PPT-Digital and Non-Linear Control

Routh Herwitz Stability Criterion RouthHurwitz Stability Criterion It is a method for determining continuous system stability It can tell whether there are roots in the RHP of the characteristic polynomial of a control system without solving it. One of the most important aspects is the sampling proces s level In continuous time control systems all the system variable s are continuous signals Whether the system is linear or nonlinear all variables are continu ously present and therefore know N is the process noise or disturbance at time are IID with 0 is independent of with 0 Linear Quadratic Stochastic Control 52 brPage 3br Control policies statefeedback control 0 N called the control policy at time roughly speaking we choo e Ax where is vector is a linear function of ie By where is then is a linear function of and By BA so matrix multiplication corresponds to composition of linear functions ie linear functions of linear functions of some variables Linear Equations a 12 22 a a mn is an arbitrary matrix Rescaling The simplest types of linear transformations are rescaling maps Consider the map on corresponding to the matrix 2 0 0 3 That is 7 2 0 0 3 00 brPage 2br Shears The next simplest type of linear transfo N with state input and process noise linear noise corrupted observations Cx t 0 N is output is measurement noise 8764N 0 X 8764N 0 W 8764N 0 V all independent Linear Quadratic Stochastic Control with Partial State Obser vation 102 br 5 CC 35 100 100 CC brPage 4br brPage 5br brPage 6br 8486 brPage 7br brPage 8br SUPPLY CURRENT mA 08 06 04 02 10 20 040 SUPPLY VOLTAGE V amb 7057520C amb 12557520C amb 057520C amb 2557520C amb 5557520C INPUT CURRENT nA 20 10 20 040 SUPPLY VOLTAGE V DOC NON DISCLOSURE AND NON CIRCUMVENT AGREEMENT This Non Disclosure and Non Circumvent Agreement this Agreement is entered into this day of 20 the Effective Date by and between the entities and in S. chrödinger Equation. By Nick Armstrong and Brandan Mantei. Introduction. A rogue wave is generally defined as a wave that has a height that is double that of the significant wave height (SWH).. The significant wave height is the average height of the largest third of the waves recorded in a given period of time.. Charlotte Kiang. May 16, 2012. About me. My name is Charlotte Kiang, and I am a junior at Wellesley College, majoring in math and computer science with a focus on engineering applications.. What I hope to accomplish today. Presented by: Johnathan Franck. Mentor: . Alex . Cloninger. Outline. Different Representations. 5 Techniques. Principal component . analysis (PCA)/. Multi-dimensional . scaling (MDS). Sammons non-linear mapping. Digital Control System Time Domain and Stability Analysis. 1. Introduction. The time response of a discrete-time linear system is the solution of the difference equation governing the system.. For the . Digital System Frequency Response and Modeling. 1. Lecture Outline. Sampling Theorem. Frequency Response. ADC Model. DAC Model. Combined Models. 2. Sampling Theorem. Sampling is necessary for the processing of analog data using digital elements.. INTRODUCTION. Introduction. . What. is a . control. . system. ?. Objective:. To make the system OUTPUT and the desired REFERENCE as close as. . possible, i.e., to make the ERROR as . small as possible.. © 2016 Pearson Education, Inc. Linear Equations in Linear Algebra LINEAR INDEPENDENCE Slide 1.7- 2 © 2016 Pearson Education, Inc. LINEAR INDEPENDENCE Definition: A set of vectors { v 1 , …,