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Summary: The attitude control problem of reusable launch vehicles (RLVs) is investigated based on multivariable supertwisting fixed‐time comprehensive control strategy. A novel multivariable supertwisting fixed‐time approach, which can guarantee that the states converge to zero within a fixed time, is proposed. According to the multiple time scale principle, the RLV attitude control system is divided into attitude angle subsystem and attitude angle rate subsystem. Based on multivariable supertwisting fixed‐time approach, comprehensive design of fixed‐time disturbance observer and controller is proposed to ensure that the attitude angle tracking error converges to zero within a fixed time. The features of the proposed control scheme contain that the settling time is independent of initial conditions and it has the better property of chattering reduction. Finally, the efficiency of the proposed method is verified through numerical simulation. [ABSTRACT FROM AUTHOR]

In this paper, a class of mismatched uncertain systems is investigated. And a novel sliding mode control design is presented. During the design process of the proposed control, a transformation scheme is proposed, which can easily transform the mismatched uncertain systems into matched systems. Based on the matched systems, a novel full order sliding mode surface is designed, which can avoid the singular issue of terminal sliding mode control. And a chattering alleviating scheme is also proposed, which can ensure that the sliding mode control is chattering free regardless of whether the conventional sliding mode control or the terminal sliding mode control is used. Compared with the recurrent controller, the complexity of the proposed controller is reduced. It is much simpler and easy to implement. Also, the need of system knowledge is also reduced. The control performance is validated by simulation. [ABSTRACT FROM AUTHOR]

The reaching law is an important part of a sliding-mode controller, which guarantees the existence of slidingmotion in finite time. Fast access to sliding motion with a weak chattering phenomenon in control input is always desired. In this paper, 2 different types of reaching laws are proposed, which guarantee finite-time convergence to the sliding manifold. Moreover, the reaching time is robust to initial conditions and can be designed by the user. Some useful discussions on the design of parameters are also presented to weaken the chattering phenomenon. A careful simulation study is finally provided to verify the effectiveness and efficiency of the proposed methods. [ABSTRACT FROM AUTHOR]

In this study, a new high order sliding mode controller (HOSMC), based on super twisting algorithm (STA), is proposed for vehicle active suspensions. It is well known that first order sliding mode controller (SMC) is insensitive to parameter variations and external disturbances. On the other hand, it suffers from chattering present in control signal that may harm the mechanical components of the system. Therefore, HOSMC is preferred in this study that attenuates chattering effectively while preserving its robustness. Proposed HOSMC uses an estimation for the equivalent part of the control signal and uses the STA for the discontinuous part of the control law. Additionally, the controller gains are obtained by offline multi-objective genetic algorithm search. Extensive simulations and experimental results are presented to reveal the performance of the proposed controller. First order SMC is also designed and used for comparison. The results indicate the superior performance of the proposed HOSMC. [ABSTRACT FROM AUTHOR]

In this paper, real-time results for a novel continuous-time adaptive tracking controller algorithm for nonlinear multiple input multiple output systems are presented. The control algorithm includes the combination of a recurrent high order neural network with block control transformation using a high order sliding modes technique as control law. A neural network is used to identify the dynamic plant behavior where a filtered error algorithm is used to train the neural identifier. A decentralized high order sliding mode, named the twisting algorithm, is used to design chattering-reduced independent controllers to solve the trajectory tracking problem for a robot arm with three degrees of freedom. Stability analyses are given via a Lyapunov approach. [ABSTRACT FROM AUTHOR]

A two-step formation-keeping control methodology is proposed that includes both attitude and orbital control requirements in the presence of uncertainties. Based on a nominal system model that provides the best assessment of the real-life uncertain environment, a nonlinear controller that satisfies the required attitude and orbital requirements is first developed. This controller allows the nonlinear nominal system to exactly track the desired attitude and orbital requirements without making any linearizations/approximations. In the second step, a new additional set of closed-form additive continuous controllers is developed. These continuous controllers compensate for uncertainties in the physical model of the satellite and in the forces to which it may be subjected. They obviate the problem of chattering. The desired trajectory of the nominal system is used as the tracking signal, and these controllers are based on a generalization of the concept of sliding surfaces. Error bounds on tracking due to the presence of uncertainties are analytically obtained. The resulting closed-form methodology permits the desired attitude and orbital requirements of the nominal system to be met within user-specified bounds in the presence of unknown, but bounded, uncertainties. Numerical results are provided, showing the simplicity and efficacy of the control methodology, and the reliability of the analytically obtained error bounds. [ABSTRACT FROM AUTHOR]

