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Lecture

Multivariable Control: System Theory and Linear Systems

In course

ME-422: Multivariable control

This course covers methods for the analysis and control of systems with multiple inputs and outputs, which are ubiquitous in modern technology and industry. Special emphasis will be placed on discrete-time systems due to their relevance to digital and embe ...

Description

This lecture covers the fundamentals of multivariable control, including system theory, linear systems, and time discretization. Topics include state equations, output equations, linear time-varying systems, and the discretization of continuous-time dynamics. The instructor provides insights on state trajectories, state-space models, and the characteristics of linear systems. Additionally, the lecture delves into the concept of Single-Input Single-Output (SISO) systems and Multi-input Multi-Output (MIMO) systems. Various textbooks are recommended for further reading, emphasizing digital control of dynamic systems and linear optimal control systems.

Instructor

Giancarlo Ferrari Trecate

Official source

Ontological neighbourhood

Information engineering

Control theory and engineering: Control theory

Related concepts (27)

Linear system

In systems theory, a linear system is a mathematical model of a system based on the use of a linear operator. Linear systems typically exhibit features and properties that are much simpler than the nonlinear case. As a mathematical abstraction or idealization, linear systems find important applications in automatic control theory, signal processing, and telecommunications. For example, the propagation medium for wireless communication systems can often be modeled by linear systems.

Linear time-invariant system

In system analysis, among other fields of study, a linear time-invariant (LTI) system is a system that produces an output signal from any input signal subject to the constraints of linearity and time-invariance; these terms are briefly defined below. These properties apply (exactly or approximately) to many important physical systems, in which case the response y(t) of the system to an arbitrary input x(t) can be found directly using convolution: y(t) = (x ∗ h)(t) where h(t) is called the system's impulse response and ∗ represents convolution (not to be confused with multiplication).

Adaptive control

Adaptive control is the control method used by a controller which must adapt to a controlled system with parameters which vary, or are initially uncertain.cite journal|author=Chengyu Cao, Lili Ma, Yunjun Xu|title="Adaptive Control Theory and Applications", Journal of Control Science and Engineering'|volume=2012|issue=1|year=2012|doi=10.1155/2012/827353|pages=1,2|doi-access=free For example, as an aircraft flies, its mass will slowly decrease as a result of fuel consumption; a control law is needed that adapts itself to such changing conditions.

Model predictive control

Model predictive control (MPC) is an advanced method of process control that is used to control a process while satisfying a set of constraints. It has been in use in the process industries in chemical plants and oil refineries since the 1980s. In recent years it has also been used in power system balancing models and in power electronics. Model predictive controllers rely on dynamic models of the process, most often linear empirical models obtained by system identification.

H-infinity methods in control theory

H∞ (i.e. "H-infinity") methods are used in control theory to synthesize controllers to achieve stabilization with guaranteed performance. To use H∞ methods, a control designer expresses the control problem as a mathematical optimization problem and then finds the controller that solves this optimization. H∞ techniques have the advantage over classical control techniques in that H∞ techniques are readily applicable to problems involving multivariate systems with cross-coupling between channels; disadvantages of H∞ techniques include the level of mathematical understanding needed to apply them successfully and the need for a reasonably good model of the system to be controlled.

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Multivariable Control: System Theory and Linear Systems

Introduces the basics of multivariable control, focusing on system theory and linear systems.

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Introduction to Multivariable Control

Covers the basics of multivariable control, including system modeling, temperature control, and optimal strategies, emphasizing the importance of considering all inputs and outputs simultaneously.

Controllability and Reachability

Explores reachability and controllability in multivariable control systems, discussing tests, proofs, and their implications.

Reachability and Controllability of LTI Systems