Memoryless State Feedback Controller Design for Time Delay Systems With Matched Uncertain Nonlinearities

The robust control problem for a class of uncertain time-delay systems is investigated. The systems include multiple time delays and uncertain nonlinear functions. According to the input matrix, the system is decomposed into two subsystems. The linear virtual control law is designed for the first subsystem by solving the LMI. Then, by constructing a proper Lyapunov–Krasovskii functional, the memoryless state feedback controller is developed and the closed-loop system is proved to be asymptotically stable. Simulations are presented to verify the effectiveness of the proposed method.

The double integral sliding mode synchronization method is studied for a class of super chaotic systems. Both the unknown parameters and uncertain nonlinear functions are considered for the driven and response chaotic systems. It is worthy pointing out that a kind of input nonlinearity is took into consideration when the synchronization controller is designed. So the uncertainties are very complex in this situation and the steady state error can be compensated by the introducing of integrator in the sliding mode. Also, double integral sliding mode has the advantages of both PI controller and sliding mode controller. So it is a new kind of integral sliding mode and the numerical simulation proves the rightness of the proposed method.KeywordsDouble integralSliding modeChaosSynchronizationInput nonlinearityUncertainty

A general class of uncertain nonlinear systems with uncertain input unmodeled dynamics is considered. The system structure includes a core nominal subsystem of triangular structure with additive uncertain nonlinear functions and coupled with a set of uncertain nonlinear appended dynamics as well as uncertain dynamic input nonlinearities. The dynamic input nonlinearities include an uncertain non-affine function and a dynamic perturbation through an uncertain input unmodeled dynamics subsystem. The input unmodeled dynamics subsystem is coupled with the entire system state including the unmeasured state of the uncertain nonlinear appended dynamics coupled with the nominal triangular system. The control design is based on dual controller/observer dynamic high-gain scaling with an additional dynamic scaling based on a singular-perturbation-like redesign to address the non-affine and uncertain nature of the input appearance into the system dynamics. The proposed approach yields a global robust adaptive output-feedback control design that is robust to the dynamic input uncertainties and to uncertain nonlinear functions allowed throughout the system structure.

A global robust sliding mode controller (GRSMC) is proposed for a class of uncertain systems with both state-delay and input-delay. Firstly, a linear transformation is introduced to transform the original system into one that only contains state-delay. Then an integral sliding mode surface, which can guarantee the system global robustness, is constructed in the new system of coordinates. Based on linear matrix inequality (LMI), a sufficient condition that ensures asymptotic stability of the sliding mode is derived, and furthermore the asymptotic stability of the original system is studied. A sliding mode control law is designed to satisfy the reaching condition of the sliding mode. So a GRSMC is realized. Finally, the effectiveness of the proposed method is demonstrated by applying to a networked control system with network-induced time delays.

To eliminate the effect of the uncertain disturbances and improve the control accuracy of spacecraft Attitude Control System, a nonlinear control algorithm named nonsingular terminal sliding-mode feedback controller is proposed in this work, which is mainly made up of nonsingular terminal sliding-mode controller and sliding-mode feedback controller. In the first place, nonsingular terminal sliding-mode controller is designed, which guarantees global asymptotic convergence of the attitude in the presence of the uncertain perturbations from the space. Despite that, it is the influence of the uncertain disturbances that hinder the control accuracy. Then, in order to promote the control accuracy, the sliding-mode feedback controller based on the principle of minimum sliding-mode error is proposed, which is used to compensate the control errors of the nonsingular terminal sliding-mode controller caused by the uncertainties. Hence, the determination principle of the weighting matrix in sliding-mode feedback controller is discussed, and the algorithm structure of the sliding-mode feedback controller is also analyzed, which provides the theoretical basis for the sliding-mode feedback controller. By contrast, an adaptive fuzzy algorithm is designed and introduced into the nonsingular terminal sliding-mode controller to improve the control accuracy, which named the nonsingular terminal fuzzy sliding-mode controller. Last but not the least, several numerical examples are presented to demonstrate the efficacy of the proposed nonsingular terminal sliding-mode feedback controller. Simulation results confirm that the control accuracy of the nonsingular terminal sliding-mode feedback controller is higher than the nonsingular terminal sliding-mode controller and the same as nonsingular terminal fuzzy sliding-mode controller. Not only is the calculation of the nonsingular terminal fuzzy sliding-mode feedback controller smaller than nonsingular terminal fuzzy sliding-mode controller, the adjusted parameters are also fewer than nonsingular terminal fuzzy sliding-mode controller obviously. The numerical results clearly indicate that the proposed nonsingular terminal sliding-mode feedback controller based on the principle of minimum sliding-mode error can compensate control errors accurately and quickly; therefore, it can reduce the effect of the uncertainties from the space indirectly.