The main obstacle of conventional sliding mode control is caused by discontinuous function of high control activity which is known as chattering phenomenon. In this research, the chattering phenomenon is significantly reduced by a newly developed algorithm. A fast sigmoid function with varying boundary layer algorithm is designed as a state-dependent to replace the discontinuous function in conventional sliding mode control. It is known that the switching gain of sliding mode control is proportional to the chattering level, and normally a large switching gain is applied to handle the uncertainties. This research proposes a state-dependent sliding mode control which is the switching gain and boundary layer is proportional to the sigmoid function of the sliding mode controller. As a result, the boundary layer and the switching gain will change depend on uncertainties of the motor drives system. The induction motor is controlled by vector control strategy, using indirect field orientation and Space Vector Pulse Width Modulation technique. Experimental result have proved that the proposed state-dependent sliding mode control able to deal with external load disturbances as well as effectively free from chattering phenomenon compared to conventional sliding mode control. The proposed algorithm and the vector control strategy are developed in digital signal processing board. The results have confirmed that the state-dependent sliding mode control is superior with regard to external load disturbances and variation in the reference speed setting when compared to conventional sliding mode control and fixed boundary layer sliding mode control. [ABSTRACT FROM AUTHOR]

Abstract: An innovative approach to adaptive fuzzy sliding mode control for a class of SISO continuous nonlinear systems with unknown dynamics and bounded disturbances is introduced in this paper. The main idea of the presented method consists in the introduction of the fuzzy self-tuning mechanism for adaptation of the sliding mode control parameters – extended feedback and switching gains. Such modification reduces the well-known chattering problem in classical sliding mode control. In comparison with the other algorithms eliminating this problem the proposed method results in faster convergence and more transparent and interpretable design of self-tuning mechanism. Moreover, the proposed method guaranteing the asymptotic reference signal tracking with bounded system signals can be easily implemented to high order systems. The performance of the presented control design is demonstrated on control of a nonlinear electro-hydraulic servo mechanism. [Copyright &y& Elsevier]

The article presents a study on the potential of the fuzzy sliding mode controllers (FSMC) as an alternative to the conventional sliding mode control. The simulation reveals the effectiveness of the FSMC- multi input multi output (MIMO) controller technique based on the robustness and the tracking qualities of the proposed control system. The adding of the fuzzy logic controllers to the sliding mode controllers was used to reduce the chattering of the controller.

The concept of directional factor for chatter stability analysis has been used from a long time ago. The analysis of its evolution for different feed directions in milling processes provides a good way of selecting the best cutting conditions. For very stable cutting directions, corresponding to very low directional factors, the single frequency analysis gives unacceptable results and multi-frequency, or alternative solutions as semi-discretisation must be used. It is found also that the period doubling lobes extend at both sides of the tooth pass frequency equivalent to twice the natural frequency. In these cases, helix angle has a very important effect on the stability. For end milling processes, where the mill axial pitch can be of the order of the stable limit depth of cut, a very stable situation is found except in those areas corresponding to period doubling, where instability islands are found. Besides, a graphical construction for accurate estimation of the stable limit depth of cut and starting rotational speed of the period doubling lobes is proposed. [ABSTRACT FROM AUTHOR]

Chatter presents one of the main problems in quality of machined surfaces limiting tool life, productivity, and tolerances. Chatter in milling and turning operations has been extensively analyzed; however, drilling operations have been neglected due to the complexity of drilling tools and problems that develop in the modeling of the tool. In this paper, an overview of chatter vibrations and chatter suppression in drilling has been presented. Models such as torsional–axial model, bending model, and the combination of axial and bending models have been presented showing the different effects each considers. Influence of parameters such as drill geometry, chisel edge, drill flank, pilot hole, margin engagement, stick–slip interaction, gyroscopic effect, and rotary inertia effects has been incorporated into the various models. In addition, the problem of chatter analysis and suppression in micromachining processes has been investigated. The differences in macro- and micro-scale problems have been addressed giving an overview of the current research directions and future work for both areas. The paper presents experimental as well as simulation data with the comparison of the two for clear understanding of the complex problems of chatter in drilling operations. [ABSTRACT FROM AUTHOR]

