Design method of direct adaptive fuzzy sliding mode tracking control and application

This paper addresses the synthesis of control laws for the reorientation of a small nanosatellite spacecraft of the Cube- Sat standard in the case of severe degradation of actuator efficiency. Severe degradation (or reduction of efficiency) of actuators refers to a condition where the control torque generated by the actuator is reduced to 5 % of its maximum value under nominal operating conditions. The angular motion model accounts for gravitational, aerodynamic, and disturbance torques. The spacecraft reorientation problem is solved for the case of degradation in two control channels using sliding mode control. An original nonlinear sliding surface is used for the synthesis of the control laws. During the problem-solving process, quasi-adaptive and adaptive control laws were obtained, and their performance was compared using mathematical modelling. А quasi-adaptive control law is understood as a law in which the coefficients of the sliding surface are constant but depend on the initial angular velocity. An adaptive control law, on the other hand, is one in which the coefficients of the sliding surface change according to predefined differential equations. For adjusting the two coefficients of the sliding surface, an approach based on experimentally derived relationships between these two coefficients and the initial angular velocity was proposed and implemented. Based on the results of the numerical simulations, it can be concluded that the adaptive control law provides a shorter solution time compared to the quasi-adaptive control law. The quasi-adaptive law, however, is simpler to implement, as it does not require the adaptation of the coefficients.

ABSTRACTThis paper focuses on the practically predefined‐time adaptive sliding mode tracking control for uncertain non‐linear systems using time‐base generator (TBG) methods. Firstly, a novel and non‐singular predefined‐time sliding variable, which consists of a TBG and a hyperbolic tangent function, is proposed. In the sliding phase, the TBG ensures that the tracking error achieves practical predefined‐time convergence, while the hyperbolic tangent function guarantees that the tracking error converges to an adjustable region that is not explicitly related to the convergence bound of the sliding variable. Secondly, a special case of TBG is adopted to construct an auxiliary variable that guarantees the practical predefined‐time convergence of the sliding variable in the reaching phase. In the controller design, the radial basis function neural network (RBF NN) is used to approximate the lumped disturbance. Moreover, the inverse of the class‐ function is utilized as the control gain of the sliding mode controller to deal with the reconstruction error of the RBF NN and to predefine the convergence bound of the sliding variable. Finally, digital simulations are conducted by using an unmanned surface vehicle to demonstrate the validity of the theoretical results.

This paper presents a sliding mode control for the motion control of tethered space robot. The input saturation of tension and thrusters is well taken into account, which is dealt with by a modified adaptive law to aid the expression of ideal control input in Lyapunov-based stability analysis. The adaptive law is designed to be naturally bounded such that the boundary of adaptive law is calculable and fixed to make the ideal input bounded, which satisfies the condition of the partial expression of the ideal input. For reducing the effect from disturbance and uncertainties, the relay-type control law combined with the adaptive law is used to drive the system states onto the sliding surface although the saturation occurs. Numerical simulation illustrate the results of deployment process to verify the effectiveness of the stability analysis.

In this paper, a novel flow tracking control scheme for particleboard glue system with complex disturbance and unmeasurable system state is investigated. The method is based on hyperbolic tangent extended state observer and adaptive fuzzy fractional order global sliding mode control with exponential reaching law. The novel compound control scheme has the following advantages: Firstly, the extended state observer with hyperbolic tangent function can improve the estimation ability for the system state and complex disturbance without detailed knowledge of the controlled plant and disturbance model. Secondly, the global sliding mode control method based on fractional calculus can improve the response speed and robustness of the system, and provide a more flexible controller structure than the traditional sliding mode controller. Thirdly, the adaptive fuzzy controller is introduced to approximate the sliding mode switching term, so as to reduce the chattering phenomenon of the system. In addition, the convergence of the proposed observer and asymptotic stability of the control system are verified based on strict Lyapunov analysis. Finally, the numerical simulation results show the effectiveness of the proposed compound control scheme for particleboard glue system.