The Indian Head Division, Naval Surface Warfare Center (IHDIV, NSWC) is sponsoring a program to design, develop, and implement a family of electronic time delay cartridges for a wide variety of aircrew escape and other cartridge applications throughout the U.S. Department of Defense. Currently, pyrotechnic cartridges, utilizing either a “pressed column” delay or a small column insulated delay (SCID), provide the time delays required for these applications. Implementing an electronic time delay (or digital delay) cartridge, which maintains the form, fit, and function as the current pyrotechnic cartridges while providing longer useful lifetimes and more precise time delays is the primary objective of this program. This paper presents the program approach adopted for this effort and the successes achieved by the selected contractor Special Devices, Inc. and its partner Scot Inc. to develop an electronic time delay cartridge family. BACKGROUND: Cartridge Actuated Devices and Propellant Actuated Devices (CAD/PAD) are utilized for various applications throughout the U.S. military. A cartridge is defined as an energy source utilizing one or more energetic materials. A Cartridge Actuated Device (CAD) is defined as a device releasing cartridge energy to perform a work function. A Propellant Actuated Device (PAD) is defined as a rocket powered device releasing controlled propellant energy to perform a work function. Also, an Aircrew Escape Propulsion Systems (AEPS) is a “PAD” specifically designed for aircrew systems applications. For example, on the F/A-18E/F aircraft, there are over sixty-six (66) cartridges, CADs, and AEPS (Figure (1) on the next page). As shown, the F/A-18E/F utilizes a NACES (Navy Aircrew Common Ejection Seat) ejection seat to provide the pilot escape capability during an emergency situation. In addition, as part of the overall escape system, delay cartridges are utilized to provide optimized timing for all required events. The MC50 Cartridge Actuated Initiator (Photo (1) and Figure (2)) provides supplemental ballistic pressure to the system after a 0.3 second delay. Photo 1: MC50 Cartridge Actuated Initiator For this initiator, ballistic pressure is used as the stimulus to actuate a percussion primer. This primer, in turn, initiates a pyrotechnic column that provides the required 0.3 second time delay before initiating the output charge which provides ballistic pressure to the remainder of the system. Figure 2: MC50 Cartridge Actuated Initiator Schematic 1 43rd AIAA/ASME/SAE/ASEE Joint Propulsion Conference & Exhibit 8 11 July 2007, Cincinnati, OH AIAA 2007-5133 This material is declared a work of the U.S. Government and is not subject to copyright protection in the United States. 43 AIAA/ASME/SAE/ASEE JPC AIAA 2007-5133 Figure 1: F/A-18 E/F CAD/PADs Currently, pyrotechnic cartridges provide the required time delays for a wide range of CAD/PAD systems. These cartridges contain energetic materials that burn in a column at a controlled rate and provide ballistic output after the required system delay has been achieved. These current cartridges fall into two basic categories: “pressed column” type cartridges and “small column insulated delay (SCID)” type cartridges. One example of the “pressed column” type cartridges is the CCU-40A/A (Figure (3)). This cartridge is used on the AV8B aircraft and provides a 0.575 second delay prior to generating ballistic pressure to deploy the ejection seat parachutes. Figure 3: CCU-40A/A Delay Cartridge As shown, the CCU-40A/A delay cartridge is 1.095 inches long and 0.379 inches in diameter. Included in this cartridge are the percussion primer, the delay column, and the output charge that generates the required ballistic pressure for system operation. The CCU-40A/A Delay Cartridge is the smallest of the family of current U. S. Navy and U. S. Air Force delay cartridges or initiators. By maintaining the physical envelope of the CCU-40A/A cartridge, the selected technology can be rapidly implemented into larger cartridge or initiator applications. Thusly, maintaining this physical envelope, while implementing an alternate electronic time delay technology, has been identified as the primary design challenge of this program. A critical secondary design challenge is the packaging of the sub-components that comprise the selected alternate technology. Both of these current types of delay cartridges are expensive to produce, provide imprecise delay times (a tolerance of 25% for the “pressed column” type cartridges and a tolerance of 8% for the SCID-type cartridges are considered acceptable over a standard aircraft environmental temperature range), and require change-out as often as every 18-months during the maintenance cycle for some aircraft applications. Implementing cartridges that replace the pyrotechnical delays with electronic technologies

