Control System Toolbox (Part-I) imtiaz.hussain@faculty.muet.edu.pk

Outline Introduction Transfer Function Models Pole-Zero maps From Numerator & Denominator Coefficients From Zero-Pole-Gain Pole-Zero maps Simplification of Block Diagrams Series Blocks Parallel Blocks Feedback loops

Transfer Function Model Using Numerator & Denominator Coefficients This transfer function can be stored into the MATLAB num = 100; den = [1 14 10]; sys=tf(num,den) To check your entry you can use the command printsys as shown below: printsys(num,den); 11/11/2018

Transfer Function Model Using Zeros, Poles and Gain (ZPK model) This transfer function can be stored into the MATLAB Zeros=-3; Poles= [-1 -2]; K=100; sys=zpk(Zeros,Poles,K) To check your entry you can use the command printsys as shown below: printsys(num,den); 11/11/2018

Poles & Zeros We can find poles with the help of following MATLAB command. poles = roots(den) We can find Zeros with the help of following MATLAB command zeros = roots(num) 11/11/2018

contd….. Poles & Zeros We can plot the poles of the above transfer function marked by the symbol ‘x’. plot(poles,’x’) To plot the poles and zeros of any transfer function there is a built in function pzmap in the MATLAB pzmap(num,den) 11/11/2018

Series Blocks Blocks in series can be simplified by using series command S 9S + 17 9(S+3) 2S2 + 9s + 27 num1 = [1 0]; den1 = [9 17]; num2 = 9*[1 3]; den2 = [2 9 27]; [num12, den12] = series (num1,den1,num2,den2); printsys(num12,den12); 11/11/2018

Contd… Series Blocks Blocks in series can also be simplified by using conv command S 9S + 17 9(S+3) 2S2 + 9s + 27 num1 = [1 0]; den1 = [9 17]; num2 = 9*[1 3]; den2 = [2 9 27]; num12 =conv(num1,num2); den12 = conv(,den1,den2); printsys(num12,den12); 11/11/2018

Parallel Block Blocks in parallel can be simplified by using parallel command num1 = [1 2]; den1 = [1 2 3]; num2 = [1 3]; den2 = [1 -4 1]; [num, den]=parallel(num1,den1,num2,den2); printsys(num,den); 11/11/2018

Closed-Loop Transfer Function (Unity Feedback) Closed loop transfer function with unity feedback can be simplified using cloop command. C(S) R(S) - 9 S + 5 num = 9; den = [1 5]; [numcl, dencl] = cloop(num, den,-1); printsys(numcl,dencl) 11/11/2018

Closed-loop transfer function If the feedback is not unity then we can use feedback command to simplify the canonical form. C(S) R(S) - 1 S + 1 2 S num1 = 1; den1 = [1 1]; num2 = 2; den2 = [1 0]; [numcl,dencl] = feedback(num1,den1,num2,den2,-1); printsys(numcl,dencl) 11/11/2018

Exercise#1 Simplify the following block diagram and determine the following (Assume K=10). Closed loop transfer function (C/R) Poles Zeros Pole-zero-map

Exercise#2 Simplify the following block diagram and determine the following. Closed loop transfer function (C/R) Poles Zeros Pole-Zero-map + - R C

End of Tutorial You can Download this tutorial from http://imtiazhussainkalwar.weebly.com/ End of Tutorial 11/11/2018