International Journal of Nonlinear Dynamics and Control (6 papers in press)
Design of Fuzzy Based Adaptive Controllers for Filtration Process
by Dauda Araromi, Olajide Ajala
Abstract: Filtration process uses membrane to separate solid components in a liquid suspension based on their size differences. However, the process is characterized with dynamic variability and uncertainty which makes its control difficult whenever a linear based control scheme such as conventional Proportional Integral Derivative (PID) is employed. Therefore, this work aimed to design adaptive controllers using fuzzy inference system to accommodate both the dynamic variability and uncertainty in filtration process. Experimental study was carried out on filtration unit where the slurry, a mixture of calcium carbonate (CaCO3) and water, was separated. The input and output data generated from the experiment consisted of one manipulated variable (feed pressure, Pr), one disturbance variable (concentration of the solute in the feed, Cs0) and one controlled variable (suspension concentration, Cs). The data were used to develop a model based on autoregressive integrated moving average exogenous input structure in the frame of fuzzy inference system. The fuzzy inference system was based on Takagi-Sugeno prototype. Adaptive controllers with fuzzy inference system were designed using pole placement and optimal control techniques. The controllers performances were compared with conventional PI controller using rise time, settling time and overshoot.
Keywords: Adaptive controller; PI controller; Overshoot; Takagi-Sugeno model; Fuzzy inference; MATLAB; Filtration process.
Nonlinear Modes of Large-Amplitude Ship Motion with Roll-Pitch Coupling
by Thomas Liebau
Abstract: This research pertains to the dynamics of a ship taking into account the nonlinear coupling of roll and pitch degrees of freedom. Such a nonlinearity has critical implications for large-amplitude ship motion, and can thus be useful in understanding conditions leading to capsize. The nonlinear normal modes of the conservative system are determined numerically and are displayed in a frequency-energy plot, which clarifies the bifurcations that connect the various branches of periodic orbits. Numerical simulations show that, although the solutions on most branches result in capsize if their energy is beyond a common critical value, a few branches contain stable solutions at higher energies that do not lead to capsize, suggesting possible methods of capsize mitigation. We study a class of solutions analytically using a complexification-averaging technique. Finally, we run a simulation in the case of light damping in roll with high-energy initial conditions, illustrating transitions between branches that occur in the direction of decreasing energy on the frequency-energy plot.
Keywords: nonlinear normal modes; large-amplitude ship motion; roll-pitch coupling; periodic orbits; non-smooth transformations; capsize; stability; frequency-energy plot; Floquet analysis; complexification/averaging; damped dynamics; chaotic motion; resonance captures; wavelet analysis.
Nonlinear Observer Based Robust Controller Design for Ball and Beam System: An LMI Based Approach
by Aditi Srivastava, Bhanu Pratap
Abstract: In this paper, a nonlinear observer based robust controller for ball and beam system (BBS) is proposed. The BBS consists of a long beam tilted by a servo or electric motor together in which ball rolls back and forth on the top of the beam. The concept of one-sided Lipschitz function is applied to the BBS for the observer design. The sufficient and necessary conditions that satisfy the existence of observer are explored in the form of linear matrix inequality (LMI). On the basis of estimated states obtained from the nonlinear observer, a sliding mode controller (SMC) is proposed for the BBS. In the proposed control scheme, firstly a nonlinear sliding surface is established, and then a robust control law is designed for robust performances and fast convergence of response. To ensure the sliding motion, the existence of the switching surface is proved using proposed observer based control law. Stability analysis of the overall closed loop system is done by using Lyapunov stability criteria. Simulation studies have been carried out to validate the performance of the proposed scheme. Finally, robustness issue has also been addressed on the basis of comparative evaluation.
Keywords: Ball and beam system; linear matrix inequality; one-sided Lipschitz; nonlinearity; observer based controller; robust control.
Genetic model reference adaptive control of shell heavy oil fractionator
by Dauda Araromi, Aminah Sulayman, Olajide Ajala
Abstract: Fractionators are characterized by high non-linear dynamic behaviour, strong loop interactions and model uncertainties. Relative Gain Array was used to determine the level of loop interaction. Dynamic decoupler was used to remove the interactions which were obtained using feed-forward design technique. A feedback control system is designed for the dynamic decoupled plant using Ziegler-Nichols tuned Proportional Integral (PI) controller. A Genetic Model Reference Adaptive Controller (GMRAC) is designed to control the fractionator using a second order reference model and adaptation mechanism based on genetic algorithm. Genetic algorithm uses real coded data generation for optimization. Comparison is made with the PI controller. Performance indices were based on settling time, rise time and overshoot.
Keywords: GMRAC; adaptive control; PI; MATLAB; relative gain array; shell heavy oil fractionator.
Special Issue on: Nonlinear Dynamical Systems with Oscillations, Bifurcations and Chaos
Mathematical Modeling and Parametric Resonances of a Nonlinear RLC Series Circuit
by Yélomè Kpomahou, Clément Miwadinou, Laurent Hinvi
Abstract: In order to study nonlinear parametric oscillations of a RLC series circuit consisting of a nonlinear resistor, a nonlinear inductor and a nonlinear capacitor subjected to mixed-frequency voltage, a class of nonlinear ordinary differential equations is generated. From this class, a generalized mixed Rayleigh-Li
Keywords: Nonlinear RLC circuit; Generalized mixed Rayleigh-Liénard oscillator; Multiple scales method; Nonlinear resonances ; Stability.
A scaling investigation for a Van der Pol circuit: normal form applied to a Hopf bifurcation
by Vinicius Silva, Edson Leonel
Abstract: Scaling laws are generally associated with changes in the spatial structure of dynamical systems due to variations of control parameters. A bifurcation is the scientific terminology given to these particular qualitative changes in the dynamics. In the local bifurcation theory, when an equilibrium point changes stability from stable to unstable and a stable limit cycle shows up, we say the system has undergone a Hopf bifurcation. In general, the study of the
Hopf bifurcation is of great practical concern as well as of fundamental scientific interest, once it is present in a variety of systems including electrical circuits, dynamical population, lasers and many others. Although, some of the basic questions that remain to be explored about Hopf bifurcation are the regimes for which certain
scaling laws exist and whether the exponents obtained for system obeying kinds of dynamics are valid for others. Based on this scenario, the main goal of this work is to explore the evolution towards the steady state at and nearby the supercritical Hopf bifurcation in the Van der Pol circuit by reducing explicitly the differential equations that describes the dynamics to its normal form near the Hopf bifurcation. The relative simplicity of Van der Pol circuit and the ability to generate a large variety of behaviors motivate the choice of the system. Through the scaling analysis, we obtained by considering the evolution towards the steady state the scaling properties and the critical exponents that characterize the bifurcation in study. The knowledge of these exponents allows one identify to what universality a bifurcation belongs to.
Keywords: Van der Pol oscillator; Scaling properties; Hopf bifurcation.