Neng-Sheng Pai

Generalized Projective Synchronization for the Horizontal Platform Systems via an Integral-type Sliding Mode Control

In this paper, an integral-type sliding mode controller design for generalized projective synchronization of two horizontal platform systems (HPS) is considered. The concept of extend systems is used such that continuous control input is obtained using a sliding mode design scheme. Based on the Lyapunov stability theorem, control laws are derived. It is guaranteed that under the proposed control law, an uncertain slave chaotic HPS can asymptotically track a master chaotic HPS. The converging speed of error states can be arbitrarily set by assigning the corresponding dynamics to the sliding surfaces. Numerical simulations are shown to verify the results and this control law can be applied to another chaotic system of the same design scheme.

Fuzzy logic combining controller design for chaos control of a rod-type plasma torch system

The nonlinear behavior analysis and chaos suppression control for a rod-type plasma torch system was discussed in the paper. The scenarios for the possible non-linear behavior in the plasma torch dynamics were also obtained with respect to the variation of system parameter @m via the numerical simulations, which might provide a guide for finding non-linear phenomena in the practical application of the plasma torch. From the bifurcation diagram, it shows that the plasma torch dynamics exit undesired chaotic behavior. In order to suppress the irregular chaotic motion, a fuzzy logic controller (FLC) that combines a sliding mode controller (SMC) and a state feedback controller (SFC) with guaranteed closed loop stability is designed. Each rule in this FLC has an SMC or an SFC in the consequent part. The role of the FLC is to schedule the final control under different antecedents. It is guaranteed that under the proposed control law, the rod-type plasma system with undesired chaotic motion can asymptotically stabilize to the unstable equilibrium point i.e. zero state. More importantly, the controller thus design can keep the advantages and remove the disadvantage of the two conventional controllers. Numerical simulations show the high performance of this method for chaos elimination in rod-type plasma torch system.

Robust Control Method Applied in Self-Balancing Two-Wheeled Robot

Since the beginning of the new millennium, the self-balancing two-wheeled robot (SBTWR) has become more and more popular due to its responsive yet precise movement and pollution-free. This paper is devoted to investigating both the dynamics analysis and the balance control for a SBTWR which is inherently unstable. In this dissertation, we present a robust control algorithm to stabilize the unstable SBTWR. By the Lyapunov stability theory with control term, a suitable sliding surface is proposed to ensure the stability of the controlled closed-loop system in sliding mode. Then, a sliding mode controller is designed to guarantee the hitting of the sliding surface even when the system contains system uncertainties and external disturbances. A computer simulation demonstrates the feasibility of the proposed control schemes.

Robust Exponential Converge Controller Design for a Unified Chaotic System with Structured Uncertainties via LMI

This paper focuses on the chaos control problem of the unified chaotic systems with structured uncertainties. Applying Schur-complement and some matrix manipulation techniques, the controlled uncertain unified chaotic system is then transformed into the linear matrix inequality (LMI) form. Based on Lyapunov stability theory and linear matrix inequality (LMI) formulation, a simple linear feedback control law is obtained to enforce the prespecified exponential decay dynamics of the uncertain unified chaotic system. Numerical results validate the effectiveness of the proposed robust control scheme.

Application of CMAC Neural Network to Solar Energy Heliostat Field Fault Diagnosis

Solar energy heliostat fields comprise numerous sun tracking platforms. As a result, fault detection is a highly challenging problem. Accordingly, the present study proposes a cerebellar model arithmetic computer (CMAC) neutral network for automatically diagnosing faults within the heliostat field in accordance with the rotational speed, vibration, and temperature characteristics of the individual heliostat transmission systems. As compared with radial basis function (RBF) neural network and back propagation (BP) neural network in the heliostat field fault diagnosis, the experimental results show that the proposed neural network has a low training time, good robustness, and a reliable diagnostic performance. As a result, it provides an ideal solution for fault diagnosis in modern, large-scale heliostat fields.

