The designed BSMC provides an effective robust **control** approach for quadrotor system Eq. (18). How- ever, the **control** laws Eq. (25), Eq. (26), Eq. (27), Eq. (28), Eq. (29), Eq. (30) and Eq. (31) can cause the chattering phenomenon resulting from the use of the sign function. In this context, high switching gain k i will lead to an increase in oscillations of the con- trol input signal, and therefore an excitation of high- frequency dynamics will take place, as results, a chat- tering phenomenon will be created. However, increas- ing the gain causes an increase of the oscillations in input **control** around the **sliding** surface. Moreover, a decrease in switching gain k i can reduce the chatter- ing phenomenon and improve the tracking performance despite large external disturbances. To achieve more appropriate performance, this gain must be adjusted. This adjustment is **based** on the distance between the system states and the **sliding** surface. i.e., when the trajectory of the system state deviates from the **sliding** surface, the switching gain should be increased in order to reduce chattering and vice versa. This idea can be realised by combining **Fuzzy** logic with **Backstepping**- **Sliding** **Mode** **Control** to construct FBSMC to facilitate the adaptive switch-gain (see Fig. 2) according to some appropriate **fuzzy** rules. The Architecture of the FLS is shown in Fig. 3.

Show more
12 Read more

nonlinear adaptive **control** **based** on **backstepping** techniques [4,5]. The increasing numbers of works involve linear **control**, nonlinear **control** and intelligent **control** methods. It is found that nonlinear **control** strategy has been an efﬁcient approach [6]. Veysi [7] designed an optimal **fuzzy** **sliding** **mode** controller for controlling the end-effector position in the task space. Feedback linearization method and **sliding** **mode** con- trol (SMC) were employed to overcome the uncertain- ties. Soltanpour [8] designed a **sliding** **mode** controller to **control** the position tracking of robot manipulator. The controller had global asymptotical stability in the presence of uncertainties and unmodelled dynamics. Yao [9] synthesized a robust integral of the sign of the error controller and an adaptive controller via back- stepping method for motion **control** of a hydraulic rotary actuator. The controller guaranteed asymptotic tracking performance in the presence of various uncer- tainties. **Fuzzy** **control** using linguistic information possesses several advantages such as robustness, model-free and universal approximation theorem. Wang and Mendel [10,11] proposed that **fuzzy** logic systems were capable of uniformly approximating any nonlinear function. **Fuzzy** logic system is useful for plants having difﬁculties in deriving mathematical models. SMC has been given much attention by indus- trial and academic communities. It is usually utilized to **control** the systems facing uncertainty. It has advan- tages in having a simple structure and being robust against the parameter uncertainties [12]. The disad- vantage of SMC is the chattering problem of **control** action due to its discontinuous switching part in

Show more
11 Read more

especially in traffic jams or long-distance driving cir- cumstances. However, the wheel slip **control** is the basis of active safety **control** systems and intelligent driver assistance systems. For instance, the anti-lock brake system (ABS) regulates the slip of each wheel at its optimum value to prevent it from locking during braking, such that the shortest stopping distance is achieved and the capability of directional stability and steer-handling is maintained [4]. The electronic stability program (ESP) may produce additional yaw moment by commanding the target slip of one or two wheels to prevent vehicle from spinning and drifting out of lane [29]. Finally, the adaptive cruise **control** system (ACC) can follow target speed or forward ve- hicle at the desired safety headway distance by com- manding the target slip of the wheels and the target torque of the power system [16]. As a consequence, de- signing the wheel slip controller has important theo- retical and practical significance for active safety con- trol systems and intelligent driver assistance systems. In recent years, many **control** approaches which are robust against system uncertainty and external dis- turbance have been proposed for the wheel slip con- trol due to the modeling errors, the measurement or estimation errors, and the changing of external en- vironment conditions of the wheel dynamic system, such as **sliding** **mode** **control** [23], hybrid **control** [25] and **fuzzy** **control** [13], etc. Johansen et al. [9] established the speed-dependent nominal linearized slip model with a perturbation term as a basis for the wheel slip **control**, and utilized gain-scheduled LQR approach to design the gain matrices of the **control**- ler. Pasillas-Lépine [19] adopted wheel deceleration logic-**based** switching and wheel dynamic model to design the five-phase anti-lock brake algorithm, and proved the existence and stability of limit cycles by the Poincaré map. Hsu [7] proposed an intelligent exponential **sliding**-**mode** **control** strategy for ABS, and a functional recurrent **fuzzy** neural network uncertainty estimator was designed to reduce the chattering of the exponential **sliding**-**mode** **control** strategy by approximating and compensating the unknown nolinear term of ABS dynamics on-line. Jing et al. [8] presented a switched **control** strategy for the anti-lock brake system and then analyzed the stability condition of the closed-loop system by Lyapunov-**based** method in the Filippov frame- work. The proposed **control** strategy in [7-9, 19] may

