There is, I think, something ethereal about i —the square root of minus one. I remember first hearing about it at school. It seemed an odd beast at that time—an intruder hovering on the edge of reality.

Usually familiarity dulls this sense of the bizarre, but in the case of i it was the reverse: over the years the sense of its surreal nature intensified. It seemed that it was impossible to write mathematics that described the real world in …

I and i

Networked control systems (NCSs) are spatially distributed systems for which the communication between sensors, actuators, and controllers is supported by a shared communication network. We review several recent results on estimation, analysis, and controller synthesis for NCSs. The results surveyed address channel limitations in terms of packet-rates, sampling, network delay, and packet dropouts. The results are presented in a tutorial fashion, comparing alternative methodologies

/pdf/a-survey-of-recent-results-in-networked-control-systems-2vqnhq8czm.pdf

A Survey of Recent Results in Networked Control Systems

1. Introduction. 2. Linear Algebra. 3. Linear Systems. 4. H2 and Ha Spaces. 5. Internal Stability. 6. Performance Specifications and Limitations. 7. Balanced Model Reduction. 8. Uncertainty and Robustness. 9. Linear Fractional Transformation. 10. m and m- Synthesis. 11. Controller Parameterization. 12. Algebraic Riccati Equations. 13. H2 Optimal Control. 14. Ha Control. 15. Controller Reduction. 16. Ha Loop Shaping. 17. Gap Metric and ...u- Gap Metric. 18. Miscellaneous Topics. Bibliography. Index.

/pdf/essentials-of-robust-control-3kaks6yk3h.pdf

Essentials of Robust Control

This augmented edition of a respected text teaches the reader how to use linear quadratic Gaussian methods effectively for the design of control systems. It explores linear optimal control theory from an engineering viewpoint, with step-by-step explanations that show clearly how to make practical use of the material. The three-part treatment begins with the basic theory of the linear regulator/tracker for time-invariant and time-varying systems. The Hamilton-Jacobi equation is introduced using the Principle of Optimality, and the infinite-time problem is considered. The second part outlines the engineering properties of the regulator. Topics include degree of stability, phase and gain margin, tolerance of time delay, effect of nonlinearities, asymptotic properties, and various sensitivity problems. The third section explores state estimation and robust controller design using state-estimate feedback. Numerous examples emphasize the issues related to consistent and accurate system design. Key topics include loop-recovery techniques, frequency shaping, and controller reduction, for both scalar and multivariable systems. Self-contained appendixes cover matrix theory, linear systems, the Pontryagin minimum principle, Lyapunov stability, and the Riccati equation. Newly added to this Dover edition is a complete solutions manual for the problems appearing at the conclusion of each section.

Optimal Control: Linear Quadratic Methods

https://www.control.utoronto.ca/people/profs/francis/dft.pdf

Feedback Control Theory

The force transmitted from the tires and tie rods to the steering rack of a vehicle, called the rack force, significantly influences the torque experienced by a driver at the steering wheel. As a result, estimates of rack force are used in a wide variety of advanced driver assist systems. However, existing methods for producing rack force estimates are either susceptible to the steering system disturbances or are only applicable to driving on flat road profiles. To overcome these limitations, we previously developed two models that could produce disturbance-free estimates of rack force for driving on uneven road profiles. However, our previous models were only suited to produce estimates of rack force due to low frequency road profile variations such as lateral and longitudinal road slopes. In this paper we present a model that can also handle high frequency road profile variations such as road cleats, curbs, and potholes. We validate the estimation accuracy of our model by showing results from actual driving experiments that were performed on tracks with known low and high frequency road profile variations. We further demonstrate the merits of our model relative to the existing models by comparing the various estimates to rack force measurements obtained using a sensor mounted in the test vehicle.

Rack Force Estimation for Driving on Uneven Roads.

Many researchers have studied connections between the problems of feedback control and of communicating over a channel with feedback. We study two such feedback communication schemes, and focus on properties such as phase margin, robustness with respect to unmodeled time delays, and exogenous noise inputs. In particular, we study the impact of unstable poles in the encoder or decoder on these properties, as quantified by the Bode sensitivity integral.

Feedback properties of Gaussian channels with feedback

One method to achieve lower process variance is through inter-process feedforward control. There are two problematic issues associated with feedforward recipe adjustment: (1) there is noise in the measurement tool and adjusting for inaccurate measurements could increase the variance; and (2) it is difficult to alter one parameter in a manufacturing process without worsening other key parameters. The first issue is addressed by integrating statistics theory into the controller design. One way to solve the second issue is to constrain the controller to select a recipe form a finite set of pre-qualified recipes. We call this feedforward recipe selection control (FRSC). Each recipe in FRSC has a unique adjustment and, by definition of pre-qualified, every recipe will give acceptable values for all other key characteristics. The goal of this paper is to guide the reader through a complete FRSC design. The modeling data set is from an industrial CD patterning processes. Simulation of FRSC implementation shows a standard deviation reduction of 16 percent. We also derive a re-centering methodology order to place more integrated circuits into the fastest speed grade. Our simulation doubled the number of ICs in this fastest speed grade.© (1998) COPYRIGHT SPIE--The International Society for Optical Engineering. Downloading of the abstract is permitted for personal use only.

Feedforward recipe selection control design software

In this paper previous results of the authors are used to analyze a design example.

The relation between open loop and closed loop properties of multivariable feedback systems: A practical example

The purpose of this short paper is to apply an approximation to the structured singular value, derived in [8], to analyze robustness difficulties associated with an illconditioned plant discussed in [9].

James S. Freudenberg

Papers

Rack Force Estimation for Driving on Uneven Roads.

Feedback properties of Gaussian channels with feedback

Feedforward recipe selection control design software

The relation between open loop and closed loop properties of multivariable feedback systems: A practical example

An Approximation to the Structured Singular Value