Controlling Rucklidge chaotic system with a single controller using linear feedback and passive control methods

In this paper, a novel control method that combines passive, linear feedback, and dislocated feedback control methods is proposed and applied to the control of the four-dimensional hyperchaotic finance system which has been introduced and controlled with the linear feedback and speed feedback control methods by Yu, Cai, and Li (2012). The stability of the hyperchaotic finance system at its equilibrium points is ensured on the basis of a Lyapunov function. Computer simulations are used for verifying all the theoretical analyses visually. In the simulations, the proposed control method is also compared with the speed feedback and linear feedback control methods to observe its effectiveness and the results are discussed. DOI: http://dx.doi.org/10.5755/j01.itc.47.1.16898

This article describes the design of a linear observer–linear controller-based robust output feedback scheme for output reference trajectory tracking tasks in the case of nonlinear, multivariable, nonholonomic underactuated mobile manipulators. The proposed linear feedback scheme is based on the use of a classical linear feedback controller and suitably extended, high-gain, linear Generalized Proportional Integral (GPI) observers, thus aiding the linear feedback controllers to provide an accurate simultaneous estimation of each flat output associated phase variables and of the exogenous and perturbation inputs. This information is used in the proposed feedback controller in (a) approximate, yet close, cancelations, as lumped unstructured time-varying terms, of the influence of the highly coupled nonlinearities, and (b) the devising of proper linear output feedback control laws based on the approximate estimates of the string of phase variables associated with the flat outputs simultaneously provided by the disturbance observers. Simulations reveal the effectiveness of the proposed approach.

This paper addresses the problem of designing low-order and linear robust feedback controllers that providea prioriguarantees with respect to stability and performance when applied to a fluid flow. This is challenging, since whilst many flows are governed by a set of nonlinear, partial differential–algebraic equations (the Navier–Stokes equations), the majority of established control system design assumes models of much greater simplicity, in that they are: firstly, linear; secondly, described by ordinary differential equations (ODEs); and thirdly, finite-dimensional. With this in mind, we present a set of techniques that enables the disparity between such models and the underlying flow system to be quantified in a fashion that informs the subsequent design of feedback flow controllers, specifically those based on the$\mathscr{H}_{\infty }$loop-shaping approach. Highlights include the application of a model refinement technique as a means of obtaining low-order models with an associated bound that quantifies the closed-loop degradation incurred by using such finite-dimensional approximations of the underlying flow. In addition, we demonstrate how the influence of the nonlinearity of the flow can be attenuated by a linear feedback controller that employs high loop gain over a select frequency range, and offer an explanation for this in terms of Landahl’s theory of sheared turbulence. To illustrate the application of these techniques, an$\mathscr{H}_{\infty }$loop-shaping controller is designed and applied to the problem of reducing perturbation wall shear stress in plane channel flow. Direct numerical simulation (DNS) results demonstrate robust attenuation of the perturbation shear stresses across a wide range of Reynolds numbers with a single linear controller.

Recently, magnetic telemanipulation devices have shown a great deal of promise in such areas as semi-conductor manufacturing, wind tunnels, drug delivery, and many more. However, these devices are generally associated with problems caused by payload variation and uncertainties in the parameters of the system which in turn, have limited the development and application of magnetic telemanipulation technology to its full capacity. This paper addresses and deals with these issues by implementation of a precise position control method for a magnetic telemanipulation system with high level of uncertainties in its parameters. The levitation system used in this study is primarily designed for performing remote pick and place operations. The levitated object is a 28 gr microrobot capable of grasping and releasing payloads as heavy as 8 gr. To cope with the uncertainties in the modeling and payload variation, a model reference adaptive feedback linearization (MRAFL) controller is designed and its performance compared with an ordinary feedback linearization (FL) controller. Through experimental results it is shown that the MRAFL controller enables the microrobot to grasp and transport a payload as heavy as 30% of its own weight without a considerable effect on its positioning accuracy. In the presence of the payload, the MRAFL controller resulted in a RMS positioning error of 8 μm} compared with 27.9 μm} of the FL controller. The approach presented in this work is versatile as it leads to the modeling and control of a highly nonlinear system through a modular approach that can be applied to a variety of magnetic levitation and telemanipulation systems.

