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Hi,
I have a plant transfer function Gp(s) = 4/(s*(s+2)) The denominator has a degree 2. When I convert this to discrete time using the residual method and a Zero Order Hold, I multiply the denominator by another s so the degree is now 3. Using the residual method formula in the notes, I get a Gp(z) = 4.2749/(z-0.8187)
I'm supposed to use Ragazzini's method to design a lead compensator for this system. The pole of this Gp(z) is clearly not outside the unit circle. So there is no need to eliminate any poles/zeros in the F(z) function. I'm not sure how to continue with this. In all my previous lecture examples, there has always been an unstable pole/zero in the Gp(z), which we need to cancel out by inserting a new pole/zero in the F(z) to compensate. Now that the only pole is z=0.8187, and it's stable, is it safe to say that we don't need to cancel any poles out?
I suspect that maybe I'm not applying the Residual method correctly to convert from continuous to discrete time. Remember, I have to apply a ZOH first. The way I did it was I multiplied Gp(s) by (1-exp(-s*T))/s . Then I separated the (1-exp(-s*T)) and that becomes (z-1)/z . The extra s is multiplied with the denominator of the original Gp(s), so now I am looking for the z-transform of (4 / (s^2)*(s+2))), but the original Gp(s) denominator was just s*(s+2).
I have a plant transfer function Gp(s) = 4/(s*(s+2)) The denominator has a degree 2. When I convert this to discrete time using the residual method and a Zero Order Hold, I multiply the denominator by another s so the degree is now 3. Using the residual method formula in the notes, I get a Gp(z) = 4.2749/(z-0.8187)
I'm supposed to use Ragazzini's method to design a lead compensator for this system. The pole of this Gp(z) is clearly not outside the unit circle. So there is no need to eliminate any poles/zeros in the F(z) function. I'm not sure how to continue with this. In all my previous lecture examples, there has always been an unstable pole/zero in the Gp(z), which we need to cancel out by inserting a new pole/zero in the F(z) to compensate. Now that the only pole is z=0.8187, and it's stable, is it safe to say that we don't need to cancel any poles out?
I suspect that maybe I'm not applying the Residual method correctly to convert from continuous to discrete time. Remember, I have to apply a ZOH first. The way I did it was I multiplied Gp(s) by (1-exp(-s*T))/s . Then I separated the (1-exp(-s*T)) and that becomes (z-1)/z . The extra s is multiplied with the denominator of the original Gp(s), so now I am looking for the z-transform of (4 / (s^2)*(s+2))), but the original Gp(s) denominator was just s*(s+2).