Show more
13 Read more

In this paper, a robust chattering free **backstepping** **sliding** **mode** controller is successfully developed for attitude stabilization and trajectory tracking of a quadrotor helicopter perturbed by external disturbances. First, the mathematical model of the quadrotor is introduced. Then, the proposed robust **control** system comprises a **backstepping** and a switching function is developed. The **backstepping** **control** design is derived **based** on Lyapunov function, so that the stability of the system can be guaranteed, while switching function is used to attenuate the effects caused by external disturbances. In order to eliminate the chattering phenomena, the sign function is replaced by the **fuzzy** system. Finally, the developed **control** scheme is applied to autonomous quadrotor helicopter. Simulation results show that a satisfactory **control** performance can be achieved by using the developed **control** system. Furthermore, it can be seen that a **fuzzy** system can be utilized to eliminate a chattering phenomena in the **control** inputs of the BSMC.

Show more
The application of adaptive neural networks to robot manipulator is presented in Perez et al. (2012) which explain recurrent neural networks and Lyapunov function methodology. An adaptive type-2 FLC for flexible-joint manipulators with structured and unstructured dynamical uncertainties have introduced in (Chaoui et al., 2012). In Abdel et al. (2011), the author has proposed **fuzzy** partition to the state variables **based** on the Lyapunov **synthesis**. Authors in Zeinali and Notash (2010) and Ho et al. (2009) have presented a methodology that enables the designer to systematically derive the rule base of the **control**. In Kohrt et al. (2013), authors have discussed on-line robust **control** for robot manipulator. This paper presents a new adaptive SMC for 2DOF robot manipulator; an adaptive tracking controller with a PID **sliding** surface. The adaptive SMC algorithm can estimate the value of switching gain constant (K w ) and boundary

Show more
14 Read more

There are all kinds of abundant marine resources in the ocean, such as mineral, marine organisms and ocean energy. Most of these resources are not fully developed to date. Therefore, many new devices and equipments are developed for ocean applications such as ocean surveillance and measurements. **Unmanned** underwater vehicles (UUVs) are the most widely used equipment nowadays. The features of UUVs are unoccupied, reliable and highly maneuverable. An underwater vehicle will complete missions as instructed, and exchange information and data with the ship or station. Generally speaking, UUVs can be applied for scientific research, acquiring information of oceans. They can also be used for inspections and operations of the facilities under the water [1,2,3] .

Show more
In recent years, advanced **control** has been applied in many engineering practices [20-22]. Advanced **control** in- cludes predictive **control**, **fuzzy** **control**, neural **control**, nonlinear **control** and robust **control** et al, and it has better **control** effect than the traditional PI controller. From the section II, we know that the mathematical model we estab- lished is a second-order model. Thus, we construct the virtual controller by using **backstepping** **control**. **Backstepping** **control** is a kind of nonlinear **control**, and it is widely used in the **control** of higher-order models [23]. In order to reduce the differential process of the controller, we introduce the command-filter in the controller [24]. The work in [25] applies command-filtered **backstepping** **control** to nonlinear multi-agent tracking problems. The controller is designed and the stability of the system is verified **based** on Lyapunov stability theory. It can be seen from simulation that the designed controller has satisfactory **control** performance. In the model established for the PV system, the pa- rameters of the resistance, inductance, and capacitance in the circuit are included. However, the measurement of these

Show more
18 Read more

factors, but the acquisition of **fuzzy** rules depends on the knowledge of the designers. Ref. [6] provides a neural network direct adaptive **control** method, and this method is applied to the **control** of AUV with bounded external disturbances and bounded neural network approxima- tion errors, and verified by dynamic positioning and sin- gle degree of freedom (DOF) trajectory tracking. In Ref. [8], the ocean current disturbances and AUV dynamic modeling uncertainty are considered as uncertainties, the above two uncertainties are combined; then the radial basis function (RBF) neural network is used to approxi- mate the uncertainties online, and the adaptive **sliding** **mode** **control** is adopted to **control** the AUV. However, in Refs. [6–9], the forward neural network (such as RBF or BP neural network) is difficult to reflect the time series influence of system input and output variables. There- fore, when the target trajectory of AUV has an abrupt change, the neural network weights may take a long time to convergence, leading to poor transition characteris- tics in trajectory mutation process, and may result in the overshoot of trajectory tracking.

