Output Filter Aware Optimization of the Noise Shaping Properties of {\Delta}{\Sigma} Modulators via Semi-Definite Programming

The Noise Transfer Function (NTF) of {\Delta}{\Sigma} modulators is typically designed after the features of the input signal. We suggest that in many applications, and notably those involving D/D and D/A conversion or actuation, the NTF should instead be shaped after the properties of the output/reconstruction filter. To this aim, we propose a framework for optimal design based on the Kalman-Yakubovich-Popov (KYP) lemma and semi-definite programming. Some examples illustrate how in practical cases the proposed strategy can outperform more standard approaches.Comment: 14 pages, 18 figures, journal. Code accompanying the paper is available at http://pydsm.googlecode.co

Iterative learning fault-tolerant control for differential time-delay batch processes in finite frequency domains

This paper develops a fault-tolerant iterative learning control law for a~class of~linear time-delay differential batch processes with actuator faults using the repetitive process setting. Once the dynamics are expressed in this setting, stability analysis and control law design makes use of the generalized Kalman-Yakubovich-Popov (KYP) lemma in the form of the corresponding linear matrix inequalities (LMIs). In particular, sufficient conditions for the existence of a fault-tolerant control law are developed together with design algorithms for the associated matrices. Under the action of this control law the ILC dynamics have a monotonicity property in terms of an error sequence formed from the difference between the supplied reference trajectory and the outputs produced. An extension to robust control against structured time-varying uncertainties is also developed. Finally, a simulation based case study on the model of a~two-stage chemical reactor with delayed recycle is given to demonstrate the feasibility and effectiveness of the new designs

Topics in Automotive Rollover Prevention: Robust and Adaptive Switching Strategies for Estimation and Control

The main focus in this thesis is the analysis of alternative approaches for estimation and control of automotive vehicles based on sound theoretical principles. Of particular importance is the problem rollover prevention, which is an important problem plaguing vehicles with a high center of gravity (CG). Vehicle rollover is, statistically, the most dangerous accident type, and it is difficult to prevent it due to the time varying nature of the problem. Therefore, a major objective of the thesis is to develop the necessary theoretical and practical tools for the estimation and control of rollover based on robust and adaptive techniques that are stable with respect to parameter variations. Given this background, we first consider an implementation of the multiple model switching and tuning (MMST) algorithm for estimating the unknown parameters of automotive vehicles relevant to the roll and the lateral dynamics including the position of CG. This results in high performance estimation of the CG as well as other time varying parameters, which can be used in tuning of the active safety controllers in real time. We then look into automotive rollover prevention control based on a robust stable control design methodology. As part of this we introduce a dynamic version of the load transfer ratio (LTR) as a rollover detection criterion and then design robust controllers that take into account uncertainty in the CG position. As the next step we refine the controllers by integrating them with the multiple model switched CG position estimation algorithm. This results in adaptive controllers with higher performance than the robust counterparts. In the second half of the thesis we analyze extensions of certain theoretical results with important implications for switched systems. First we obtain a non-Lyapunov stability result for a certain class of linear discrete time switched systems. Based on this result, we suggest switched controller synthesis procedures for two roll dynamics enhancement control applications. One control design approach is related to modifying the dynamical response characteristics of the automotive vehicle while guaranteeing the switching stability under parametric variations. The other control synthesis method aims to obtain transient free reference tracking of vehicle roll dynamics subject to parametric switching. In a later discussion, we consider a particular decentralized control design procedure based on vector Lyapunov functions for simultaneous, and structurally robust model reference tracking of both the lateral and the roll dynamics of automotive vehicles. We show that this controller design approach guarantees the closed loop stability subject to certain types of structural uncertainty. Finally, assuming a purely theoretical pitch, and motivated by the problems considered during the course of the thesis, we give new stability results on common Lyapunov solution (CLS) existence for two classes of switching linear systems; one is concerned with switching pair of systems in companion form and with interval uncertainty, and the other is concerned with switching pair of companion matrices with general inertia. For both problems we give easily verifiable spectral conditions that are sufficient for the CLS existence. For proving the second result we also obtain a certain generalization of the classical Kalman-Yacubovic-Popov lemma for matrices with general inertia

