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Control of Chaotic and Hyperchaotic Systems
Published in Wilfrid Perruquetti, Jean-Pierre Barbot, Chaos in Automatic Control, 2018
As mentioned by Prigogine and Stengers [46], the more complex a system is, the more numerous are the perturbations, disturbances, or fluctuations that threaten its stability. As the system becomes more vulnerable to these disturbances, its energy requirement increases as it tries to maintain its structural properties. In contrast, any chaotic system can be considered as having its own limited energy source. Therefore, by controlling only one or several states, the system may be able to stabilize itself by using its own energy source. Such notions are interesting enough to motivate the consideration of the system energy for both designing control laws and taming chaos. Following this purpose, an energy-based control strategy for chaotic (possibly hyperchaotic) systems was proposed [37, 38]. This strategy mainly consists in a Variable Structure Control (VSC) approach which considers explicitly the system energy for both controller design and system stabilization. More precisely, with this strategy, the control objective is to regulate the system energy with respect to a shaped, nominal representation, implicitly related to system trajectories, robustness, and performance. From a more technical viewpoint, this control approach can be presented as follows.
Precise Position Control of Piezo Actuator
Published in Bogdan M. Wilamowski, J. David Irwin, Control and Mechatronics, 2018
Jian-Xin Xu, Sanjib Kumar Panda
Sliding mode control (SMC) has been proven to be a powerful control method for the complex nonlinear systems [7,8]. The underlying idea of SMC is to design a variable structure control law such that the system state is forced to reach and stay on a predefined surface, called sliding surface.
Integral sliding mode control of networked robotic manipulator: a dynamic event-triggered design
Published in Advanced Robotics, 2023
Krishanu Nath, Manas Kumar Bera
In a real-time application, the design of ETC for practical systems is an open challenge. One such challenging control problem is the motion control of robotic manipulators connected in a cyber-physical framework. The control of networked robotic manipulators is an active area of research where high precision and robust tracking of the desired trajectories is demanded under the adverse influence of imperfect models and external disturbances with limited network resources [13]. The design of controllers for robotic manipulators with ETC can be found in [14–16] and the references therein. In these works, it has been highlighted that the deployment of ETC for the networked application of robotic manipulators leads to reduced usage of the shared communication network and the computational hardware. Also, these works on ETC are based on feedback design using backstepping like adaptive control laws, where robustness is not guaranteed. As the manipulators are working in a dynamic environment, there exists a mismatch between the model and physical hardware. To ensure robustness against the mismatch or uncertainty, a nonlinear robust control technique known as sliding mode control (SMC) [17] is a potential candidate. SMC is a variable structure control with inherent properties to compensate for the matched perturbations. The conventional continuous-time design of various forms of SMC has been widely used for the control of robotic manipulators, and related works can be found in [18,19] and the references therein.
A Novel Conformable Fractional-Order Terminal Sliding Mode Controller for a Class of Uncertain Nonlinear Systems
Published in IETE Journal of Research, 2023
Variable structure control (VSC) is a well-known and efficient method for the control of uncertain systems. Emelyanov proposed VSC for the first time in [1]. In [2], an integral VSC was designed to enhance its robustness. Sliding mode control (SMC) is an effective VSC approach that has attracted considerable attention. It has several advantages, such as robustness against uncertainties and disturbances, a simple control scheme, and excellent performance. Classic SMC with good performance needs high control effort. Furthermore, an important drawback of SMC is that the system states are not guaranteed to reach an equilibrium point in finite time. So, terminal sliding mode control (TSMC) was introduced to overcome this problem. It can improve the transient performance [3]. However, TSMC has two drawbacks. The first is a singularity problem that may result in the unboundedness of the control input. Therefore, the non-singular TSMC (NTSMC) approach was proposed to solve the singularity problem. The second is that low convergence speed for the system state is far from the equilibrium point. Therefore, fast terminal sliding control (FTSMC) was proposed in [4]. In [5], an adaptive non-singular integral terminal sliding mode (ANITSMC) scheme was designed for trajectory tracking control of autonomous underwater vehicles with uncertainties and time-varying external disturbances. In [5], the proposed scheme has a slow convergence rate for the states that are far from the equilibrium point. So, to tackle this problem, an adaptive fast non-singular ITSMC controller was proposed in [6].
Implementation of higher order sliding mode control of DC–DC buck converter fed permanent magnet DC motor with improved performance
Published in Automatika, 2023
Dhanasekar Ravikumar, Ganesh Kumar Srinivasan
Variable structure control (VSC) is a viable control which controls any kind of non-linear systems in an effective way. This increases the attraction of control engineers to implement the same for various practical applications [12]. VSC with SMC is especially meant for attracting to control the nonlinear systems due to its capabilities in invariance, robustness, order reduction and chattering free [13]. SMC is a variable structure approach which can be applicable to various types of non –linear systems. This approach involves discontinuous control law which forces the system trajectory into the specified sliding surface and maintains the trajectory in the surface. SMC is characterized by its new concept, robustness to uncertainties and low sensitive to parameter variations. Regardless of the robustness properties the major drawback is a chattering effect in real time implementation [14].