chapter 7 multivariable and optimal control n.
Download
Skip this Video
Loading SlideShow in 5 Seconds..
Chapter 7 Multivariable and Optimal Control PowerPoint Presentation
Download Presentation
Chapter 7 Multivariable and Optimal Control

Loading in 2 Seconds...

play fullscreen
1 / 91

Chapter 7 Multivariable and Optimal Control - PowerPoint PPT Presentation


  • 174 Views
  • Uploaded on

Chapter 7 Multivariable and Optimal Control. Time-Varying Optimal Control - deterministic systems. LQ problem (Linear Quadratic)–Finite time problem. Using Lagrange multipliers. Control gains vs. time. 10. Q2 = 0.01. 8. 6. K theta. 4. Q2 = 0.1. 2. Q2 = 1.0. 0. 0. 5. 10. 15. 20.

loader
I am the owner, or an agent authorized to act on behalf of the owner, of the copyrighted work described.
capcha
Download Presentation

Chapter 7 Multivariable and Optimal Control


An Image/Link below is provided (as is) to download presentation

Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author.While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server.


- - - - - - - - - - - - - - - - - - - - - - - - - - E N D - - - - - - - - - - - - - - - - - - - - - - - - - -
    Presentation Transcript
    1. Chapter 7Multivariable and Optimal Control

    2. Time-Varying Optimal Control - deterministic systems

    3. LQ problem (Linear Quadratic)–Finite time problem Using Lagrange multipliers

    4. Control gains vs. time 10 Q2 = 0.01 8 6 K theta 4 Q2 = 0.1 2 Q2 = 1.0 0 0 5 10 15 20 25 30 35 40 45 50 k 5 Q2 = 0.01 4 3 Q2 = 0.1 K theta dot 2 Q2 = 1.0 1 0 0 5 10 15 20 25 30 35 40 45 50 k

    5. LQR (Linear Quadratic Regulator) -Infinite time problem • ARE(Algebraic Riccati Equation) • analytic solution is impossible in most cases. • numerical solution is required.

    6. Remark : Using reciprocal root propertiesin p372

    7. Symmetric root locus 1.5 1 0.5 Imag Axis 0 -0.5 -1 -1.5 -1.5 -1 -0.5 0 0.5 1 1.5 Real Axis

    8. Eigenvector Decomposition

    9. outside the unit circle inside the unit circle

    10. Cost Equivalents

    11. Least Squares Estimation n1 unknown vector pn matrix p1 measurement error vector p1 measurement vector

    12. Sales fit and prediction 14 12 10 8 Sales ($1000) 6 4 2 0 0 5 10 15 20 25 Months

    13. Weighted Least Squares

    14. Recursive Least Square

    15. old estimate covariance of old estimate new estimate old estimate

    16. Sometime, it is a scalar. That is ifwe use just one new information.

    17. Stochastic Models of Disturbance • We have dealt with well-known well-defined, ideal systems. • disturbance (process, load variation) • measurement noise sample point in sample space(event) s 0 real line new (range) sample space

    18. X F(X, t1) X F(X, t3) F(X, t2) X(•, 3) X(•, 2) X(•, 1) t 1 0 0 t2 t3 t1

    19. Remark: