Chua’s Circuit Simulation Experiment Based on Saturation Function

This paper designs a Chua's diode circuit based on saturation function. It uses Matlab/Simulink to model Chua's circuit, and simulates and analyzes the dynamic behavior of chaos, the model simply generates efficient chaotic signals, and intuitively displays processes of the chaotic attractor, chaotic synchronization, period doubling and the road to chaos through the virtual oscilloscope, which is conducive to chaotic beginners' understanding of the basic characteristics and application of chaos. The electrical and mathematical analysis of the instrument is carried out by simulation, to explore the functions of each parameter, and helps beginners to understand its working principle more quickly and conduct experimental operations. It provides theoretical support for the improvement and optimization of Chua's circuit.

Robust Temperature Control of a Variable-Speed Refrigeration System Based on Sliding Mode Control with Optimal Parameters Derived Using the Genetic Algorithm

A sliding mode control (SMC) technique based on a state observer with a Kalman filter and feedforward controller was established for a variable-speed refrigeration system (VSRS) to ensure robust control against model uncertainties and disturbances, including noise. The SMC was designed using a state-space model transformed from a practical transfer function model, which was derived by conducting dynamic characteristic experiments. Fewer parameters affecting the model uncertainty were required to be identified, which facilitated modeling. The state observer for estimating the state variables was designed using a Kalman filter to ensure robustness against noise. A feedforward controller was added to the control system to compensate for the deterioration in the transient characteristics due to the saturation function used to avoid chattering. A genetic algorithm was used to alleviate the trial and error involved in determining the design parameters of the saturation function and select optimal values. Simulations and experiments were conducted to verify the control performance of the proposed SMC. The results show that the proposed controller can realize robust temperature control for a VSRS despite stepwise changes in the reference and external heat load, and avoid the trial and error process to design parameters for the saturation function.

Design and Characterization of Second Order Sliding Mode Controller for Pendulum System

The main purpose of this paper is to design a robust second order sliding mode controller that can deal with uncertain nonlinear systems. This controller can keep the main advantages of the first order sliding mode controller, such as the ability to make the system asymptotically stable by forcing the error and its derivatives to have a zero value, the simplicity in the operation, and the robustness in the existence of perturbations. In spite of the features that characterize the first order sliding mode controller (1 SMC), it still suffers from the unwanted phenomenon “chattering”, which originates from a discontinuous control part (sign function). In this context, saturation function can be used instead of sign function to reduce this problematic chattering. Different from the saturation function method, the second order sliding mode controller can be used to overcome the chattering; suffered by the first order sliding mode controller and to retain the stability and performance of the system. In this paper, the twisting and the super twisting second-order algorithms of the sliding mode controller were used, and their results were compared with the first order sliding mode controller. So, this subject focused on the chattering problem who suffers from it the 1 SMC and try to reduce it by using the 2 SMC, the uncertain pendulum system was adopted in this work for the purpose of checking the three controllers. The simulations results showed that the second order sliding mode controller has the ability to reduce both the chattering magnitude and the steady state error and achieve an asymptotically stable system. The results were obtained by using MATLAB programming.

Hybrid H-infinity synchronization for uncertain continuous chaotic systems based on digital redesign approach

In this paper, the design of hybrid H-infinity synchronization control for continuous chaotic systems based on sliding mode control (SMC) is considered. H-infinity discrete sliding mode controllers integrated with the digital redesign approach are newly designed to achieve robust chaos synchronization. By the proposed design procedure, an H-infinity discrete-time SMC can be easily obtained to guarantee the robustness of synchronization even if the system is disturbed with unmatched perturbations. Besides, since the saturation function is adopted to eliminate the unexpected chattering phenomenon, this paper also discusses the effect of saturation function in multi-input multi-output (MIMO) SMC and the upper bounds of sliding mode trajectories are obtained which is not indicated in the literature. Finally, we perform the simulation to verify the effectiveness of the proposed controller.

A Robust Control Scheme for a PVTOL System Subject to Wind Disturbances

In this study, a control scheme that allows performing height position regulation and stabilization for an unmanned planar vertical take-off and landing aerial vehicle, in the presence of disturbance due to wind, is presented. To this end, the backstepping procedure together with nested saturation function method is used. Firstly, a convenient change of coordinates in the aerial vehicle model is carried out to dissociate the rotational dynamics from the translational one. Secondly, the backstepping procedure is applied to obtain the height position controller, allowing the reduction of the system and expressing it as an integrator chain with nonlinear disturbance. Therefore, the nested saturation function method is used to obtain a stabilizing controller for the horizontal position and roll angle. The corresponding stability analysis is conducted via the Lyapunov second method. In addition, to estimate the disturbance due to wind, an extended state observer is used. The effectiveness of the proposed control scheme is assessed through numerical simulations, from which convincing results have been obtained.

Saturation-allowed zeroing neural networks activated by various functions for time-varying quadratic programming

Zeroing neural networks (ZNN) approach, has been presented to solve a lot of time-varying problems activated by monotonically increasing functions. However, the existing ZNN models for timevarying quadratic programming based on ZNN approach may be different from each other in structures, but share two common restrictions, i.e., the function must be convex and unbounded. In order to relax the above restrictions in solving time-varying quadratic programming (TVQP) problems, this paper proposes a saturation-allowed zeroing neural networks (SAZNN) model based on the ZNN approach. Comparing with existing models, the activation function (AF) of SAZNN model tolerates more kinds of functions, e.g., saturation function, non-convex function and unbounded function. Finally, this paper provides simulation results synthesized by the proposed SAZNN model activated by various AFs and verifies the superiority of the proposed SAZNN model in terms of convergence, efficiency and stability.