Volume 10, Number 4, 2013
Special Issue on Advanced Works on Controlling and Observing Nonlinear Systems (pp.267-334)
In this paper, we investigate the problem of global stabilization for a general class of high-order and non-smoothly stabilizable nonlinear systems with both lower-order and higher-order growth conditions. The designed continuous state feedback controller is recursively constructed to guarantee the global strong stabilization of the closed-loop system.
An observer-based adaptive fuzzy control is presented for a class of nonlinear systems with unknown time delays. The state observer is first designed, and then the controller is designed via the adaptive fuzzy control method based on the observed states. Both the designed observer and controller are independent of time delays. Using an appropriate Lyapunov-Krasovskii functional, the uncertainty of the unknown time delay is compensated, and then the fuzzy logic system in Mamdani type is utilized to approximate the unknown nonlinear functions. Based on the Lyapunov stability theory, the constructed observer-based controller and the closed-loop system are proved to be asymptotically stable. The designed control law is independent of the time delays and has a simple form with only one adaptive parameter vector, which is to be updated on-line. Simulation results are presented to demonstrate the effectiveness of the proposed approach.
Power system stability is enhanced through a novel stabilizer developed around an adaptive fuzzy sliding mode approach which applies the Nussbaum gain to a nonlinear model of a single-machine infinite-bus (SMIB) and multi-machine power system stabilizer subjected to a three phase fault. The Nussbaum gain is used to avoid the positive sign constraint and the problem of controllability of the system. A comparative simulation study is presented to evaluate the achieved performance.
The control of time delay systems is still an open area for research. This paper proposes an enhanced model predictive discrete-time sliding mode control with a new sliding function for a linear system with state delay. Firstly, a new sliding function including a present value and a past value of the state, called dynamic surface, is designed by means of linear matrix inequalities (LMIs). Then, using this dynamic function and the rolling optimization method in the predictive control strategy, a discrete predictive sliding mode controller is synthesized. This new strategy is proposed to eliminate the undesirable effect of the delay term in the closed loop system. Also, the designed control strategy is more robust, and has a chattering reduction property and a faster convergence of the system s state. Finally, a numerical example is given to illustrate the effectiveness of the proposed control.
This paper is concerned with the problem of the full-order observer design for a class of fractional-order Lipschitz nonlinear systems. By introducing a continuous frequency distributed equivalent model and using an indirect Lyapunov approach, the sufficient condition for asymptotic stability of the full-order observer error dynamic system is presented. The stability condition is obtained in terms of LMI, which is less conservative than the existing one. A numerical example demonstrates the validity of this approach.
A robust sliding mode approach combined with a field oriented control (FOC) for induction motor (IM) speed control is presented. The proposed sliding mode control (SMC) design uses an adaptive switching gain and an integrator. This approach guarantees the same robustness and dynamic performance of traditional SMC algorithms. And at the same time, it attenuates the chattering phenomenon, which is the main drawback in actual implementation of this technique. This approach is insensitive to uncertainties and permits to decrease the requirement for the bound of these uncertainties. The stability and robustness of the closedloop system are proven analytically using the Lyapunov synthesis approach. The proposed method attenuates the effect of both uncertainties and external disturbances. Experimental results are presented to validate the effectiveness and the good performance of the developed method.
The problem of exponential synchronization for a class of general complex dynamical networks with nonlinear coupling delays by adaptive pinning periodically intermittent control is considered in this paper. We use the methods of the adaptive control, pinning control and periodically intermittent control. Based on the piecewise Lyapunov stability theory, some less conservative criteria are derived for the global exponential synchronization of the complex dynamical networks with coupling delays. And several corresponding adaptive pinning feedback synchronization controllers are designed. These controllers have strong robustness against the coupling strength and topological structure of the network. Using the delayed nonlinear system as the nodes of the networks, a numerical example of the complex dynamical networks with nonlinear coupling delays is given to demonstrate the effectiveness of the control strategy.
