Time-Varying Input and State Delay Compensation for Uncertain Nonlinear Systems

A robust controller is developed for uncertain, second-order nonlinear systems subject to simultaneous unknown, time-varying state delays and known, time-varying input delays in addition to additive, sufficiently smooth disturbances. An integral term composed of previous control values facilitates a delay-free open-loop error system and the development of the feedback control structure. A stability analysis based on Lyapunov-Krasovskii (LK) functionals guarantees uniformly ultimately bounded tracking under the assumption that the delays are bounded and slowly varying

State feedback control with time delay

In this thesis we start with an introduction to the theory of vibration control. We broadly classify the control methods into passive and active schemes. We introduce the problem of state feedback control and provide the classical solution in the form of Ackermann formula. We then identify the limitations of the classical approach and present the more elegant solution of partial pole assignment without spillover. We highlight the problem with model uncertainties and describe the method of pole assignment using data from measured receptances. This approach is extended for pole assignment for a linear vibrating system by using state feedback control delayed in time. This approach is significantly advantageous over various conventional state-space approaches which need to use information of , and matrices. Since the method relies solely on measured receptances, it negates the need to know , and matrices. It is shown that for a system with degrees of freedom, we may assign eigenvalues. Assigning eigenvalues in a time delayed system does not necessarily regulate the dynamics of the system or guarantee its stability. We separate the eigenvalues into two groups, primary and secondary, and propose method of a posteriori analysis to ensure that the primary eigenvalues have been assigned. The method is demonstrated by various examples. For state feedback control, the control is achieved by measuring the states of the system and feeding them back into the system after multiplying them with appropriate control gain. This makes it imperative to measure all the states of the system. In practical control applications, all states are not accessible for measurement. We address the problem of inaccessibility of states making it difficult to implement the state feedback control. We introduce the theory of linear state estimation also called observer design. We identify the limitations of this approach and introduce the concept of state reconstruction by delayed action. We develop a method to reconstruct the inaccessible states by introducing delay in the system and using information from accessible states. The results are demonstrated by examples

Separation Framework: An Enabler for Cooperative and D2D Communication for Future 5G Networks

Soaring capacity and coverage demands dictate that future cellular networks need to soon migrate towards ultra-dense networks. However, network densification comes with a host of challenges that include compromised energy efficiency, complex interference management, cumbersome mobility management, burdensome signaling overheads and higher backhaul costs. Interestingly, most of the problems, that beleaguer network densification, stem from legacy networks' one common feature i.e., tight coupling between the control and data planes regardless of their degree of heterogeneity and cell density. Consequently, in wake of 5G, control and data planes separation architecture (SARC) has recently been conceived as a promising paradigm that has potential to address most of aforementioned challenges. In this article, we review various proposals that have been presented in literature so far to enable SARC. More specifically, we analyze how and to what degree various SARC proposals address the four main challenges in network densification namely: energy efficiency, system level capacity maximization, interference management and mobility management. We then focus on two salient features of future cellular networks that have not yet been adapted in legacy networks at wide scale and thus remain a hallmark of 5G, i.e., coordinated multipoint (CoMP), and device-to-device (D2D) communications. After providing necessary background on CoMP and D2D, we analyze how SARC can particularly act as a major enabler for CoMP and D2D in context of 5G. This article thus serves as both a tutorial as well as an up to date survey on SARC, CoMP and D2D. Most importantly, the article provides an extensive outlook of challenges and opportunities that lie at the crossroads of these three mutually entangled emerging technologies.Comment: 28 pages, 11 figures, IEEE Communications Surveys & Tutorials 201

Pole Placement and Reduced-Order Modelling for Time-Delayed Systems Using Galerkin Approximations

The dynamics of time-delayed systems (TDS) are governed by delay differential equa- tions (DDEs), which are infinite dimensional and pose computational challenges. The Galerkin approximation method is one of several techniques to obtain the spectrum of DDEs for stability and stabilization studies. In the literature, Galerkin approximations for DDEs have primarily dealt with second-order TDS (second-order Galerkin method), and the for- mulations have resulted in spurious roots, i.e., roots that are not among the characteristic roots of the DDE. Although these spurious roots do not affect stability studies, they never- theless add to the complexity and computation time for control and reduced-order modelling studies of DDEs. A refined mathematical model, called the first-order Galerkin method, is proposed to avoid spurious roots, and the subtle differences between the two formulations (second-order and first-order Galerkin methods) are highlighted with examples. For embedding the boundary conditions in the first-order Galerkin method, a new pseudoinverse-based technique is developed. This method not only gives the exact location of the rightmost root but also, on average, has a higher number of converged roots when compared to the existing pseudospectral differencing method. The proposed method is combined with an optimization framework to develop a pole-placement technique for DDEs to design closed-loop feedback gains that stabilize TDS. A rotary inverted pendulum system apparatus with inherent sensing delays as well as deliberately introduced time delays is used to experimentally validate the Galerkin approximation-based optimization framework for the pole placement of DDEs. Optimization-based techniques cannot always place the rightmost root at the desired location; also, one has no control over the placement of the next set of rightmost roots. However, one has the precise location of the rightmost root. To overcome this, a pole- placement technique for second-order TDS is proposed, which combines the strengths of the method of receptances and an optimization-based strategy. When the method of receptances provides an unsatisfactory solution, particle swarm optimization is used to improve the location of the rightmost pole. The proposed approach is demonstrated with numerical studies and is validated experimentally using a 3D hovercraft apparatus. The Galerkin approximation method contains both converged and unconverged roots of the DDE. By using only the information about the converged roots and applying the eigenvalue decomposition, one obtains an r-dimensional reduced-order model (ROM) of the DDE. To analyze the dynamics of DDEs, we first choose an appropriate value for r; we then select the minimum value of the order of the Galerkin approximation method system at which at least r roots converge. By judiciously selecting r, solutions of the ROM and the original DDE are found to match closely. Finally, an r-dimensional ROM of a 3D hovercraft apparatus in the presence of delay is validated experimentally

Predictive scheme for observer-based control of LTI systems with unknown disturbances

International audienceIn this work, it is shown that the results introduced in [1], that hold for full state measurement, can be extended to partial state measurement. In particular, it is proven that the combination of an observer with the new predictive scheme of [1] leads to a better disturbance attenuation than using the same observer with the standard predictive scheme. Finally, some simulations illustrate the results for constant and time-varying disturbances