This paper proposes the theoretical framework and the consequent application of the input-output Feedback Linearization (FL) control technique to Linear Induction Motors (LIM). LIM, additionally to Rotating Induction Motor (RIM), presents other strong non-linearities caused by the dynamic end effects, leading to a space-vector dynamic model with time-varying inductance and resistance terms and a braking force term. This paper, starting from a recently developed dynamic model of the LIM taking into consideration its end effects, defines a FL technique suited for LIMs, since it inherently considers its dynamic end effects. Additionally, it proposes a technique for the on-line estimation of the inductor resistance, based on Model Reference Adaptive System (MRAS) on-line estimator, exploited for adapting on-line the FL control action versus inductor resistance variations leading to undesirable steady-state tracking errors. The stability of the proposed MRAS on-line estimator has been proven theoretically, adopting the Popov’s criterion for hyperstability. The proposed approach has been validated experimentally on a suitably developed test set-up, under both no load and loaded conditions. It has been compared firstly with the simplest control structure, which is the scalar V/f control, secondly, under the same closed-loop bandwidths of the flux and speed systems, with the industrial standard in terms of high performance control technique: Field Oriented Control (FOC).

This paper deals with the chaotic synchronization of a discrete chaotic system. Based on a stable analysis, improved piece-wise linear feedback and nonlinear feedback control methods were given. Both the methods can achieve chaotic synchronization efficiently with one control input. The range of coupling coefficient is calculated in both the methods. Compared with nonlinear controls, the improved piece-wise linear controls have simpler structures and can be obtained more easily. Finally, the numerical simulation results verified the effectiveness of both the methods.

In this paper, a novel adaptive interval type-2 fuzzy sliding mode control (AIT2FSMC) methodology is proposed based on the integration of sliding mode control and adaptive interval type-2 fuzzy control for chaotic system. The AIT2FSMC system is comprised of a fuzzy control design and a hitting control design. In the fuzzy control design, an interval type-2 fuzzy controller is designed to mimic a feedback linearization (FL) control law. In the hitting control design, a hitting controller is designed to compensate the approximation error between the FL control law and the interval type-2 fuzzy controller. The parameters of the interval type-2 fuzzy controller, as well as the uncertainty bound of the approximation error, are tuned adaptively. The adaptive laws are derived in the sense of Lyapunov stability theorem, thus the stability of the system can be guaranteed. The proposed control system compared to adaptive fuzzy sliding mode control (AFSMC). Simulation results show that the proposed control systems can achieve favorable performance and robust with respect to system uncertainties and external disturbances.

In this paper, advanced interval type-2 fuzzy sliding mode control (AIT2FSMC) for robot manipulator is proposed. The proposed AIT2FSMC is a combination of interval type-2 fuzzy system and sliding mode control. For resembling a feedback linearization (FL) control law, interval type-2 fuzzy system is designed. For compensating the approximation error between the FL control law and interval type-2 fuzzy system, sliding mode controller is designed, respectively. The tuning algorithms are derived in the sense of Lyapunov stability theorem. Two-link rigid robot manipulator with nonlinearity is used to test and the simulation results are presented to show the effectiveness of the proposed method that can control unknown system well.

Examines the application of linear optimal control theory to a low-order nonlinear chaotic convection problem. Linear control feedback is found to be fully effective only when it is switched off while the state is far from the desired equilibrium point, relying on the attractor of the system to bring the state into a neighborhood of the equilibrium point before control is applied. Linear estimator feedback is found to be fully effective only when (a) the Lyapunov exponent of the state estimation error is negative, indicating that the state estimate converges to the uncontrolled state, and (b) the estimator is stable in the vicinity of the desired equilibrium point. The aim in studying the present problem is to understand better some possible pitfalls of applying linear feedback to nonlinear systems in a low-dimensional framework. Such an exercise foreshadows problems likely to be encountered when applying linear feedback to infinite-dimensional nonlinear systems such as turbulence. It is important to understand these problems and the remedies available in a low-dimensional framework before moving to more complex systems such as turbulence.

