Short Tutorial on Matlab Part 7 Control Toolbox 1

ööæŁ-ç-ççö÷łŁ÷÷÷--Ł-çæłŁ÷çæççöłł-÷-÷æ-Short Tutorial on Matlab(©2004 by Tomas Co)Part 7. The Control Toolbox. Basics for SISO LTI systems1. Building models for linear time-invariant systemsThere are three types of models which can easily be transformed to each other:a) state spaceb) transfer functionc) zero-pole-gainExample 1: Creating a State Space ModelGiven the set of linear differential equations:dh1 = 2h + 3h + 2v1 2dtdh2 = 4h h v1 2dt1q = h 2h + v1 22where the states are h and h , the input is v and the output is q.1 2This can be rewritten in matrix form as:dx = Ax + Budty = Cx + Duwhere,h1 ( ) ( )x = ; u = v ; y = qh22 3 2A = ; B =4 1 11( )C = 1 2 ; D =2So in Matlab command window, we first input matrices A, B, C and D:>> A=[-2,3;4,-1];>> B=[2;-1];>> C=[1,-2];>> D=[1/2];1Then to create a state space object, use the ss command:>> ht_model = ss(A,B,C,D);this creates the object ht_model. You can see this in your workspace, as shownin Figure 1.Figure 1.To see what is inside this object, just like any variable, simply type the objectname:>> ht_modela = x1 x2 x1 -2 3 x2 4 -1b = u1 x1 2 x2 -1c = x1 x2 y1 1 -2d = u1 y1 0.5Continuous-time model.2Example 2: Creating Transfer Function and Zero-Pole-Gain ModelsSuppose we are given transfer functions written in two forms:2s +1G =23s + 2s + 4(s +1)(s + 3)H = 7(s + 2)(s + ...