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Lecture

Observability and Governability

In course

ME-273: Introduction to control of dynamical systems

Cours introductif à la commande des systèmes dynamiques. On part de quatre exemples concrets et on introduit au fur et à mesure un haut niveau d'abstraction permettant de résoudre de manière unifiée les problèmes d'asservissement et de régulation, en parti ...

Description

This lecture covers the concepts of observability and governability in dynamic systems, focusing on criteria, transfer functions, state representations, and canonical forms. It explains how to determine the governability of a system and the importance of observable canonical forms. The instructor discusses the state regulator, control strategies, and the transformation of matrices to ensure system stability.

Instructor

Philippe Müllhaupt

Official source

Related concepts (30)

Control theory

Control theory is a field of control engineering and applied mathematics that deals with the control of dynamical systems in engineered processes and machines. The objective is to develop a model or algorithm governing the application of system inputs to drive the system to a desired state, while minimizing any delay, overshoot, or steady-state error and ensuring a level of control stability; often with the aim to achieve a degree of optimality. To do this, a controller with the requisite corrective behavior is required.

State-space representation

In control engineering, model based fault detection and system identification a state-space representation is a mathematical model of a physical system specified as a set of input, output and variables related by first-order (not involving second derivatives) differential equations or difference equations. Such variables, called state variables, evolve over time in a way that depends on the values they have at any given instant and on the externally imposed values of input variables.

Quantum dynamics

In physics, quantum dynamics is the quantum version of classical dynamics. Quantum dynamics deals with the motions, and energy and momentum exchanges of systems whose behavior is governed by the laws of quantum mechanics. Quantum dynamics is relevant for burgeoning fields, such as quantum computing and atomic optics. In mathematics, quantum dynamics is the study of the mathematics behind quantum mechanics. Specifically, as a study of dynamics, this field investigates how quantum mechanical observables change over time.

Open quantum system

In physics, an open quantum system is a quantum-mechanical system that interacts with an external quantum system, which is known as the environment or a bath. In general, these interactions significantly change the dynamics of the system and result in quantum dissipation, such that the information contained in the system is lost to its environment. Because no quantum system is completely isolated from its surroundings, it is important to develop a theoretical framework for treating these interactions in order to obtain an accurate understanding of quantum systems.

Linear–quadratic regulator

The theory of optimal control is concerned with operating a dynamic system at minimum cost. The case where the system dynamics are described by a set of linear differential equations and the cost is described by a quadratic function is called the LQ problem. One of the main results in the theory is that the solution is provided by the linear–quadratic regulator (LQR), a feedback controller whose equations are given below. LQR controllers possess inherent robustness with guaranteed gain and phase margin, and they also are part of the solution to the LQG (linear–quadratic–Gaussian) problem.

Related lectures (30)

State-Space Representation: Controllability and Observability

Explores state-space representation, controllability, observability, and regulator calculation using the Ackermann method.

Stability: Poles, Zeros, and Control

Covers stability, poles, zeros, and control in dynamic systems, emphasizing the importance of observability.

State-Space Representation: Basics & Transformations

Covers the basics of state-space representation and explores transformations to different forms.

State-Space Representation: Structure Theorem

Covers the structure theorem for state-space representations and companion forms.

Multivariable Control: Weight Design and Stability Analysis