Variable Structure Control Research Articles

Three-dimensional cooperative guidance law for multiple missile based on sliding mode control

Based on the missile-target three-dimensional relative motion model, a multi-missile coordinated three-dimensional guidance law with attack time constraints is designed for attacking stationary targets. The sliding mode variable structure control is adopted in the pitch channel, and the dynamic inverse control is adopted in the yaw channel. By maneuvering in the yaw channel, adjusting the missile's attack time and comparing with the results of using augmented proportional guidance, the simulation results show that the algorithm designed in this article can achieve coordinated attack and high hitting accuracy, which verifies the correctness and superiority of the algorithm.

Trajectory tracking of in-wheel motor electric vehicles based on preview time adaptive and torque difference control

In order to improve the accuracy of trajectory tracking of in-wheel motor electric vehicles, a preview time adaptive trajectory tracking method based on iterative algorithm and fuzzy control is proposed. Firstly, based on the vehicle’s three-degree-of-freedom model, the vehicle is controlled to track trajectory based on model predictive control (MPC). The preview step size and sampling period of MPC are adjusted by iterative function and fuzzy controller, respectively. Then, In order to optimize MPC active steering control, a differential torque controller is established to realize the trajectory tracking control of differential torque steering. Finally, Carsim/Simulink co-simulation analysis and real vehicle verification are done. The simulation results show that the controller can complete the trajectory tracking control of the in-wheel motor intelligent vehicle, and the stability and steering performance are good. The controller has good robustness and adaptability according to road adhesion conditions and vehicle speed changes. At the same time, the trajectory tracking accuracy of the MPC controller is better than sliding mode variable structure control (SMC). The real vehicle verification results show that when the real vehicle tracking under different speeds, the adaptive preview time controller designed in this paper has good trajectory tracking performance and stability.

Soft variable structure control of linear fractional-order systems with actuators saturation

In this paper, a new method of soft variable structure control for Fractional-Order System (FOS) is proposed to achieve faster response while the control signal is continuous and satisfies actuators’ constraints. Our proposed method, by describing a desired commensurate FOS, with the help of a pole placement algorithm and applying an optimization routine, in the form of a procedure, leads the system to the desired character. The routine is done by solving an optimization problem subject to a control signal constraint qua we obtain the fastest response possible in the sense of stability region. The sufficient condition of stability of the control system is developed based on the stability theory of Fractional Order (FO) linear differential equations, and attributes of the Mittag-Leffler function. Finally, an example and corresponding numerical simulations are presented to show the efficiency of the proposed method. In the proposed method, a new control strategy for the FOS is presented, a complex problem is solved in a simple way, and it can exploit the benefits of using FOS in the modeling and control of complex physical phenomena.

Analysis of chattering in step down converter via sliding mode reaching law

The reaching law approach is broadly used for chattering repression, minimization of steady state error and reaching pace kept minimsed. The reasons of chattering, in this paper proposes sliding mode reaching law. In one hand, they assurance the scheme arrives at the sliding face swiftly and stay on it, in another way they deteriorate the chattering inefficiently, even matchless certainties and disturbances. This proposed reaching law gives uniqueness of the response. The reaching law is compared with Gao’s reaching law. Sliding mode reaching laws gives the efficacy in reducing the chattering of the variable structure control (VSC). This reaching law also reduces the losses in the switching diplomacy. In turns efficiency of the step-down converter increases. Simulation results give significant decrease of chattering and extremely fewer receptive in supply and load variation.

Research on Urban Distribution Optimization Under Point-based Billing on Simulated Annealing with Variable Neighborhood

In this paper, we study the optimization of urban distribution networks with leased third-party logistics fleets under point-based billing and construct a mathematical model of multi-model vehicle path optimization (MVRPTW) with time windows aiming at the lowest logistics expenditure under point-based billing mode. For the problem that the simulated annealing solution to the VRPTW problem tends to fall into slow convergence, a variable neighborhood structure and adaptive temperature control are introduced to improve the simulated annealing. Finally, using the order data of a Beijing’s third-party logistics company Z, the model is solved by first clustering the customer nodes through the K-Means algorithm to generate the initial solution and then optimizing it with the improved simulated annealing algorithm. Compared with the simulated manual empirical scheduling, algorithmic scheduling can reduce the logistics cost by 88.1%.

