Fall 2001 6.3116-2 Estimation schemes . assume that the system model is of the form Ac+ Bu, a(0) unknown Where 1. A.B. and C are known 2. u(t) is known 3. Measurable outputs are y(t) from C+I e Goal: Develop a dynamic system whose state for all time t20. Two primary approaches Open-loop Closed-loop Open-loop Estimator Given that we know the plant matrices and the inputs, we can just perform a simulation that runs in parallel with the system (t)=A+B(t) Then i(t=a(t)v t provided that i(0=a(o Major Problem: We do not know a(0)Fall 2001 16.31 16—2 Estimation Schemes • Assume that the system model is of the form: x˙ = Ax + Bu , x(0) unknown y = Cx where 1. A, B, and C are known. 2. u(t) is known 3. Measurable outputs are y(t) from C 6= I • Goal: Develop a dynamic system whose state xˆ(t) = x(t) for all time t ≥ 0. Two primary approaches: — Open-loop. — Closed-loop. Open-loop Estimator • Given that we know the plant matrices and the inputs, we can just perform a simulation that runs in parallel with the system ˙ xˆ(t) = Axˆ + Bu(t) • Then ˆx(t) ≡ x(t) ∀ t provided that ˆx(0) = x(0) • Major Problem: We do not know x(0)