The paper considers certain impedimental issues related to the use of magnetic gearbox and magnetic coupling technologies in high performance servo control systems. A prototype magnetic coupling is used as a basis for demonstrating that the underlying torque transfer characteristic is significantly nonlinear when transmitted torque approaches the maximum designed pull-out torque of the device. It is shown that linear controllers for speed control proportional plus integral (PI) and position control proportional plus derivative (PD) result in acceptable performance provided the magnetic coupling operates below 80% of designed pull-out torque. To fully compensate for the inherent nonlinearity of the torque transfer characteristic, feedback linearizing control laws and state transformations are derived resulting in exactly linear input-output characteristic for position and speed control of magnetically-geared drive-trains. With the addition of state feedback, the closed-loop dynamics for both position and speed control of a magneticallygeared drive-train can be designed to satisfy the integral of time multiplied by absolute error (ITAE) optimized linear response for a step input. Outstanding results are demonstrated through simulation and experimental real-time implementation on a demonstrator magnetically-geared drive-train.
This paper deals with the problem of delay size stability analysis of single input-delayed linear and nonlinear systems. Conventional reduction, reduction linked by sliding mode, and linear memoryless control approaches are used for simple input-delayed systems to obtain the stability conditions. Several first order examples are investigated systematically to demonstrate the capabilities and limitations of the advanced stability analysis techniques including Lyapunov-Krasovskii functionals, Newton-Leibniz formula, and a newly addressed Lagrange mean value theorem. Numerical comparative results show the usefulness and effectiveness of the advanced delay size analysis techniques proposed in this paper.
In this paper, an adaptive type-2 fuzzy sliding mode control to tolerate actuator faults of unknown nonlinear systems with external disturbances is presented. Based on a redundant actuation structure, a novel type-2 adaptive fuzzy fault tolerant control scheme is proposed using sliding mode control. Two adaptive type-2 fuzzy logic systems are used to approximate the unknown functions, whose adaptation laws are deduced from the stability analysis. The proposed approach allows to ensure good tracking performance despite the presence of actuator failures and external disturbances, as illustrated through a simulation example.
This paper deals with the problem of designing a robust discrete output-feedback based repetitive-control system for a class of linear plants with periodic uncertainties. The periodicity of the repetitive-control system is exploited to establish a two-dimensional (2D) model that converts the design problem into a robust stabilization problem for a discrete 2D system. By employing Lyapunov stability theory and the singular-value decomposition of the output matrix, a linear-matrix-inequality (LMI) based stability condition is derived. The condition can be used directly to design the gains of the repetitive controller. Two tuning parameters in the LMI enable the preferential adjustment of control and learning. A numerical example illustrates the design procedure and demonstrates the validity of the method.
This paper proposes a new impulsive complex delayed dynamical network model with output coupling, which is totally different from some existing network models. Then, by employing impulsive delay differential inequalities, some sufficient conditions are obtained to guarantee the global exponential state synchronization and output synchronization of the impulsive complex delayed dynamical network. Finally, two numerical examples are given to demonstrate the effectiveness of the obtained results.
A position/force hybrid control system based on impedance control scheme is designed to align a small gripper to a special ring object. The vision information provided by microscope vision system is used as the feedback to indicate the position relationship between the gripper and the ring object. Multiple image features of the gripper and the ring object are extracted to estimate the relative positions between them. The end-effector of the gripper is tracked using the extracted features to keep the gripper moving in the field of view. The force information from the force sensor serves as the feedback to ensure that the contact force between the gripper and the ring object is limited in a small safe range. Experimental results verify the effectiveness of the proposed control strategy.
This paper investigates the H filtering problem for a class of linear continuous-time systems with both time delay and saturation. Such systems have time delay in their state equations and saturation in their output equations, and their process and measurement noises have unknown statistical characteristics and bounded energies. Based on the Lyapunov-Krasovskii stability theorem and the linear matrix inequalities (LMIs) technique, a generalized dynamic filter architecture is proposed, and a filter design method is developed. The linear H filter designed by the method can guarantee the H performance. The parameters of the designed filter can be obtained by solving a kind of LMI. An illustrative example shows that the design method proposed in this paper is very effective.
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