In this paper, we performed the numerical and experimental study of unsteady cavitation surge around a semi-circular leading-edge flat plate using a passive flow control method. We mounted a miniature spanwise wedge-type vortex generator on the suction side of the model close to its leading edge. To mitigate the destructive impact of this type of cavitation on the hydrofoil performance, we analyzed the effects of the passive control on the dynamics of cavitation surge. First, we investigated experimentally the unsteady cavitating flow around the semi-circular leading-edge flat plate without passive control using high-speed visualization, acoustic measurements and particle image velocimetry method. Next, we simulated numerically the dynamics of unsteady flow under the cavitation surge conditions with an open source code and validated the numerical results using the experimental data. We used a proper interaction between turbulence and cavitation model to capture a highly unsteady behavior of cavitation surge. Finally, we considered the effects of the passive control device on the mechanism of the cavitation surge instability. Our results revealed that using the passive control method, it is possible to stabilize the attached cavity on the suction side of the flat plate, to hinder the development of the spanwise instability of the attached cavity and to mitigate large-scale cavity structures. Furthermore, high-pressure pulsations in the wake region induced by unsteady cavitation surge were considerably reduced.

Single-phase power converters with the active pulsating-power-buffering (PPB) function are essentially highly coupled and nonlinear systems. Advanced control techniques are needed for this emerging class of converters to achieve fast transient response and large-signal stability. Existing control solutions are based on either 1) linear control techniques that are operating-point specific or 2) nonlinear control techniques that are generally topology-dependent. The proposed work is an evolved generalized feedback-linearization (FBL) control approach that incorporates the direct Lyapunov control method. The proposed control provides good stabilization of the internal dynamics of the system (which is unviable with FBL control) while still retaining all the best features of FBL control. A kind of single-phase power conversion system with active PPB is described. It is shown that FBL control naturally destabilizes the system and that the proposed control can globally stabilize the system under various operating conditions while yielding fast dynamics.

The refuge of prey species is a biological factor necessary for the coexistence of the species and hence it is yet another factor of great interest due to defensive properties of the prey against the predation. We propose a class of discrete differential algebraic prey predator system with Holling Type II functional response and prey refuge. The system is found to possess trivial, semi-trivial and interior equilibrium states existing under certain conditions. Also we examine the existence and uniqueness of the solutions of the system. Dynamical behaviour of the system is investigated through linear stability analysis of the equilibrium states. Moreover, this system undergoes bifurcation when the chosen parameter passes through a critical value, and closed invariant curves arise from a stable equilibrium state. The analytical results are strengthened with appropriate numerical examples and they demonstrate chaotic behaviours over a wild range of parameters. The computation of maximal Lyapunov exponents confirms the existence of chaos. Finally chaos control is achieved by linear feedback control and hybrid control methods.

In this paper the problem of stabilizing a linear timeinvariant system with quantized feedback is addressed. We focus on systems with rectilinear quantization where only some of the outputs are quantized either by limited sensor precision or data rate constraints and the rest of the output is sent to the controller without quantization. We call these systems partly-quantized feedback systems. Aside from the rectilinear boxes that we know output resides in, we determine moving hyperplanes in output space such that exact value of output has to lie on these planes too. Using the intersection of rectilinear boxes and hyperplanes, we find the best estimate of output to be used in linear feedback controllers and hence we reduce the maximum quantization error and find a smaller invariant region around origin. A simulation of the proposed controller is also presented.

Objective: This paper implies a comparison between sliding mode control and linear state feedback controller. When the linear systems are given bounded disturbance their robustness properties are studied. Method: Pole placement, classical sliding mode control using constant rate reaching law and constant plus proportional rate reaching law, super-twisting controller. Findings: Finite time asymptotic convergence is not achieved in linear feedback controller, Sliding Mode Control when used produced finite time asymptotic convergence. The measure of the control variable is obtained by taking norm of the control input. Applications: Process Control, Aerodynamics.

A novel procedure is presented to design a linear constant state feedback controller with a prespecified performance measure. The method is an iterative technique based on the sensitivity of a quadratic cost functional with respect to the feedback gains. At each iteration, a Riccati-type algebraic matrix equation is solved to compute the sensitivity expressions needed to update the feedback gains.