This study focuses on the design of a backstepping particle-swarm-optimisation control (BSPSOC) for the on-line levitated balancing and propulsive positioning of a magnetic levitation (maglev) transportation system. The dynamic model of a maglev transportation system including levitated electromagnets and a propulsive linear induction motor (LIM) based on the concepts of mechanical geometry and motion dynamics is first constructed. The aim is to design an on-line particle-swarm-optimisation (PSO) control methodology to cope with the problem of the complicated control transformation and the chattering control effort in backstepping control (BSC) design, and to directly ensure the stability of the controlled system without the requirement of strict constraints, detailed system information and auxiliary compensated controllers despite the existence of uncertainties. In the proposed BSPSOC scheme, a PSO control is utilised to be the major control role, and adaptation laws derived from Lyapunov stability analyses are manipulated to adjust appropriate evolutionary coefficients. The effectiveness of the proposed control strategy for the maglev transportation system is verified by experimental results, and the superiority of the BSPSOC scheme is indicated in comparison with the total sliding-mode control (TSMC) and BSC strategies. [ABSTRACT FROM AUTHOR]

Chatter suppression is essential for achieving high precision and surface quality in machining processes. In this paper, a control strategy is presented for chatter suppression in cutting process in the presence of tool wear and parameter uncertainties. A single-degree-of-freedom model of a turning process in the orthogonal cutting configuration is used to set up the nonlinear delay differential equation of motion that includes the effects of tool flank wear. Uncertainties in cutting velocity, tool wear size and parameters of the dynamic model are included in the model of the cutting process. The force provided by a piezo-actuator is taken as the control input of the system. A sliding mode control scheme is used and an effective control law is derived that suppresses chatter. Results of stability analysis and sliding mode control for two distinct cases of sharp and worn tools are presented and compared, which show the effectiveness of the approach. [ABSTRACT FROM AUTHOR]

The drawbacks of Sliding Mode Control (SMC) in terms of high control gains and chattering are overcome by merging of the Fuzzy Logic Controller (FLC) with the variable structure of the SMC to form a Fuzzy Sliding Mode Controller (FSMC). This paper presents the study of stabilization with motion planning of the four rotors mini-flying robot (helicopter with four rotors) through the hybrid FSMC. Simulation results and a comparison with a SMC are presented and discussed. We studied the robustness of the two used controllers in the presence of disturbances. We presented the case of the white noise disturbances. This permits to prove the effectiveness of the proposed control law. [ABSTRACT FROM AUTHOR]

Abstract: The simplex sliding mode control method is further developed by considering uncertain control systems non-affine in the control law. In order to reduce chattering effects, a set of integrators is added in the input channels. The augmented system is then controlled by a switching logic based on the simplex control method. As a result, the original control vector turns out to be continuous. A second order sliding mode observer is used when the sliding output is not available. Explicit conditions are identified about systems uncertainties and the simplex geometry in order to guarantee the convergence of the proposed methodology. [Copyright &y& Elsevier]

This paper focuses on the design of reduced chattering sliding mode controllers and its application to the optimization of a wind energy system. It develops, in an accessible way, an enhanced control design method suitable for a wide range of engineering applications, namely those that accept a certain degree of discontinuous action in their input and that can be described as non-linear systems affine in the control with a vector of bounds for the uncertainties. The proposed systematic method is based on a geometric approach developed by the authors in a previous work. This new proposal reduces the chattering while maintaining the attractive features of tile original method, those are robustness, tuning simplicity and reaching mode control. Taking advantage of these attributes, a robust low chattering controller for an autonomous wind energy conversion system based on a permanent magnet generator is developed. [ABSTRACT FROM AUTHOR]

