Classical control theory

Root locus

In control theory and stability theory, root locus analysis is a graphical method for examining how the roots of a system change with variation of a certain system parameter, commonly a gain within a feedback system. This is a technique used as a stability criterion in the field of classical control theory developed by Walter R. Evans which can determine stability of the system. The root locus plots the poles of the closed loop transfer function in the complex s-plane as a function of a gain parameter (see pole–zero plot). An analog computer called a "Spirule" can compute root loci. (Wikipedia).

Root locus
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Understanding and Sketching the Root Locus

In this video we discuss how to sketch the root locus for a system by developing a series of 5 core rules augmented by 5 supplemental rules (for a total of 10 rules). These rules will help us gain an understanding and intuition on how the root locus behaves as the parameter K increases fr

From playlist Control Theory

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Using Root Locus to Meet Performance Requirements

In this video we investigate how to use the root locus technique to design a controller that meets certain performance specifications. Topics and timestamps: (0:17) – Introduction and performance requirements (3:39) – Example designing a controller using root locus (21:16) – Verify contro

From playlist Control Theory

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Parabolas 3 Algebra Regents

In this video we review the basic components of a parabola

From playlist Parabolas

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AQA Core 3 9.01a Locating Roots

I look at how we can show that a curve has a root between two values on the x-axis.

From playlist [OLD SPEC] TEACHING AQA CORE 3 (C3)

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Locus in a Plane Examples

How to find Locus in a Plane. We go through how to find these sets of points in a number of examples in this free math video tutorial by Mario's Math Tutoring. 0:23 What is a Locus 0:32 Example 1 Find the Locus of Points that are 3 Inches From a Circle of Radius 5 Inches in a Plane. 2:23

From playlist Locus

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Parabolas 5 Algebra Regents

In this video we review the basic components of a parabola

From playlist Parabolas

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Locus of a Parabola (1 of 3: Defining features)

More resources available at www.misterwootube.com

From playlist Further Work with Functions (related content)

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Find the nth root on desmos

In this video, we show how to find the nth root on desmos

From playlist desmos

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Given a Rooted Tree, Determine Relationships

This video analyzes the relationships of vertices in a rooted tree. mathispower4u.com

From playlist Graph Theory (Discrete Math)

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Using ‘rlocus’ in Matlab to Plot the Root Locus

This tutorial illustrates how to use the ‘rlocus’ command in Matlab to quickly and easily sketch the root locus. Discussion on the 3 example transfer functions we investigate in this video can be found at: G1(s): https://youtu.be/gA-KOk3SAb0?t=215 G6(s): https://youtu.be/gA-KOk3SAb0?t=628

From playlist Working with Matlab

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5. Root Locus

MIT Electronic Feedback Systems (1985) View the complete course: http://ocw.mit.edu/RES6-010S13 Instructor: James K. Roberge License: Creative Commons BY-NC-SA More information at http://ocw.mit.edu/terms More courses at http://ocw.mit.edu

From playlist MIT Electronic Feedback Systems (1985)

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6. More Root Locus

MIT Electronic Feedback Systems (1985) View the complete course: http://ocw.mit.edu/RES6-010S13 Instructor: James K. Roberge License: Creative Commons BY-NC-SA More information at http://ocw.mit.edu/terms More courses at http://ocw.mit.edu

From playlist MIT Electronic Feedback Systems (1985)

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Designing a PID Controller Using the Root Locus Method

In this video we discuss how to use the root locus method to design a PID controller. In addition to discussing the theory, we look at Matlab tools to enable this workflow. In addition, we demonstrate the effectiveness of the resulting controller on a real system. Finally, we discuss ho

From playlist Control Theory

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Using the Control System Designer in Matlab

In this video we show how to use the Control System Designer to quickly and effectively design control systems for a linear system. We show how to add multiple design requirements and iterate on control design until satisfactory performance is achieved. Topics and timestamps: 0:00 – Revi

From playlist Working with Matlab

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Locus of Complex Equation Z^2 = 1+z/1-z for |z|=1.

Complex Analysis: Find the locus of Z from the equation Z^2 = 1+z/1-z for all z with modulus equal to 1. Steps include parametrizing the unit circle and applying DeMoivre's Theorem to get square roots of complex numbers.

From playlist Complex Analysis

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Danny Calegari: Big Mapping Class Groups - lecture 5

Part I - Theory : In the "theory" part of this mini-course, we will present recent objects and phenomena related to the study of big mapping class groups. In particular, we will define two faithful actions of some big mapping class groups. The first is an action by isometries on a Gromov-h

From playlist Topology

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4. Stability

MIT Electronic Feedback Systems (1985) View the complete course: http://ocw.mit.edu/RES6-010S13 Instructor: James K. Roberge License: Creative Commons BY-NC-SA More information at http://ocw.mit.edu/terms More courses at http://ocw.mit.edu

From playlist MIT Electronic Feedback Systems (1985)

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Parabolas 8 Algebra Regents

In this video we review the basic components of a parabola

From playlist Parabolas

Related pages

Feedback | Z-transform | Nyquist stability criterion | Phase margin | Magnitude condition | Aliasing | Transfer function | Classical control theory | Closed-loop transfer function | Stable polynomial | Stability criterion | Degree (angle) | Pole–zero plot | Control theory | Bode plot | Routh–Hurwitz stability criterion | PID controller | Asymptote | Angle condition | Zeros and poles | Stability theory