This study concerns the robust tracking control problem for an underactuated surface vessel with parameter uncertainties. In recent work by McNinch and collegeaues, a sliding mode control (SMC) law is presented and experimentally implemented for trajectory tracking of an underactuated autonomous surface vessel. The authors believe, however, their theory formulation involves essential flaws. Motivated by the obtained result by McNinch and collegeaues, a new revised SMC law is proposed under the same assumptions. The control law is similarly developed by introducing a first-order sliding surface in terms of surge tracking errors and a second-order surface in terms of lateral motion tracking errors; however, the desired surge and sway velocities are presented as a new form to guarantee the convergence of position tracking errors. Simulation results are provided to validate their method.

Neural network approximation-based backstepping sliding mode control for spacecraft with input saturation and dynamics uncertainty

This paper is concerned with the development of fully Autonomous Underwater Vehicles (AUVs) for deep ocean scientific and commercial applications. Specifically, it is regarding the design of automatic feedback control systems for AUV attitude control. The design method used in this paper formulates the AUV attitude control problem within the framework of the Optimal Control Theory. This approach determines an optimal control law that keeps the state of a dynamic system near a constant reference state while minimizing a quadratic cost functional. This study has developed four optimal control laws based on different performance criteria. First, the standard Linear Quadratic performance index was used to obtain a baseline control design. The LQR control law has been found to be undesirable because it resulted in a closed-loop system with fast and slow dynamics. In order to place the closed-loop eigenvalues close to each other, a pole placement algorithm has been used in connection with the LQR performance index. Two control laws have been designed based on this approach. Finally, a fourth design has been obtained by using a Hilbert Space Norm (also known as H/sub 2/ Norm or Root-Mean-Square) performance index. The main reason for designing a control law based on H/sub 2/ Norm performance index was to minimize the fuel consumption of the AUV for longer endurance. The stability and performance characteristics of the four optimal control laws have been analyzed via computer simulation and frequency response studies. All the closed-loop AUV systems exhibited overdamped response without any overshoot. Because the yaw and pitch channels have right hand zeros indicating the controllers have finite gain margins in these two channels. Hence, stability robustness of the AUV controllers can not be ignored and must be the subject of more detailed investigation in the future.

SummaryThis article investigates the fuzzy sliding mode tracking problem for discrete‐time nonlinear interconnected systems (ICSs) via a previewable information approach. First, an augmented system containing tracking errors and previewable reference and disturbance signals is established for discrete‐time nonlinear ICSs according to a previewable length. Second, novel sliding surfaces are given and some sufficient conditions of making the sliding motion asymptotically stable are derived in term of linear matrix inequalities (LMIs). Next, fuzzy sliding mode control (SMC) laws are designed so that the controlled system can reach the sliding surfaces and keep on them thereafter, and compared to not having previewable signals, these designed control laws can also enable system outputs to better track the reference signals asymptotically. Finally, a simulation example is given to demonstrate the effectiveness of the proposed control law.

In this paper, the sigma adaptive sliding mode control (SASMC) which is a combination of sliding mode control (SMC) and sigma adaptive law for a class of 2nd order nonlinear systems is developed. The proposed SASMC for the 2nd order nonlinear systems can overcome the drawbacks due to SMC. It can achieve a smaller mean tracking error than SMC, suppress chattering due to SMC, improve transient response due to modeling error, and reduce the gain of the controller.

In this paper, a novel adaptive interval type-2 fuzzy sliding mode control (AIT2FSMC) methodology is proposed based on the integration of sliding mode control and adaptive interval type-2 fuzzy control for chaotic system. The AIT2FSMC system is comprised of a fuzzy control design and a hitting control design. In the fuzzy control design, an interval type-2 fuzzy controller is designed to mimic a feedback linearization (FL) control law. In the hitting control design, a hitting controller is designed to compensate the approximation error between the FL control law and the interval type-2 fuzzy controller. The parameters of the interval type-2 fuzzy controller, as well as the uncertainty bound of the approximation error, are tuned adaptively. The adaptive laws are derived in the sense of Lyapunov stability theorem, thus the stability of the system can be guaranteed. The proposed control system compared to adaptive fuzzy sliding mode control (AFSMC). Simulation results show that the proposed control systems can achieve favorable performance and robust with respect to system uncertainties and external disturbances.

