Tham khảo tài liệu 'ogata - modern control engineering part 13', kỹ thuật - công nghệ, cơ khí - chế tạo máy phục vụ nhu cầu học tập, nghiên cứu và làm việc hiệu quả | The block diagram of the system with observed-state feedback is shown in Figure 12-8. Referring to Equation 12-66 the transfer function of the controller-observer is -Y S - K I - A BK 1 Kf 5 16 -1 1 16 5 _ 52 Figure 12-9 shows a block diagram of the system. The dynamics of the observed-state feedback control system just designed can be described by the following equations For the plant 1 _ r 0 1 Xi 0 x2 0 X2 1 Figure 12-8 Block diagram of system with observed-state feedback Example 12-3 . Section 12-5 State Observers 829 u - For the observer -16 1 X 16 X2 The system as a whole is of fourth order. The characteristic equation for the system is sl - A BK sI - A K c 9 16s 64 s4 576 0 The characteristic equation can also be obtained from the block diagram for the system shown in Figure 12-9. Since the closed-loop transfer function is y s 7 s s2 - the characteristic equation is s2 s2 - s4 576 0 As a matter of course the characteristic equation is the same for the system in state-space representation and that in transfer-function representation. Minimum-order observer. The observers discussed thus far are designed to reconstruct all the state variables. In practice some of the state variables may be accurately measured. Such accurately measurable state variables need not be estimated. Suppose that the state vector X is an tt-vector and the output vector y is an m-vector that can be measured. Since m output variables are linear combinations of the state variables m state variables need not be estimated. We need to estimate only n - m state variables. Then the reduced-order observer becomes an n m th-order observer. Such an n - m th-order observer is the minimum-order observer. Figure 12-10 shows the block diagram of a system