Robust Controller Design for Modified Projective Synchronization of Chen-Lee Chaotic Systems with Nonlinear Inputs

This study demonstrates the modified projective synchronization in Chen-Lee chaotic system. The variable structure control technology is used to design the synchronization controller with input nonlinearity. Based on Lyapunov stability theory, a nonlinear controller and some generic sufficient conditions can be obtained to guarantee the modified projective synchronization, including synchronization, antisynchronization, and projective synchronization in spite of the input nonlinearity. The numerical simulation results show that the synchronization and antisynchronization can coexist in Chen-Lee chaotic systems. It demonstrates the validity and feasibility of the proposed controller.

Bifurcation analysis of a microcantilever in AFM system

The atomic force microscope system (AFM) has become a popular and useful instrument to measure the intermolecular forces with atomic resolution that can be applied in electronics, biological analysis, materials, semiconductors, etc. This paper studies the bifurcation phenomenon and complex nonlinear dynamic behavior of the probe tip between the sample and microcantilever of an atomic force microscope using the differential transformation method. The dynamic behavior of the probe tip is characterized with reference to bifurcation diagrams, phase portraits, power spectra, Poincare maps, and maximum Lyapunov exponent plots produced using the time-series data obtained from differential transformation method. The results indicate that the probe tip behavior is significantly dependent on the magnitude of the vibrational amplitude. Specifically, the probe tip motion changes from T-periodic to 3T-periodic, then from 6T-periodic to multi-periodic, and finally to chaotic motion with windows of periodic motion as the vibrational amplitude is increased from 0 to 5.0. Furthermore, it is demonstrated that the differential transformation method is in good agreement for the considered system.

Corrigendum: Comments on Fuzzy logic combining controller design for chaos control of a rod-type plasma torch system

The authors would like to make a notice that part of the introduction and system description sections of the work by Pai, Yau, and Kuo(2010) can be referred to the work by Liaw, Chang, Li, Huang, and Tzeng (2009) and should be cited even it was under the status of in pressat Journal of Aeronautics, Astronautics and Aviation. The problem considered by Pai et al. which focused on the design of an algorithm tostabilizethe chaotic rod-typeplasmatorch system,is stronglyinspiredbyProf. Liaw et al. whichoffersthe nonlinearbehaviorinarc plasmadynamics. The authors also like to make an acknowledgement to thank Prof. Liaw et al. for their kindness and inspiration.References

Adaptive Fuzzy Sliding Mode Controller Design for Lorenz System

This paper presents an adaptive fuzzy sliding mode control (AFSMC) scheme for chaos control of Lorenz system. In this scheme, the reaching law required to drive the system states of Lorenz system to the sliding surface is inferred by an adaptive technique and a set of fuzzy logic rules based upon the output of a sliding mode controller (SMC). The feasibility and effectiveness of the AFSMC scheme are demonstrated via a numerical simulation. The numerical results demonstrate the ability of AFSMC scheme to suppress the chaotic Lorenz system and reveal that the control signal is chatter free.

Bifurcation and nonlinear dynamic analysis of heart blood vessel system

Many studies have been shown and focused that variation of the quantity of vasoconstriction and blood pressure will cause the nonlinear chaotic behaviors in the heart blood vessel system and then induce the cardiovascular effect. Due to this kind of non-periodic motion is random and difficult to control, it is important to analyze and understand the status of dynamic system under different parametric conditions. In this paper, the differential transformation method is used to investigate the governing equations of system, and the dynamic behavior is characterized by reference to bifurcation diagrams, phase portraits, power spectra, and Poincaré map produced. The results indicate that the system behavior is significantly dependent on the magnitude of the vibrational amplitude. Specifically, the motion changes from T-periodic to 2T-periodic, then from 4T-periodic to 8-periodic, and finally to chaotic motion with windows of periodic motion as the vibrational amplitude is increased from 0.3 to 0.6. The results can be used as the basis for subsequent development of the control system design, and also reduced the possibility of cardiopathy.