Abstract: In turning operations, a common problem that can drastically degrade the quality of a machined part is regenerative chatter. Proper machine design, such as increased stiffness and damping of the machine tool structure can broaden the range of stable operating conditions. However, the inherent geometry of the tool and workpiece can sometimes severely limit the range of stable cutting. In this case, active control is needed in order to allow for a sufficiently broad range of stability. This work investigates turning relatively compliant workpieces, therefore it is the body that undergoes the bulk of the motion during chatter. Since it is highly impractical to instrument the workpiece, a Neural Network trained with Particle Swarm Optimization is used to transform a radial displacement measurement made at the cutting tool to an estimation of the radial displacement of the workpiece. This could serve as an observer in a real time control system that could mitigate chatter by appropriately actuating an active toolholder such as a fast tool servo. The workpiece displacement was predicted with an average RMSE of 1.41 and 1.70μm for the two testing datasets. This current approach differs from other chatter detection investigations because with the direct displacement measurement of the toolholder and the output from the Neural Network observer, there is information about both bodies’ motions. In this way, direct conclusions can be made about the stability of cutting in a chatter detection scheme. In addition, the nature of the transition from stable cutting to chatter is investigated by experimentally measuring the variation in uncut chip thickness over time. [Copyright &y& Elsevier]

The levitation control in a linear magnetic levitation (maglev) rail system is a subject of considerable scientific interest because of highly nonlinear and unstable behaviours. The authors mainly focus on the sequential developments of backstepping-based control systems including a backstepping control (BSC), an adaptive BSC (ABSC) and an adaptive dynamic surface control (ADSC) for the levitated positioning of the linear maglev rail system. In the proposed ADSC system, a filter mechanism is incorporated with BSC to cope with the problem of the explosion terms caused by repeated differentiations in backstepping design procedure. Moreover, a robust observer is designed for predicting system uncertainties to solve the trouble of chattering phenomena caused by a sign function in BSC and ABSC law despite the utilisation of a fixed value or an adaptive tuning algorithm for the lumped uncertainty bound. The effectiveness of the proposed control schemes for the levitation control of a maglev system is verified by numerical simulations and experimental results, and the superiority of the ADSC system is indicated in comparison with the BSC and ABSC systems. [ABSTRACT FROM AUTHOR]

Proof-mass actuators have been considered for a broad range of structural vibration control problems, from seismic protection for tall buildings to the improvement of metal machining productivity by stabilizing the self-excited vibrations known as chatter. This broad range of potential applications means that a variety of controllers have been proposed, without drawing direct comparisons with other controller designs that have been considered for different applications. This article takes three controllers that are potentially suitable for the machining chatter problem: Direct velocity feedback, tuned-mass-damper control (or vibration absorber control), and active-tuned-mass-damper control (or active vibration absorber control). These control strategies are restated within the more general framework of Virtual Passive Control. Their performance is first compared using root locus techniques, with a model based on experimental data, including the low frequency dynamics of the proof-mass. The frequency response of the test structure is then illustrated under open and closed-loop conditions. The application of the control strategies to avoid machine-tool chatter vibrations is then discussed, without going into detail on the underlying physical mechanisms of chatter. It is concluded that virtual passive absorber control is more straightforward to implement than virtual skyhook damping, and may be better suited to the problem of machining chatter. [ABSTRACT FROM AUTHOR]

In this part of the paper series, chatter experiments are conducted in order to verify the proposed stability models presented in the first part (Ozlu, E., and Budak, E., 2007, ASME J. Manuf Sci. Eng., 129(4), pp. 726-732). Turning and boring chatter experiments are conducted for the cases where the tool or the workpiece is the most flexible component of the cutting system. In addition, chatter experiments demonstrating the effect of the insert nose radius on the stability limit are presented. Satisfactory agreement is observed between the analytical predictions and the experimental results. [ABSTRACT FROM AUTHOR]

