Control toolbox in Matlab: General Creating linear models. System - PDF document

Dr. – Ing. W. Wang, Dept. of Automatic Control, SJTU Introduction to Matlab Not required for final examination what is Matlab? Matlab — stands for matrix laboratory MATLAB is a software or a high-performance language for technical computing, developed by MathWorks Ltd. in USA. Control toolbox in Matlab: General Creating linear models. System interconnections. Data extraction. Frequency-domain analysis. Conversions. Classical design. Model dynamics. Pole placement. Time-domain analysis State-space models. LQR/LQG design. Model dimensions and Time delays. characteristics. Overloaded arithmetic operations. Demonstrations. Matrix equation solvers. Automatic Control System 1

Dr. – Ing. W. Wang, Dept. of Automatic Control, SJTU Models of control systems in Matlab − n n 1 d c ( t ) d c ( t ) dc ( t ) + + + + a a L a a c ( t ) − − n n 1 1 0 n n 1 dt dt dt − m m 1 d r ( t ) d r ( t ) dr ( t ) = + + + + ( ) b b L b b r t − − m m 1 1 0 m m 1 dt dt dt − + + + + m m 1 C ( s ) b s b s L b s b = = − m m 1 1 0 G ( s ) + − + + + n 1 R ( s ) a a s a s a L − n n 1 1 0 − + + + + m m 1 C ( s ) b s b s L b s b = = − m m 1 1 0 G ( s ) + − + + + n 1 R ( s ) a a s L a s a − n n 1 1 0 num = [b m , b m-1 , … ,b 1 , b 0 ] den = [a n , a n-1 , … ,a 1 , a 0 ] sys = tf [num, den] Automatic Control System 2

Dr. – Ing. W. Wang, Dept. of Automatic Control, SJTU Ex + + + + 3 2 ( ) 6 12 6 10 C s s s L s = = G ( s ) + + + + 4 3 2 R ( s ) s 2 s 3 s s 1 num = [6, 12, 6, 10] den = [1 2 3 1 1] sys = tf (num, den) Transfer function: 6 s^3 + 12 s^2 + 6 s + 10 --------------------------- s^4 + 2 s^3 + 3 s^2 + s + 1 Input of vector , summation of two vectors Input of matrix, summation of two matrices       1 1 2 3 3 4 = + =       c       1 1 4 5 5 6       1 2 3 = + =       c       1 4 5 Automatic Control System 3