Question

GIVEN THE SYSTEM: \(\dot{y} - K_1y = K_2\beta + K_3w(t)\) \((K_1, K_2, K_3) > 0\) ? Design a control-law (?) such that \(y \to y_{sp}\) for all initial conditions. Only \(E_y, y, y_{sp}\) are measurable. \(w(t) = C_1 + C_2t\). Assume that \((C_1, C_2, y_{sp})\) are piece-wise constant. \(w(t)\) is unknown and unmeasurable. Design the control-law such that the overall system behaves like a 2nd order system with this characteristic equation: \(\tau^2 + 6\tau + 27\). ? Plot the poles of this 2nd order system. ? Estimate ? and ?n of the final design. ? Draw the math-flow diagram (MFD) of the original system and super- impose the control-law ? Define the state variables and state evolution equations

          GIVEN THE SYSTEM: \(\dot{y} - K_1y = K_2\beta + K_3w(t)\) \((K_1, K_2, K_3) > 0\)

? Design a control-law (?) such that \(y \to y_{sp}\) for all initial conditions.
Only \(E_y, y, y_{sp}\) are measurable. \(w(t) = C_1 + C_2t\). Assume that
\((C_1, C_2, y_{sp})\) are piece-wise constant. \(w(t)\) is unknown and unmeasurable.

Design the control-law such that the overall system behaves like a
2<sup>nd</sup> order system with this characteristic equation: \(\tau^2 + 6\tau + 27\).
? Plot the poles of this 2<sup>nd</sup> order system.
? Estimate ? and ?<sub>n</sub> of the final design.
? Draw the math-flow diagram (MFD) of the original system and super-
impose the control-law
? Define the state variables and state evolution equations

GIVEN THE SYSTEM: ẏ - K1y = K2β + K3w(t) (K1, K2, K3) > 0

? Design a control-law (?) such that y → ysp for all initial conditions.
Only Ey, y, ysp are measurable. w(t) = C1 + C2t. Assume that
(C1, C2, ysp) are piece-wise constant. w(t) is unknown and unmeasurable.

Design the control-law such that the overall system behaves like a
2<sup>nd</sup> order system with this characteristic equation: τ^2 + 6τ + 27.
? Plot the poles of this 2<sup>nd</sup> order system.
? Estimate ? and ?<sub>n</sub> of the final design.
? Draw the math-flow diagram (MFD) of the original system and super-
impose the control-law
? Define the state variables and state evolution equations

Added by Rodrigo J.

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