The high-performance control of direct-drive (DD) systems requires the full system dynamic effects to be taken into account owing to the eliminated gear mechanism. The actuator dynamics and structural flexibilities become of increased importance, particularly when high-speed, high-accuracy operation of lightweight structures is aimed for; however, in most related literature, these effects are neglected to avoid increased computational complexity at the expense of compromising the tracking accuracy of the system in the transient and steady state. As a solution to the problem, in this study, high-order, sliding-mode (HOSM) controllers (HOSMCs) are developed, which exploit the robustness properties of sliding-mode controllers (SMCs) while also increasing accuracy by reducing chattering effects. Different from standard HOSMCs, which are derived by artificially increasing the system order, the third-order HOSM (3-HOSM) control laws in this study are derived by including the actuator dynamics and structural flexibilities in the control design process. Two HOSMCs are developed for this purpose: one with a discontinuous input and one with a continuous input aimed at reducing chattering. The performance of the novel HOSMCs is tested by simulations for the precise position and tracking control of a one-degree-of-freedom (1DOF) DD weapon-positioning system as an example of a direct-drive system under heavy uncertainties and external disturbances. The improved accuracy obtained, particularly with the novel continuous-input 3-HOSMC, motivates the implementation of the schemes for demanding control applications under heavy uncertainties. [ABSTRACT FROM AUTHOR]

This paper presents a robust control method, combining sliding mode control (SMC) and quantitative feedback theory (QFT) to track the tip of an inverted pendulum, subject to base excitation. A non-linear inverted pendulum (IP) model is considered to analyse tracking control characteristics through computer simulation in order to demonstrate the effectiveness of the proposed control methodology. The sliding mode control is used to track the trajectory of the tip of the inverted pendulum. However, when the system enters into sliding regime, chattering occurs due to switching delays as well as base vibrations. The chattering is eliminated with the introduction of QFT inside the boundary layer to ensure smooth tracking. Problems with noise amplification, resonances, presence of uncertainties, and unmodelled high-frequency dynamics can largely be avoided with the use of QFT over other optimization methods. In addition, the QFT design methodology guides design evolution rather than replacing human intervention as would appear to be the case in some control synthesis methodologies. [ABSTRACT FROM AUTHOR]

Abstract: We consider a linear model of a rotating Timoshenko beam, which is clamped at one end to a disk the other being free. The motion of the beam is controlled by the angular acceleration of the disk. We study the minimization problem of mean square deviation of the Timoshenko beam from a given position. For the minimization problem of the first mode we prove that optimal control is the chattering control, i.e., it has an infinite number of switches in a finite time interval. We construct a suboptimal control with a finite number of switches. To cite this article: M.I. Zelikin, L.A. Manita, C. R. Mecanique 334 (2006). [Copyright &y& Elsevier]

This paper proposes a nonlinear multi-input control law using sliding mode concepts for continuous-time, uncertain, linear systems. The control law introduces a state-dependent layer around the sliding mode plane to remove chattering. This layer combines two types of boundary layers: a constant layer and a sector-shaped layer. The states will always enter the state-dependent boundary layer and the choice of the sliding mode will be seen to determine the ultimate system performance. A proof of stability shows ultimate boundedness. The controller is applied to a nonlinear simulation model of a cart-pendulum and exhibits a high degree of robustness. The new boundary layer in connection with a novel dynamically changing, state-dependent gain can be used to obtain a narrow boundary-layer shape in the operating region of interest. This permits rejection of disturbances without chattering of the control and improves on the performance expected of a sliding-mode control with constant boundary layer. [ABSTRACT FROM AUTHOR]

Sliding mode control (SMC) methods possess several advantageous properties such as robustness against parameter variation, disturbance rejection, straightforward design, and are simple to implement. In this paper, a sliding mode control algorithm (which considers the non-linear friction dynamics) based on an equivalent control technique is designed and implemented on a non-linear induction machine system with non-linear friction dynamics such as Coulomb, windage, Stribeck, and static friction. The chattering phenomenon, which is inherent in the standard sliding mode algorithm, is discussed, as well as the techniques to reduce the chattering effect. A sixth-order non-linear induction machine model is employed for simulation analysis. The developed control algorithms are then tested for position control of a practical vector-controlled induction machine, in three different operating conditions (nominal load, high inertial load, and rotor resistance mismatch). The controller performance results are compared practically with several different sliding mode control algorithms as well as with a fixed-gain controller test. [ABSTRACT FROM AUTHOR]

Dynamic sliding mode control and higher order sliding mode are studied. Dynamic sliding mode control adds additional dynamics, which can be considered as compensators. The sliding system with compensators is an augmented system. These compensators (extra dynamics) are designed for achieving and/or improving the system stability, hence obtaining desired system behaviour and performance. Higher order sliding mode control and dynamic sliding mode control yield more accuracy and also reduce and/or remove the chattering resulting from the high frequency switching of the control. It is proved that certain J-trajectories reach a sliding mode in a finite time. A sliding mode differentiator is also considered. [ABSTRACT FROM AUTHOR]

