Design of state variable FS2017b mk lecture notes

CONTROL SYSTEM DESIGN Lecture Notes The Design of State Variable Feedback Systems Page Notes - xˆ : the estimate value of x - xɺ : the time – derivative of x - K : the full – state matrix - L: the observer gain matrix -n=3 14 - det(λI − (A − BK)) = : the characteristic equation 16 - (λ + 2ζωn λ + ωn2 )(λ + ζωn ) = : the desired characteristic equation 18 - For SISO systems - K = [ 0 ⋯ 1] Pc−1q(A) : Ackermann’s formula 21 - det(λI − (A − LC)) = : the characteristic equation 30 - Design procedure 39 - K: the feedback gain matrix 44 - L: the observer gain matrix 51 - J = t g (x, u, t )dt : the performance index ∫ f - tf: the final time 52 tf - J = ∫ xT xdt : the specific form of the performance index : s + αs + β s +1 - T ( s) = 53 54 58 61 the normalized, third-order, closed-loop transfer function - HT P + PH = −I : an assumption - xT (∞)Px(∞) = : if the system is stable 1 1 - x(0) =   : initial conditions ∞ - J = ∫ (xT Ix + λuT u)dt : To account for the expenditure of the energy of the control signal, we will use this performance index - λ : a scalar weighting factor - Q: define such a matrix 67 xɺ = A x r r - r : r = d x  r r + consider a reference input to be generated by a linear system of this form Page Notes + initial conditions are unknown - r = xr , xɺr = : a step reference input with zero steady – state error ...Page Notes + initial conditions are unknown - r = xr , xɺr = : a step reference input with zero steady – state error