Show more
16 Read more

Abstract. In this paper, an adaptive **fuzzy** **backstepping** **control** using dynamic **sliding** **mode** **control** (AFBCDSMC) is presented for a micro-electromechanical system (MEMS) vibratory z-axis gyroscope. **Based** on an adaptive **fuzzy** **backstepping** **control** method, a dynamic **sliding** **mode** **control** is proposed to compensate and adjust the external disturbances and model uncertainties. The **fuzzy** **control** method with adaptive **backstepping** controller can approximate the system nonlinearities well without accurate system model and. It can make the controller have the ability to learn and adjust the **fuzzy** parameters in real time. In addition, dynamic **sliding** **mode** **control** can transfer discontinuous terms to the first-order derivative of the **control** input in order to effectively reduce the chattering. Simulation studies are investigated to demonstrate the satisfactory performance of the proposed method.

Show more
PMs have strong non-linearity and time-varying properties [22], which may cause difficulties in implementing precise **control** [23]. In order to solve these problems, a variety of **control** approaches have been developed. Zhao et al. [24] used neural network to adjust the parameters of PID controller. However, the method has the problems of long response time, poor tracking on desired trajectory and low tracking accuracy in the step response experiment. Zhang et al. [25] proposed a hybrid **fuzzy** controller to **control** the elbow exoskeleton robot actuated by PMs. However, this method cannot estimate the external disturbance when chattering happens, resulting in a large overshoot of step response. For the safety of human-robot interaction, Choi et al. [26] proposed a new approach to **control** the compliance and associated position independently. However, when an external disturbance occurs suddenly, the **control** method cannot detect the external disturbance quickly and it takes a long time to re-track the desired trajectory. Meng et al. [9] proposed an iterative feedback tuning **control** method for the repetitive training. However, the actual trajectory changed in a ladder shape because the external disturbance cannot be estimated. Jiang et al. also [27] proposed an adaptive **fuzzy** **control** algorithm **based** on neural network optimization to **control** the humanoid lower limb device driven by pneumatic muscles. However, this method cannot achieve high-accuracy tracking **control** and the error would significantly increase when the external load changes.

Show more
21 Read more

In this paper, a composite nonlinear controller has been proposed for the IM flux and speed **control** that is robust to all electromechanical parameter variations and uncertainties. First a **backstepping** controller is designed for a three-phase IM. This controller provides speed and flux tracking for desired trajectories, but it needs electrical and mechanical parameters to be known and if some uncertainties exist in the **control** system, the controller can not do its rule properly. So, to

12 Read more

The rollover stability has become the focus of the world automobile research in recent years.Differential braking can reduce the inhibition of lateral acceleration, yaw velocity and does not change the purpose of the driver, but the cost is low.Therefore,using differential braking to improve the vehicle roll stability is a better choice.The paper [1] has proposed a nonlinear asymptotic tracking **control** strategy to ensure the reference yaw angle **control** strategy to prevent rollover. The paper [2] has improved the stability of the car through direct yaw moment **control**, using optimal LQR **control** strategy. The paper [3] has established a nonlinear vehicle model developing a differential braking stability **control** and a **fuzzy** logic controller. The paper [4]has built a vehicle stability **control** by using model predictive **control** theory framework tolimit the maximum roll angle of the car. The linear matrix inequality (LMI) used in this paper is a powerful tool for the design of **control** field, to construct the effective computer algorithm for solving problems[5]. Before the linear matrix inequality (LMI) are widely used in **control** ,most problems are solved by method of Riccati equation or inequality method [6-8].In the processing of the solution of the Riccati equation or inequality, there are a large number of parameters and the positive definite symmetric matrices to be adjusted. The linear matrix inequality method can make up the shortcomings of Riccati equation method.

Show more
The **sliding** **mode** **control** is robust to plant uncertainties and insensitive to external disturbances. It is widely used to obtain good dynamic performance of controlled systems. However, the chattering phenomena due to the finite speed of the switching devices can affect the system behavior significantly. Additionally, the **sliding** **control** requires the knowledge of mathematical model of the system with bounded uncertainties. Reduced chattering may be achieved without sacrificing robust performance by combining the attractive features of **fuzzy** **control** with SMC. **Fuzzy** logic is a potent tool for controlling ill-defined or parameter-variant plants. By generalizing **fuzzy** rules, a **fuzzy** logic controller can cope well with severe uncertainties. **Fuzzy** schemes with explicit expressions for tuning can avoid the heavy computational burden [11-14].