Critical non-structural equipment, including life-saving equipment in hospitals, circuit breakers, computers, high technology instrumentations, etc., is vulnerable to strong earthquakes, and on top of that, the failure of the vibration-sensitive equipment will cause severe economic loss. In order to protect vibration-sensitive equipment or machinery against strong earthquakes, various innovative control algorithms are developed to compensate the internal forces that to be applied. These new or improved control strategies, such as the control algorithms based on optimal control theory and sliding mode control (SMC), are also developed for structures engineering as a key element in smart structure technology. The optimal control theory, one of the most common methodologies in feedback control, finds control forces through achieving a certain optimal criterion by minimizing a cost function. For example, the linear-quadratic regulator (LQR) was the most popular control algorithm over the past three decades, and a number of modifications have been proposed to increase the efficiency of classical LQR algorithm. However, except to the advantage of simplicity and ease of implementation, LQR are susceptible to parameter uncertainty and modeling error due to complex nature of civil structures. Different from LQR control, a robust and easy to be implemented control algorithm, SMC has also been studied. SMC is a nonlinear control methodology that forces the structural system to slide along surfaces or boundaries; hence this control algorithm is naturally robust with respect to parametric uncertainties of a structure. Early attempts at protecting vibration-sensitive equipment were based on the use of existing control algorithms as described above. However, in recent years, researchers have tried to renew the existing control algorithms or developing a new control algorithm to adapt the complex nature of civil structures which include the control of both structures and non-structural components. The aim of this paper is to develop a hybrid control algorithm on the control of both structures and equipments simultaneously to overcome the limitations of classical feedback control through combining the advantage of classic LQR and SMC. To suppress vibrations with the frequency contents of strong earthquakes differing from the natural frequencies of civil structures, the hybrid control algorithms integrated with the wavelet-base vibration control algorithm is developed. The performance of classical, hybrid, and wavelet-based hybrid control algorithms as well as the responses of structure and non-structural components are evaluated and discussed through numerical simulation in this study.

This paper proposes a position tracking control scheme for the ball and plate system. At first, the property of the ball and plate control system is analyzed, and the path tracking control problem is divided into subproblems of ball position control and plate angle control. Afterwards, a path tracking sliding mode control algorithm is proposed for the ball position control based on dynamic model of the ball motion system and basic principle of sliding mode control, asymptotical stability of the close-loop system is proved mathematically through Lyapunov stability theory as well. The proposed sliding mode control algorithm eliminates the effect of time-varying uncertain friction while the ball is rolling on the plate surface, and thus the path tracking precision is improved. Finally, control performance of the proposed sliding mode control algorithm is validated by simulation experiment.

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 work we are interested to discrete robust fuzzy sliding mode control. The discrete SISO nonlinear uncertain system is presented by the Takgi- Sugeno type fuzzy model state. We recall the principle of the sliding mode control theory then we combine the fuzzy systems with the sliding mode control technique to compute at each sampling time the control law. The control law comports two terms: equivalent control law and switching control law which has a high frequency. The uncertainty is replaced by its upper bound. Inverted pendulum and mass spring dumper are used to check performance of the proposed fuzzy robust sliding mode control scheme.

This paper focuses in the design of an adaptive sliding mode control (SMC) for induction motor drives, that reduces the high frequency chattering that usually appears in the SMC schemes. The proposed design consist of a sliding mode control law that incorporates an adaptive switching gain. This adaptive switching gain avoids the need of calculating an upper limit of the system uncertainties as it is usual in the traditional SMC schemes. The proposed scheme uses the so-called field oriented control theory that allows to control the induction motor like a separately excited direct current motor drive, where the field flux (produced by the field current) and the armature flux (produced by the armature current) are decoupled. A stability analysis based on Lyapunov theory is also performed in order to guarantee the closed loop stability.