisting of position control, attitude control, and control allocation. First, the mathematical model of the UAV is given by using the Newton–Euler formulation. Second, a cascade flight controller consisting of the position controller and the attitude controller is developed based on sliding mode control (SMC). For the position controller, an auxiliary dynamic system composed of the hyperbolic tangent functions is introduced to the SMC approach for constraining the output magnitude of the thrust and the reference attitudes. Besides, a disturbance observer is applied to the attitude controller to alleviate the chattering and improve robustness. Furthermore, according to the structural characteristics of the tilt tri-rotor UAV, a control allocation algorithm is developed to map the virtual control quantities calculated by the cascade flight controller to the actual actuators. Simulations are conducted to verify the robustness against the external disturbances and parameter variations, and the performance comparisons with two other control schemes are also given. Finally, the experiment is also carried out to validate the performance of the proposed control scheme.

Second order sliding mode controllers for altitude control of a quadrotor UAS: Real-time implementation in outdoor environments