Slideshare uses cookies to improve functionality and performance, and to provide you with relevant advertising. If you continue browsing the site, you agree to the use of cookies on this website. See our User Agreement and Privacy Policy.

Slideshare uses cookies to improve functionality and performance, and to provide you with relevant advertising. If you continue browsing the site, you agree to the use of cookies on this website. See our Privacy Policy and User Agreement for details.

Like this presentation? Why not share!

- Lecture 16 ME 176 7 Root Locus Tech... by leonidesdeocampo 6796 views
- Lecture 0 ME 176 0 Overview by leonidesdeocampo 434 views
- Lecture 1 ME 176 1 Introduction by leonidesdeocampo 1151 views
- Lecture 11 ME 176 5 Stability by leonidesdeocampo 6422 views
- Lecture 12 ME 176 6 Steady State Error by leonidesdeocampo 25664 views
- Lecture 14 ME 176 7 Root Locus Tech... by leonidesdeocampo 5072 views

No Downloads

Total views

781

On SlideShare

0

From Embeds

0

Number of Embeds

5

Shares

0

Downloads

0

Comments

0

Likes

5

No embeds

No notes for slide

- 1. ME 176 Control Systems Engineering Department of Mechanical Engineering Mathematical Modeling
- 2. Mathematical Modeling: Introduction Mathematical Models are representation of a system's schematics, which in turn is a representation of a system simplified using assumptions in order to keep the model manageable and still an approximation of reality. 1. Transfer Functions (Frequency Domain) 2. State Equations (Time Domain) First step in creating a mathematical model is applying the fundamental laws of physics and engineering: Electrical Networks - Ohm's law and Kirchhoff's laws Mechanical Systems - Newton's laws. Department of Mechanical Engineering
- 3. Mathematical Modeling: Transfer Functions Differential Equation Representation: Transfer Function : - Distinct and Separate - Cascaded Interconnection Department of Mechanical Engineering
- 4. Mathematical Modeling: Laplace Transform Represents relations of subsystems as separate entities. Interrelationship are algebraic. Laplace Transform: Inverse Laplace Transform: Department of Mechanical Engineering
- 5. Mathematical Modeling: Laplace Transform Department of Mechanical Engineering Laplace Transform Table Unit Impulse Unit Step Ramp Exponential Decay Sine Cosine Laplace Transform Theorems Linearity Frequency Shift Time Shift Scaling Differentiation Integration Initial Value Final Value
- 6. Mathematical Modeling: Laplace Transform Partial Fraction Expansion, where roots of the Denominator of F(s) are: Note: N(s) must be less order that D(s) . 1. Real and Distinct where, Department of Mechanical Engineering
- 7. Mathematical Modeling: Laplace Transform Partial Fraction Expansion, where roots of the Denominator of F(s) are: 2. Real and Repeated where, Department of Mechanical Engineering
- 8. Mathematical Modeling: Laplace Transform Partial Fraction Expansion, where roots of the Denominator of F(s) are: 3. Complex or Imaginary (Part 1) - compute for residues Steps: a. Solve for known residues. b. Multiply by lowest common denominator and clearing fractions. c. Balancing coefficients. Department of Mechanical Engineering
- 9. Mathematical Modeling: Laplace Transform Partial Fraction Expansion, where roots of the Denominator of F(s) are: 3. Complex or Imaginary (Part 2) - put into proper form Steps: a. Complete squares of denominator. b. Adjust numerator. Department of Mechanical Engineering
- 10. Mathematical Modeling: Transfer Functions c(t) - Output r(t) - Input Systems that can be represented by linear time invariant differential equations. Initial conditions are assumed to be zero . Permits interconnections of physical systems which can be algebraically manipulated. Department of Mechanical Engineering
- 11. Mathematical Modeling: Transfer Functions Department of Mechanical Engineering

No public clipboards found for this slide

×
### Save the most important slides with Clipping

Clipping is a handy way to collect and organize the most important slides from a presentation. You can keep your great finds in clipboards organized around topics.

Be the first to comment