Hello everyone,
I am currently struggling to understand why if I do the series of these two STABLE discrete-systems, the resulting system is UNSTABLE.
tECU = 0.001;z = tf('z', tECU);opts = bodeoptions;opts.FreqUnits = 'Hz';%% HP filter simple
G1 = tECU/(tECU+0.1*2*pi); HP1 = (z-1)/(z-1+G1);%% HP filter 4th order
B1 = 0.999326955592380;B2 = -3.997307427851055;B3 = 5.995960944517369;B4 = -3.997307427851056;B5 = 0.999326955592380; A1 = 1.000000000000000;A2 = -3.998653063327113;A3 = 5.995960491528685;A4 = -3.995961792374911;A5 = 0.998654364173536;HP4 = (z^4*B1 + z^3*B2 + z^2*B3 + z*B4 + B5)/(z^4*A1 + z^3*A2 + z^2*A3 + z*A4 + A5);%% poles
p1 = pole(HP1);p2 = pole(HP4);p_tot = pole(HP1*HP4);%% plot Pole-Zero map
figure; hold on; pzmap(HP1, HP4, HP1*HP4, opts);legend('HP1','HP1*HP4','HP4');
Both HP1 and HP4 have stable poles, but when I do the series of HP1 and HP4 Matlab says that the resulting system has an unstable pole. Furthermore, all the poles and zeros seems to change position.
Any help or suggestion is appreciated.
Thanks
Best Answer