Based on RBF Neural Network of Hypersonic Re-entry Vehicle Attitude Control

In this paper, an attitude control method combining radial basis (RBF) neural network with integral sliding mode control is proposed for the re-entry stage of hypersonic vehicle with uncertain aerodynamic parameters and atmospheric density. Firstly, the Time-scale separation model of nonlinear equations for aircraft is established. Meanwhile, the feedback linearization method is used to linearize the time scale separation model. For fast and slow control subloops, a global sliding mode variable structure control was designed, and the stability of the closed-loop system was verified by Lyapunov theory. Finally, RBF neural network online regulation law is designed to adjust the controller parameters online to reduce chattering. The simulation results show that the controller can maintain good dynamic characteristics even when the aerodynamic data are greatly deviated.

Displacement characteristics hierarchical control of electro-hydraulic compound steering for commercial vehicle

The electro-hydraulic compound steering combines the function of electric power steering and hydraulic power steering, which can reduce the energy consumption of steering, ensure the stability of vehicles, and meet the steering demand under unmanned driving. In order to fully coordinate the steering stability and path tracking requirements in the unmanned steering process, this paper proposes a hierarchical control strategy of displacement characteristics for commercial vehicle electro-hydraulic compound steering. The mixed H2/H∞ controller for the vehicle stability is designed in the upper layer, which takes the vehicle yaw rate as the control variable. Based on the motor model and sliding-mode control theory, the sliding-mode variable structure controller of motor angle is designed in the lower layer, and the hydraulic power distribution is completed by estimating the steering resistance torque. Simulation results show that the designed controller can effectively track the yaw rate on the premise of ensuring path tracking effect. Combined with steering torque estimation and hydraulic power distribution rules, it can effectively realize the coordinated control of hydraulic power and motor rotation angle.

Composite Non-Linear Control of Hybrid Energy-Storage System in Electric Vehicle

The underlying circuit control is a key problem of the hybrid energy-storage system (HESS) in electric vehicles (EV). In this paper, a composite non-linear control strategy (CNC) is proposed for the accurate tracking current/voltage of the fully-active HESS by combining the exact feedback linearization method and the sliding mode variable structure control technology. Firstly, by analyzing the circuit characteristics of HESS, the affine non-linear model of fully-active HESS is derived. Then, a rule-based energy management strategy (EMS) is designed to generate the reference current value. Finally, the HESS is linearized by the exact feedback linearization method, and the proposed CNC strategy is developed combined with sliding mode variable structure control technology to ensure fast response, high performance, and robustness. At the same time, the stability proof based on the Lyapunov method is given. Moreover, the performance of the CNC strategy is thoroughly investigated and compared with simulation studies with the traditional PI control and a modified sliding mode control, and its effectiveness under different driving conditions is fully verified.

Robust attitude consensus control for multiple spacecraft systems with unknown disturbances via variable structure control and adaptive sliding mode control

This paper addresses the robust attitude consensus tracking problem for spacecraft formation flying (SFF) systems in the presence of unknown lumped disturbances including external disturbances and model uncertainties. Firstly, a nonlinear disturbance observer (NDO) considering that the derivatives of the lumped disturbances are nonvanishing is developed to estimate the lumped disturbances. Secondly, based on NDO, sliding mode control and adaptive control theories, a novel variable structure control algorithm is proposed to avoid the introduction of large observation errors of the NDO while ensuring that state errors of the SFF system can converge to zero asymptotically. The designed controller does not need accurate upper bounds of angular acceleration, disturbances, and disturbance derivatives, which makes the control system robust to the lumped disturbances. Moreover, the asymptotical stability can be guaranteed by Lyapunov theory. Finally, numerical simulations are carried out to verify the effectiveness of the proposed control scheme.

Proportional and Integral Variable Structure Controller (PI –VSC) for Grid Connected PWM Voltage Source Converter

Proportional and Integral Variable Structure Controller (PI –VSC) for Grid Connected PWM Voltage Source Converter

Design of a Fixed-Wing UAV Controller Combined Fuzzy Adaptive Method and Sliding Mode Control

To overcome the complexity of the coupled nonlinear model of a fixed-wing UAV system and the uncertainty caused by a large number of interference factors, a control algorithm combining fuzzy adaptive control and sliding mode variable structure control was proposed. The controller algorithm mainly relies on the sliding mode variable structure control method to solve the control problem of the strongly coupled complex nonlinear system. Based on sliding mode control, a fuzzy adaptive method is introduced to reduce the chattering problem of the traditional sliding mode control, and the uncertain parameters and unknown functions caused by external disturbances are approximated by this method. In this study, two types of fuzzy adaptive sliding mode controller were designed according to the different object ranges of the fuzzy adaptive algorithm. In addition, the stability of the controllers was verified using the Lyapunov method. Finally, numerical simulations are performed to demonstrate the effectiveness of the proposed controllers by comparing with the traditional sliding mode controller.