Dissipative Imitation Learning for Discrete Dynamic Output Feedback Control with Sparse Data Sets

Imitation learning enables the synthesis of controllers for complex objectives and highly uncertain plant models. However, methods to provide stability guarantees to imitation learned controllers often rely on large amounts of data and/or known plant models. In this paper, we explore an input-output (IO) stability approach to dissipative imitation learning, which achieves stability with sparse data sets and with little known about the plant model. A closed-loop stable dynamic output feedback controller is learned using expert data, a coarse IO plant model, and a new constraint to enforce dissipativity on the learned controller. While the learning objective is nonconvex, iterative convex overbounding (ICO) and projected gradient descent (PGD) are explored as methods to successfully learn the controller. This new imitation learning method is applied to two unknown plants and compared to traditionally learned dynamic output feedback controller and neural network controller. With little knowledge of the plant model and a small data set, the dissipativity constrained learned controller achieves closed loop stability and successfully mimics the behavior of the expert controller, while other methods often fail to maintain stability and achieve good performance

Probabilistic Decentralized Active Vibration Control: Stability, Performance, and Robustness

This research develops probabilistic decentralized active vibration control design and synthesis techniques for uncertain complex structures. The uncertainty and complexity of the structures studied in this thesis are concentrated at the point where two portions of a structure adjoin --- the structural interconnection. This uncertainty is characterized using random variables. The controller design and synthesis approaches that are developed in this research lead to decentralized controller architectures while accounting for random uncertainty at structural interconnections. Ancillary to probabilistic robust controller design and synthesis is the development of analysis tools that enable the designer to evaluate the robust stability and robust performance of the synthesized controllers, given that the plant uncertainty is random. The control approaches developed in this thesis fall into two distinct categories: 1. Full state feedback control design and synthesis for a lightly damped, lumped parameter model with random interconnection uncertainty. 2. Dynamic output feedback control design and synthesis for a lightly damped, high dimensional beam model derived using finite element theory with random interconnection element uncertainty. For both the full state and dynamic output feedback control approaches that are developed in this research, the dynamic systems are modeled as generalized plants for control design and synthesis. Control laws that are decentralized, attenuate the disturbance input to performance output channels in a system infinity-norm sense, and that are robust against random interconnection uncertainty are then designed and synthesized. The models used in this research represent random, lightly damped structures. Control design philosophies and approaches are catered to, and exploit, properties specific to lightly damped structures

Advance Servo Control for Hard Disk Drive in Mobile Application

Ph.DDOCTOR OF PHILOSOPH

Data-driven extraction of uniformly stable and passive parameterized macromodels

A Robust algorithm for the extraction of reduced-order behavioral models from sampled frequency responses is proposed. The system under investigation can be any Linear and Time Invariant structure, although the main emphasis is on devices that are relevant for Signal and Power Integrity and RF design, such as electrical interconnects and integrated passive components. We assume that the device under modeling is parameterized by one or more design variables, which can be related to geometry or materials. Therefore, we seek for multivariate macromodels that reproduce the dynamic behavior over a predefined frequency band, with an explicit embedded dependence of the model equations on these external parameters. Such parameterized macromodels may be used to construct component libraries and prove very useful in fast system-level numerical simulations in time or frequency domain, including optimization, what-if, and sensitivity analysis. The main novel contribution is the formulation of a finite set of convex constraints that are applied during model identification, which provide sufficient conditions for uniform model stability and passivity throughout the parameter space. Such constraints are characterized by an explicit control allowing for a trade-off between model accuracy and runtime, thanks to some special properties of Bernstein polynomials. In summary, we solve the longstanding problem of multivariate stability and passivity enforcement in data-driven model order reduction, which insofar has been tackled only via either overconservative or heuristic and possibly unreliable methods