Abstract: A frequency-domain method of the input–output analysis of a class of relay feedback systems is proposed. The approach is based on the notion of the locus of a perturbed relay system (LPRS). The proposed LPRS is defined as a characteristic of the response of a linear part to an unequally spaced pulse control of variable frequency in a closed-loop system. Consequently, the LPRS comprises oscillatory and transfer properties of the relay system. Formulas for computing the LPRS are derived. An example of input–output analysis is given. [Copyright &y& Elsevier]

A hybrid proportional-derivative–sliding mode control scheme is proposed for robot manipulators. This hybrid controller is composed of a proportional-derivative controller and a semi-continuous sliding mode controller. The hybrid controller has a robust performance in the reaching phase, which does not possess the invariance property of the sliding mode, and it has chattering-free characteristics in the sliding mode. Thus, the proportional-derivative–sliding mode hybrid controller has a robust performance in the whole control region. The controller was applied to a two-link SCARA (selective compliant articulated robot for assembly) robot manipulator. It was shown that the proposed control has a good transient response and trajectory tracking performance in the presence of model uncertainties. [ABSTRACT FROM AUTHOR]

In the sliding mode control with a boundary layer approach, the thickness of the boundary layer required to completely eliminate the control input chattering depends on the magnitude of the switching gain used. A controller with higher switching gain produces higher amplitude of chattering and thus needs to use a thicker boundary layer. On the other hand, the value of the switching gain used depends on the bounds of system uncertainties. Hence, a system with large uncertainties needs to use a thicker boundary layer to eliminate chattering. However, the control system is actually changing to a system without sliding mode if we continuously increase the boundary layer thickness in order to cater for systems with large uncertainties. To solve this problem, it is proposed here to use neural networks to model the unknown parts of the system nonlinear functions such that we can obtain a better description of the plant, and hence enable a lower switching gain to be used. The network outputs were combined with the available knowledge, which formed the so-called hybrid models, to approximate the actual nonlinear functions. The controller performance is demonstrated through simulation studies on a two-tank level control system and a continuous stirred tank reactor system. The results showed that the incorporation of networks has enabled a lower switching gain to be used, and thus the chattering in the control inputs can be eliminated even though with a thin boundary layer. [Copyright &y& Elsevier]

This paper proposes an approach of cooperative control that is based on the concept of combining neural networks and the methodology of sliding mode control (SMC). The main purpose is to eliminate the chattering phenomenon. Next, the system performance can be improved by using the method of SMC. In the present approach, two parallel Neural Networks are utilized to realize a neuro-sliding mode control (NSMC), where the equivalent control and the corrective control are the outputs of neural network 1 and neural network 2, respectively. Based on expressions of the SMC, the weight adaptations of neural network can be determined. Furthermore, the gradient descent method is used to minimize the control force so that the chattering phenomenon can be eliminated. Finally, experimental results are given to show the effectiveness and feasibility of the approach. [ABSTRACT FROM AUTHOR]

The presence of chatter in the connection management procedures of an Internet Draft transport protocol, the Datagram Congestion Control Protocol, is illustrated. Circumstances are identified in which the client and server repeatedly and needlessly exchange long sequences of packets. [ABSTRACT FROM AUTHOR]

We enhanced the bang-bang vibration control by using an electrical resonance mechanism. The bang-bang method is used in many engineering applications because of its simplified hardware configuration in which a constant-voltage supplier is shared by multiple actuators. However, its control performance is restricted, because the supplied voltage is constant and the sharp modulation of the control input induces chattering, which wastes a significant amount of energy. Our approach to overcome these problems was to combine the bang-bang method with tuned electrical resonance. Based on an elaborate analysis of phase relations between mechanical and electrical vibrations, three switching logics were devised for the hybrid method. Experiments on a 10-bay truss structure demonstrated that our hybrid method not only enhanced vibration suppression of the bang-bang method, but also prevented control chattering. [ABSTRACT FROM AUTHOR]