Analysis of Control Systems in State Space

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Presentation transcript:

Analysis of Control Systems in State Space 2009 Lecture Side January 2009 Lecture by Suradet Tantrairatn Instructor and Researcher Analysis of Control Systems in State Space Chapter Eleven week2 Control Engineering

Review Exercise จงแปลง Transfer Function ให้อยู่ในรูปบัญญัติ ( Controllable และ Jordan Canonical Form ) ? Control Engineering 2009 Subject Name Automotive Automatic Control Month 200X

Solving the time-invariant state equation review the solution of the scalar differential equation by assume a solution x(t) of the form Als; t = 0 : Aerospace Engineering 2009 Subject Name Aircraft Materials Month 200X

Solving the time-invariant state equation (2) now solve the vector-matrix differential equation assume that the solution in the form of vector power series in t, also, Aerospace Engineering 2009 Subject Name Aircraft Materials Month 200X

Solving the time-invariant state equation (3) Aerospace Engineering 2009 Subject Name Aircraft Materials Month 200X

Laplace Transform Approach to the Solution of Homogeneous State Equation Take Laplace transform Take inverse Laplace transform Control Engineering 2009 Subject Name Automotive Automatic Control Month 200X

Laplace Transform Approach to the Solution of Homogeneous State Equation (2) Control Engineering 2009 Subject Name Automotive Automatic Control Month 200X

State - Transition Matrix Control Engineering 2009 Subject Name Automotive Automatic Control Month 200X

Example Control Engineering 2009 Subject Name Automotive Automatic Control Month 200X

Exercise 1 Find x1(t) , x2(t) The initial condition Control Engineering 2009 Subject Name Automotive Automatic Control Month 200X

Exercise 1 (Solution) Control Engineering 2009 Subject Name Automotive Automatic Control Month 200X

Solution of Nonhomogeneous State Equation Control Engineering 2009 Subject Name Automotive Automatic Control Month 200X

Solution of Nonhomogeneous State Equation (2) Control Engineering 2009 Subject Name Automotive Automatic Control Month 200X

Solution of Nonhomogeneous State Equation (3) Control Engineering 2009 Subject Name Automotive Automatic Control Month 200X

Example 2 Control Engineering 2009 Subject Name Automotive Automatic Control Month 200X

Exercise 2 Find x1(t) , x2(t) The initial condition Input is Unit Step Control Engineering 2009 Subject Name Automotive Automatic Control Month 200X

Exercise 2 (Solution) Control Engineering 2009 Subject Name Automotive Automatic Control Month 200X

Matrix Exponential eAt Control Engineering 2009 Subject Name Automotive Automatic Control Month 200X

Matrix Exponential eAt Method 1 : Solution Control Engineering 2009 Subject Name Automotive Automatic Control Month 200X

Example 3 Control Engineering 2009 Subject Name Automotive Automatic Control Month 200X

Example 3 Control Engineering 2009 Subject Name Automotive Automatic Control Month 200X

Matrix Exponential eAt Control Engineering 2009 Subject Name Automotive Automatic Control Month 200X

Matrix Exponential eAt Control Engineering 2009 Subject Name Automotive Automatic Control Month 200X

Example 4 Control Engineering 2009 Subject Name Automotive Automatic Control Month 200X

Exercise 4 ( โดยการหา state-transition matrix ใช้ทั้ง 3 วิธี) Control Engineering 2009 Subject Name Automotive Automatic Control Month 200X

Exercise 4 Control Engineering 2009 Subject Name Automotive Automatic Control Month 200X

Laplace Transform Control Engineering 2009 Subject Name Automotive Automatic Control Month 200X