Formation Control of Fixed Wing UAV with a Novel Transition Function

A variable structure controller is designed to achieve the formation of fixed wing aircraft under various trajectory conditions. A novel transition function is designed to improve the control performance. The effectiveness of the control law is proved by theory and simulation.

Adaptive Fault Tolerant Attitude Control of a Nano-Satellite with Three Magnetorquers and One Reaction Wheel

In this paper, a passive fault tolerant attitude control is investigated for a nano-satellite with three magnetorquers and one reaction wheel in the presence of actuator constraints, external disturbances, and partial loss of actuator effectiveness as unknown actuator faults. For this purpose, a variable structure control approach is employed due to its ability to deal with the partial loss of actuator effectiveness and adjusting the maximum amplitude of the control signal by a control gain. A modified sliding variable is designed based on angular velocity and attitude errors with an adaptive parameter coefficient. The dynamics equation of the adaptive parameter is extracted during the stability proof of the closed-loop system. Changing the value of this parameter changes the effect intensity of the quaternion errors on the sliding variable and causes the attitude errors to maintain within a limited range. Applying this parameter to the modified sliding variable makes the controller perform well even if the adaptive parameter is significantly reduced. Furthermore, directly using the adaptive parameter in the structure of control law makes the controller generate a chattering-free torque. Comparing the simulation results with the results of two variable structure control methods designed in previous articles shows that its performance in attitude tracking commands has improved. In addition, Monte Carlo simulations with random actuator faults are performed to show the robustness of the proposed controller in the presence of actuator constraints and external disturbances.

Variable Structure Control of Second Order Systems With Nonlinear Uncertain Discontinuous Input Functions Using Approximate Inverses

We consider second order nonlinear systems in control canonical form, where the functional relation between the control variable and the system acceleration is nonlinear, uncertain and discontinuous. We approximate the nonlinear uncertain and discontinuous function with an invertible one, and use variable structure control theory to suppress the error of the approximate inverse. We rewrite the finite time reaching law or the terminal reaching law into the form of inequalities and use these inequalities to design a control law that drives the system state to the sliding surface in finite time, and one that ensures the convergence of the system speed and position errors to a narrow, adjustable width band around zero. The stability of the control system is also analyzed and proven. We demonstrate how to ensure the sufficiency of the available control effort, by the proper design of control parameters. The method is then validated on a numerical model of a nonlinear system with nonlinear, uncertain and discontinuous input function.

Fault Tolerant Variable Structure Control Of Six-phase Induction Generator For Wind Turbines

In this paper, a fault-tolerant control of a symmetrical six-phase induction generator based on a variable structure strategy is experimentally tested and compared with a classical proportional-integral controller. For this, we use a linear feedback sliding mode controller with switched feedback gains in such a way to control the inner current loops of this machine. One main drawback of the classical three-phase induction generator is that it is no longer possible to generate electrical power if only one phase is lost on the stator side. To overcome this issue, we will use a squirrel cage six-phase induction machine that can still operate when at least three phases remain on the stator side. This article proposes to use a variable structure control in order to cope with unbalanced currents and also maintain the generation of power when a loss of the stator's phases occurs. The proposed controller shows its robustness and good regulation performance in healthy and faulty modes. The simulation and experimental tests were carried out with a 24 kW induction machine that represents 1/100 of the electrical power of a real wind turbine.

