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Lecture# State-Space Representation: Controllability and Observability

Description

This lecture covers the conversion of a system to a first-order differential equation, state-space representation, controllability, observability, and the calculation of a regulator using the Ackermann method. The instructor explains how to find the state-space representation from a transfer function, the importance of controllability and observability, and the significance of placing poles in the desired locations for system stability.

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In course

Instructors (2)

ME-326: Control systems and discrete-time control

Ce cours inclut la modélisation et l'analyse de systèmes dynamiques, l'introduction des principes de base et l'analyse de systèmes en rétroaction, la synthèse de régulateurs dans le domain fréquentiel

Related concepts (73)

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.

Industrial control system

An industrial control system (ICS) is an electronic control system and associated instrumentation used for industrial process control. Control systems can range in size from a few modular panel-mounted controllers to large interconnected and interactive distributed control systems (DCSs) with many thousands of field connections. Control systems receive data from remote sensors measuring process variables (PVs), compare the collected data with desired setpoints (SPs), and derive command functions that are used to control a process through the final control elements (FCEs), such as control valves.

Distributed control system

A distributed control system (DCS) is a computerised control system for a process or plant usually with many control loops, in which autonomous controllers are distributed throughout the system, but there is no central operator supervisory control. This is in contrast to systems that use centralized controllers; either discrete controllers located at a central control room or within a central computer. The DCS concept increases reliability and reduces installation costs by localising control functions near the process plant, with remote monitoring and supervision.

Nonlinear control

Nonlinear control theory is the area of control theory which deals with systems that are nonlinear, time-variant, or both. Control theory is an interdisciplinary branch of engineering and mathematics that is concerned with the behavior of dynamical systems with inputs, and how to modify the output by changes in the input using feedback, feedforward, or signal filtering. The system to be controlled is called the "plant".

Frequency response

In signal processing and electronics, the frequency response of a system is the quantitative measure of the magnitude and phase of the output as a function of input frequency. The frequency response is widely used in the design and analysis of systems, such as audio and control systems, where they simplify mathematical analysis by converting governing differential equations into algebraic equations.

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Designing PID Controllers with Ziegler-Nichols Method

Explores the Ziegler-Nichols method for PID controller design and manual tuning in industry.

Optimal Control and State Estimation

Covers the design of a regulator and state estimator for optimal control.

Nyquist Stability Criteria

Explains Nyquist stability criteria and loop shaping for system performance and robustness.