Relay Feedback and Multivariable Control

Research output: ThesisDoctoral Thesis (compilation)


title = "Relay Feedback and Multivariable Control",
abstract = "This doctoral thesis treats three issues in control engineering related to relay feedback and multivariable control systems. Linear systems with relay feedback is the first topic. Such systems are shown to exhibit several interesting behaviors. It is proved that there exist multiple fast relay switches if and only if the sign of the first non-vanishing Markov parameter of the linear system is positive. It is also shown that these fast switches can appear as part of a stable limit cycle. A linear system with pole excess one or two is demonstrated to be particularly interesting. Stability conditions for these cases are derived. It is also discussed how fast relay switches can be approximated by sliding modes. Performance limitations in linear multivariable control systems is the second topic. It is proved that if the top left submatrices of a stable transfer matrix have no right half-plane zeros and a certain high-frequency condition holds, then there exists a diagonal stabilizing feedback that makes a weighted sensitivity function arbitrarily small. Implications on control structure design and sequential loop-closure are given. A novel multivariable laboratory process is also presented. Its linearized dynamics have a transmission zero that can be located anywhere on the real axis by simply adjusting two valves. This process is well suited to illustrate many issues in multivariable control, for example, control design limitations due to right half-plane zeros. The third topic is a combination of relay feedback and multivariable control. Tuning of individual loops in an existing multivariable control system is discussed. It is shown that a specific relay feedback experiment can be used to obtain process information suitable for performance improvement in a loop, without any prior knowledge of the system dynamics. The influence of the loop retuning on the overall closed-loop performance is derived and interpreted in several ways.",
keywords = "robotics, Automation, Frequency methods, Process control, Sequential control, Automatic tuning, Control education, Laboratory process, Performance limitations, Decentralized control, Multivariable zero, Multivariable systems, Hybrid control, Nonlinear dynamics, Limit cycles, Oscillations, Relay feedback, Sliding modes, control engineering, Automatiska system, robotteknik, reglerteknik",
author = "Johansson, {Karl Henrik}",
note = "Defence details Date: 1997-11-25 Time: 10:15 Place: Room M:B, M-building, Lund Institute of Technology. External reviewer(s) Name: Nijmeijer, Hendrik Title: Prof Affiliation: Dept. of Applied Mathematics, University of Twente, the Netherlands ---",
year = "1997",
language = "English",
series = "PhD Thesis TFRT-1048",
publisher = "Department of Automatic Control, Lund Institute of Technology (LTH)",
school = "Department of Automatic Control",