The performance of the suspension is a crucial criterion for evaluating both vehicle handling and passenger comfort. To enhance suspension performance, this study proposes the design of a Quantum Genetic Fuzzy Sliding Mode Controller (S-QFSMC) based on the Smith predictor estimator, building upon the foundation of the vehicle magneto-rheological semi-active air suspension. According to the physical model of the vehicle suspension, a mechanical model of a quarter-vehicle magneto-rheological semi-active air suspension with time delay is established. On this basis, a conventional sliding mode controller is designed, and quantum genetic algorithm and fuzzy control principles are employed to optimize the chattering issue associated with sliding mode control. The Smith predictor estimator is utilized to effectively compensate for the time delay in the suspension system. Subsequently, a simulation analysis of the vehicle suspension performance is conducted. The results indicate that, compared to passive suspension control, both the QFSMC controller and the S-QFSMC controller improve the suspension performance, with the S-QFSMC controller exhibiting superior comprehensive improvement. This validates the effectiveness of the designed controllers.

Design of Robust Adaptive Controllers for Nonlinear Systems with Dynamic Uncertainties

For all first order plus time delay (FOPTD) systems, a fractional order PI (FOPI) or a traditional integer order PID (IOPID) controller can be designed to fulfill three design specifications: gain crossover frequency, phase margin, and a flat phase constraint simultaneously. In this paper, a guideline for choosing feasible or achievable gain crossover frequency and phase margin specifications, and a new FOPI/IOPID controller synthesis are proposed for all FOPTD systems. Using this synthesis scheme, the complete feasible region of the gain crossover frequency and phase margin can be obtained and visualized in the plane. With this region as the prior knowledge, all combinations of the phase margin and gain crossover frequency can be verified before the controller design. Only if the combination is chosen from this achievable region, the existence of the stabilizing and desired FOPI/IOPID controller design can be guaranteed. Especially, it is interesting to compare the areas of these two feasible regions for the IOPID controller and the FOPI controller. This area comparison reveals, for the first time, the potential advantages of one controller over the other in terms of achievable performances. As a basic step, a scheme for finding the stabilizing region of the FOPI/IOPID controller is presented first, and then a new scheme for designing a stabilizing FOPI/IOPID controller satisfying the given gain crossover frequency, phase margin and flat phase constraint is proposed in details. Thereafter, the complete information about the feasible region of gain crossover frequency and phase margin is collected. This feasible region for the FOPI controller is compared with that for the traditional IOPID controller. This area comparison shows the advantage of the FOPI over the traditional IOPID clearly. Simulation illustration is presented to show the effectiveness and the performance of the designed FOPI controller comparing with the designed IOPID controller following the same synthesis in this paper.