Delay-Dependent Sliding Mode Variable Structure Control of Vehicle Magneto-Rheological Semi-Active Suspension

The vehicle semi-active suspension with Magneto-Rheological Damper (MRD) has been a hot research topic of this decade, featuring the challenging task of the robust control with actuator time delay considerations. In this study, a delay dependent sliding mode variable structure control, based on the Linear Matrix Inequality (LMI), is proposed to suppress the vibration of the Magneto-Rheological Semi-Active Suspension (MRSS) control system. In accordance with the nonlinear characteristics of MRD, a dynamic model of automotive semi-active suspension system, considering time delay, is established. By defining a parameter-dependent Lyapunov switching functional, the conditions for asymptotic stability of closed-loop time delay system are derived, while the sliding mode variable structure control with reduced conservatism is designed. According to the method of LMI, the asymptotic stability problem of sliding mode is transformed into a feasibility problem, which can be solved by the solver ‘feasp’ in LMI toolbox. In addition, the calculation of the critical time delay of MRSS is expressed as a generalized eigenvalue optimization problem. For comparison purposes, three representative controllers, including a conventional sliding mode controller, a delay dependent controller, and a smith compensation, are studied. Simulation and real vehicle testing on bump and random road responses show that, the designed delay dependent controller can ensure the stability of the suspension system, weaken the influence of time delay on the control performance and effectively improve the ride comfort of the vehicle.

Vibration pile driving system based on Sliding Mode Control

The sliding mode variable structure synchronous control of vibration pile driving system driven by double DC motors is studied. Firstly, the model of double machine driven vibratory pile driving system is established, and the theoretical derivation of system synchronization and stability is carried out. Secondly, the sliding mode variable structure control method is used to realize the phase speed synchronous control of two motors in the vibration system. Finally, Simulink is used to verify the correctness of the theoretical derivation, and the vibration displacement of the pile driving system is simulated and analyzed. The research shows that the sliding mode variable structure control can realize the synchronous control of the double machine driven vibratory pile driving system, which provides a theoretical and practical engineering basis for the design of this type of vibratory pile driving system.

Photoelectric pod control method based on sliding mode variable structure control and prediction tracking

光电吊舱在稳像和目标跟踪过程中存在摩擦力矩、不平衡力矩等干扰力矩，从而影响速度环响应精度；另一方面，吊舱视频跟踪器图像传输和处理造成的延迟也会造成跟踪滞后，因此必须进行延时补偿。提出基于预测跟踪的滑模变结构控制方法，采用微分预测跟踪器实现对视频跟踪器的延迟补偿，采用预测跟踪器估计出的目标运动角速率构成自适应补偿参数，以调整滑模变结构控制量，改进的滑模控制算法在补偿干扰力矩的同时抑制了抖振现象。仿真及实验结果表明：改进的控制方法能够有效补偿干扰力矩和跟踪器延迟造成的误差，相对于传统PID控制，其跟踪误差减小为原来的1/3，并且该算法已经在相关系统上得到应用。

Sliding-mode variable structure control for complex automatic systems: a survey.

Automatic systems (ASs) can automatically control the work of controlled objects without unattended participation. They have been extensively used in industry, agriculture, automobiles, robots and other fields in recent years. However, the performance of the controller cannot meet the work requirements under complex environmental conditions. Therefore, improving the control performance is one of the difficult problems that automated systems should solve. Sliding-mode variable structure control has the advantages of fast response, insensitivity to uncertainty and interference and easy implementation; thus, it has been extensively used in the field of complex control systems. This article analyses and explains the research status of motors, microgrids, switched systems, aviation guidance, robots, mechanical systems, automobiles and unmanned aerial vehicles (UAVs) and prospects for the application of sliding-mode variable structure control in complex ASs.

Coriolis Force Sliding Mode Control Method for the Rotary Motion of the Central Rigid Body-Flexible Cantilever Beam System in TBM

Beam slab structure is often encountered in a complex tunnel boring machine. Beam slab structure is subject to dynamic load, which is easy to cause fatigue damage and affect its service life. Therefore, it is necessary to control the vibration of this kind of beam slab structure. In this study, the central rigid body-flexible beam model is established for the rotating beam and plate rotating around the y-axis. Based on the Hamilton variational principle, the dynamic equation of the central rigid body-flexible beam system is established, and the dynamic model of the central rigid body-flexible beam system considering the influence of Coriolis force and centrifugal force is given. The vibration control of the central rigid body-flexible beam system is studied. The vibration mode of the rotating Euler Bernoulli beam is determined by using the elastic wave and vibration mode theory. The influence of the rotating motion on the beam vibration is analyzed, and the variable structure control law is designed to suppress the beam vibration. Numerical simulation results show that the control method can effectively suppress the first-order and second-order vibration of the beam and verify the effectiveness of the control strategy.