326 research outputs found
Adaptive Control of the Chaotic System via Singular System Approach
This paper deals with the control problem of the chaotic system subject to disturbance. The sliding mode surface is designed by singular system approach, and sufficient condition for convergence is given. Then, the adaptive sliding mode controller is designed to make the state arrive at the sliding mode surface in finite time. Finally, Lorenz system is considered as an example to show the effectiveness of the proposed method
Adaptive Neural Gradient Descent Control for a Class of Nonlinear Dynamic Systems with Chaotic Phenomenon
A neural network controller design is studied for a class of nonlinear chaotic systems with uncertain parameters. Because the chaos phenomena are often in this class of systems, it is indispensable to control this class of systems. At the same time, due to the presence of uncertainties in the chaotic systems, it results in the difficulties of the controller design. The neural networks are employed to estimate the uncertainties of the systems and a controller is designed to overcome the chaos phenomena. The main contribution of this paper is that the adaptation law can be determined via the gradient descent algorithm to minimize a cost function of error. It can prove the stability of the closed-loop system. The numerical simulation is specified to pinpoint the validation of the approach
Output Feedback Fractional-Order Nonsingular Terminal Sliding Mode Control of Underwater Remotely Operated Vehicles
For the 4-DOF (degrees of freedom) trajectory tracking control problem of underwater remotely operated vehicles (ROVs) in the presence of model uncertainties and external disturbances, a novel output feedback fractional-order nonsingular terminal sliding mode control (FO-NTSMC) technique is introduced in light of the equivalent output injection sliding mode observer (SMO) and TSMC principle and fractional calculus technology. The equivalent output injection SMO is applied to reconstruct the full states in finite time. Meanwhile, the FO-NTSMC algorithm, based on a new proposed fractional-order switching manifold, is designed to stabilize the tracking error to equilibrium points in finite time. The corresponding stability analysis of the closed-loop system is presented using the fractional-order version of the Lyapunov stability theory. Comparative numerical simulation results are presented and analyzed to demonstrate the effectiveness of the proposed method. Finally, it is noteworthy that the proposed output feedback FO-NTSMC technique can be used to control a broad range of nonlinear second-order dynamical systems in finite time
Nonlinear Time-Frequency Control Theory with Applications
Nonlinear control is an important subject drawing much attention. When a nonlinear system undergoes route-to-chaos, its response is naturally bounded in the time-domain while in the meantime becoming unstably broadband in the frequency-domain. Control scheme facilitated either in the time- or frequency-domain alone is insufficient in controlling route-to-chaos, where the corresponding response deteriorates in the time and frequency domains simultaneously. It is necessary to facilitate nonlinear control in both the time and frequency domains without obscuring or misinterpreting the true dynamics. The objective of the dissertation is to formulate a novel nonlinear control theory that addresses the fundamental characteristics inherent of all nonlinear systems undergoing route-to-chaos, one that requires no linearization or closed-form solution so that the genuine underlying features of the system being considered are preserved. The theory developed herein is able to identify the dynamic state of the system in real-time and restrain time-varying spectrum from becoming broadband. Applications of the theory are demonstrated using several engineering examples including the control of a non-stationary Duffing oscillator, a 1-DOF time-delayed milling model, a 2-DOF micro-milling system, unsynchronized chaotic circuits, and a friction-excited vibrating disk.
Not subject to all the mathematical constraint conditions and assumptions upon which common nonlinear control theories are based and derived, the novel theory has its philosophical basis established in the simultaneous time-frequency control, on-line system identification, and feedforward adaptive control. It adopts multi-rate control, hence enabling control over nonstationary, nonlinear response with increasing bandwidth ? a physical condition oftentimes fails the contemporary control theories. The applicability of the theory to complex multi-input-multi-output (MIMO) systems without resorting to mathematical manipulation and extensive computation is demonstrated through the multi-variable control of a micro-milling system. The research is of a broad impact on the control of a wide range of nonlinear and chaotic systems. The implications of the nonlinear time-frequency control theory in cutting, micro-machining, communication security, and the mitigation of friction-induced vibrations are both significant and immediate
Exploring the resilience of uncertain nonlinear handling chain systems in container ports with a novel sliding mode control
Uncertain handling chain system (HCS) of container ports brings steady-state error to the original control decisions, and even worse, dramatically degrades the system performance. The steady-state error will cause unsatisfied freight requirement to be much higher than the expected value for a long time, resulting in the decrease of system robustness and resilience. In this work, a novel sliding mode control with power integral reaching law (SMC-P) is presented for nonlinear HCS of container ports under uncertainty. Specifically, the integral of system state variable, the exponential reaching law and the power of the switching function are integrated to the traditional reaching law. And it is proven that the eliminated steady-state error, the accelerated approach speed, and the reduced chattering can be effectively obtained by SMC-P. A nonlinear HCS in container ports with uncertain freight requirement and handling ability is considered. SMC-P is compared with traditional method, genetic algorithm, quasi-sliding mode control and integral sliding mode control. Simulation results show that SMC-P does not only balance both steady-state error reduction and chattering avoidance caused by uncertainty, but also optimize the performance, robustness, and resilience of the uncertain nonlinear HCS. This study also brings economic and sustainability contributions for port authorities.info:eu-repo/semantics/publishedVersio
A Model-Free Control Algorithm Derived Using the Sliding Model Control Method
In this work, a model-free sliding mode control scheme is derived and applied to linear and nonlinear systems that is solely based on observable measurements and therefore does not require a theoretical system model in developing the controller form. The general sliding mode controller form is derived for an nth-order system and is strictly limited to a single-input unit input influence gain case for this work. The controller form is based solely on system measurements assuming the order of the system is known. The switching gain form is developed so that stability of the closed-loop sliding mode controller system is guaranteed using Lyapunov’s Direct Method. The controller form is reformulated using a smoothing moving boundary layer to eliminate chattering of the control effort. A simulation study is presented for a single-input unit input influence gain case applied to both a linear and nonlinear system with and without a smoothing boundary layer. The measurement based controller form is shown to be identical regardless of the system’s kinematics to be controlled assuming the order is known. Results of the simulation efforts show good state tracking performance is achieved with stable convergence for the tracking performance regardless of the system to be controlled
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