This article studies the problem of global stabilization of discrete-time linear systems subject to input saturation and time delay. The considered time-delay systems are first transformed into delay-free systems based on prediction technique. Then, by utilizing saturation functions technique, the corresponding global stabilizing controllers are proposed for two special discrete-time linear systems-a chain of integrators and oscillators, and explicit conditions guaranteeing stability are also given. Both current and delayed feedback information are utilized in the controller design, and some free parameters are also introduced into these controllers. These advantages can help improve the control performance significantly. Subsequently, a systematic control design procedure for globally stabilizing general discrete-time linear systems subject to multiple inputs and/or multiple inputs delays is proposed. The design procedure is in an explicit and recursive way with explicit conditions guaranteeing stability being given, and thus is easier to use than the existing one. Finally, the effectiveness of the proposed approaches are illustrated by three numerical examples.

In this paper, the problem of robust stabilization is considered for a class of uncertain time-delay dynamical systems with completely unknown upper bounds of the delayed state perturbations, uncertainties, and external disturbances. For such a class of uncertain time-delay dynamical systems, a new design method is presented whereby a class of continuous memoryless adaptation-free robust state feedback controllers is constructed. That is, no adaptation law is introduced to update those completely unknown upper bounds. It is also shown that the solutions of the resulting closed-loop time-delay dynamical systems can be guaranteed to be uniformly exponentially bounded, instead of uniform ultimate boundedness. Finally, as an application of the results, the problem of water pollution control is considered for uncertain river time-delay systems due to industrial waste treatment facility, and the corresponding simulations are provided to demonstrate the validity of the theoretical results.

Markovian jumping systems have arisen naturally in the mathematical modeling of phenomena spanning disciplines in the social sciences, natural sciences, and engineering. This kind of stochastic dynamical systems can be employed to model the dynamics when parameters are subject to random abrupt changes due to sudden environment changes, subsystem switching, system noises, executor faults, and so forth. Much attention has been given to modeling, optimization, and real applications of such stochastic dynamical systems in the literature in recent years. As the advanced control and optimization will provide a basis for the design and application of such stochastic systems, these advanced techniques would result in substantial and sustainable benefits. The accepted papers in this special issue include stochastic stability, stabilization, stochastic control optimization, system modeling and identification methods, predictive control, signal processing, robust filtering, multiagent systems, networked control systems, time-delayed systems, neural networks, the Takagi-Sugeno fuzzy systems, simulated annealing, and fault detection methods.

The paper presents a new methodology of the controller design for unstable time delay systems. The proposed method based on polynomial approach and LQ control theory yields a class of CT controllers ensuring setpoint tracking as well as load disturbance attenuation. Both control configurations, a 1DOF one with a feedback controller and a 2DOF one with a feedback and feedforward ones, were considered. Moreover, the resulting controllers obtained via polynomial Diophantine equations and spectral factorization technique are stable ones. Time delay terms are approximated by two methods and they are incorporated into the control design as a perturbation. Obtained control algorithms were compared and analysed for unstable first order time delay systems.

The problem of stabilizing a class of uncertain time-delay systems via memoryless linear feedback is examined. The systems under consideration are linear systems with time-varying state delays. They also contain uncertain parameters (possibly time-varying) whose values are known only to within a prescribed compact bounding set. The main contribution given is to enlarge the class of time-delay systems for which one can construct a stabilizing memoryless linear feedback controller. Within this framework, a novel notion of robust memoryless stabilizability is first introduced via the method of Lyapunov functionals. Then a sufficient condition for the stabilizability is proposed. It is shown that solvability of a parameterized Riccati equation can be used to determine whether the time-delay system satisfies the sufficient condition. If there exists a positive definite symmetric solution satisfying the Riccati equation, a suitable memoryless linear feedback law can be derived.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>

Fuzzy sliding mode controller design for uncertain time-delayed systems with nonlinear input