Fal!2001 16.3118-3 Example ● Consider the“( art on a stick” system, with the dynamics as given in the notes on the web define Then with y=a Ax+ Bu Cx For the parameters given in the notes, the system has an unstable pole at +5.6 and one at s=0. There are plant zeros at +5 The target locations for the poles were determined using the SrL for both the regulator and estimator Assumes that the process noise enters through the actuators Bw= b, which is a useful approximation Regulator and estimator have the same srL Choose the process/sensor ratio to be r/10 so that the estimator poles are faster than the regulator ones The resulting compensator is unstable(+16 But this was expected.(why?Fall 2001 16.31 18—3 Example • Consider the “cart on a stick” system, with the dynamics as given in the notes on the web. Define q = ∙ θ x ¸ , x = ∙ q q˙ ¸ Then with y = x x˙ = Ax + Bu y = Cx • For the parameters given in the notes, the system has an unstable pole at +5.6 and one at s = 0. There are plant zeros at ±5. • The target locations for the poles were determined using the SRL for both the regulator and estimator. — Assumes that the process noise enters through the actuators Bw ≡ B, which is a useful approximation. — Regulator and estimator have the same SRL. — Choose the process/sensor ratio to be r/10 so that the estimator poles are faster than the regulator ones. • The resulting compensator is unstable (+16!!) — But this was expected. (why?)