Show more
A lot of efforts have been devoted to PV micro-grid in the past. In reference [9], a fractional order **sliding** **mode** controller was applied to an islanded distributed energy resource system, and the output voltage tracking **control** was realized. However, in the simulation, the authors used the DC source instead of the distributed energy . When the PV array was connected to the DC side of the system, the **control** effect of the designed controller was unknown. The work in [10] proposed a voltage and frequency **control** strategy for the distributed energy resource system, different types of loads were used to be simulated the **control** effect , and the parallel operation of multiple distributed-resource units was simulated. However, there was no use of the distributed energy resource in the author’s simulation, and the energy storage unit was not considered in the system. Also in the work of [11], the maximum power point tracking (MPPT) was realized through the use of **sliding** **mode** **control**. Then the Lyapunov function-**based** **control** method was utilized in VSC, the simulation showed that the controller had better **control** effect. However, the **control** algorithm presented in this work possessed some limitations, and the **control** effect also had space for improvement , in addition, the energy storage unit was also not considered in the system.

Show more
18 Read more

Voice coil motor (VCM) has excellent characteristic of its simple structure, low friction between motor and motor device and ability of high-frequency repeatability movement. The VCM is used in the applications of linear positioning **control** systems with small **control** range, such as an optical read/write head of a hard disk [1]. However, the dynamic equation of a VCM is difficult to obtain due to the nonlinear and time- varying motor behaviors. From the **control** design viewpoint, the conventional **control** technologies are always **based** on a good understanding of the **control** system dynamics, so it is very difficult to **control** a VCM by using conventional **control** theory.

Show more
In order to improve the performance of single-input single-output (SISO) nonlinear systems with uncertainties, an adaptive **fuzzy** **sliding** **mode** controller (AFSMC) that combines linearization feedback is presented in this paper. The **fuzzy** logic system is used to approximate the unknown system function and the AFSMC algorithm is designed by used of **sliding** **mode** **control** techniques. **Based** on the Lyapunov theory, the continuous function is designed to eliminate the chatting action of the **control** signal. The simplicity of the proposed scheme facilitates its implementation and the overall **control** scheme guarantees the global asymptotic stability if all the signals involved are uniformly bounded. Simulation results have shown that the proposed controller shows superior tracking performance. AFSMC can effectively achieve desired performance and have much more advantages over conventional SMC.

Show more
The most common form of electromechanical drive for industrial, commercial and domestic applications is an Induction machine due to its cost, reliability and performance. Induction machines have simpler and more rugged structure, higher maintainability and economy than DC motors [1]. Basically, there are two types of instantaneous electromagnetic torque-controlled AC drives used for high performance applications. They are Vector **Control**(Field oriented **control**) and Direct Torque **control**. **Based** on operating principles these two methods are different, but their aims are same. Vector **Control** is **based** on stator current **control** in the field rotating reference using PWM inverter **control**. And Direct Torque **Control** (DTC) is **based** on stator flux **control** in the stator fixed reference frame using direct **control** of the inverter switching.

Show more
12 Read more

In this paper, an adaptive **fuzzy** **sliding**-**mode** controller (AF-SMC) **based** on fractional calculus for uncertain chaotic nonlinear systems were proposed. Three **fuzzy** logic systems were designed to approximate the unknown system functions and the switching term of SMC, respectively. Stability of the closed-loop system was proved and adaptive laws for the tuned parameters were obtained by using Lyapunov arguments. Numerical simulations are done on the chaotic nonlinear gyroscope system and results show that the proposed fractional

Show more
linear matrix inequalities techniques to **control** the velocity of a dc motor driven by a dc/dc Buck converter, was presented. The results showed, via numerical simulations, that the proposed **control** scheme guarantees fast angular velocity tracking with minimal duty cycles. More recently, in 2013, Sira-Ram´ ırez and Oliver-Salazar [14] described a robust **control** law **based** on active disturbance rejection **control** and flatness-**based** **control**, taking into account an unknown time-varying load, for two combinations of dc/dc Buck converters and dc motors. Numerical simulations showed the robustness of this technique for the angular velocity **control** of the motor shaft. Finally, in 2013, Silva- Ortigoza et al. [15] introduced a two-stage **control** **based** on differential flatness for the angular velocity **control** without taking into account velocity measurements of a dc/dc Buck converter–dc motor system. They showed, through numerical simulations that included an Σ − Δ modulator, that the proposed **control** scheme effectively provides robustness to the tracking performance when parametric uncertainties related to the system appear. Additionally, important contributions related to the connection of other dc/dc power converters and dc motors have been reported in [8], [16]–[23].

Show more
14 Read more

In [1], an active safety system was developed **based** on the by-wire technologies to improve yaw moment **control** system that depends on the braking action on the left and right wheels. Other types of active steering systems have been reported such as Active Front Steering (AFS) [2] [3] [4], Active Rear Steering (ARS) [5] and Active Four Wheel Steering (W4S) [6]. Active steering is an effective way that can improve drivers comfort and handling. The vehicle handling and lateral stability can be controlled at the same time, if both the external yaw moment and active steering angle are adopted [7].

Show more