1 數位控制（十一）

2 Methods of Pole Placement Method 1: Simple substitution Method 2: Use of Transformation matrix Method 3: Ackermann’s formula Method 4: Use of Eigenvector and deadbeat

3 Method 2: Use of Transformation matrix

4 Method 1: Simple Substitution

5 Solution of Method 2

6 Deadbeat Response

7 Deadbeat response of a CSCS

8 Control System with Reference Input

9 The state feedback can change the characteristic equation for the system, but in doing so the steady-state gain of the entire system is changed. It is necessary to have an adjustable gain K 0 in the system. The gain should be adjusted such that the unit-step response of the system at steady state is unity or y(∞)=1.

10 Reference Input (ex. 6-8)

11 State Space Design for Digital Bus Suspension Control (bus.m)

12 Controllability matrix

13 Observability The system is completely observable if every initial state x(0) can be determined from the observation of y(kT) over a finite number of sampling periods.

14 Complete State Controllability

15 Complete Observability

16 For multiple eigenvectors (Jordan form) The system is completely observable if and only if No two Jordan blocks are associated with the same eigenvalues, None of the column of the transformed C that corresponds to the first row of each Jordan block consists of all zero elements, The elements of each column of the transformed C that correspond to distinct eigenvalues are not all zero,

17 Example - Completely observable

18 Example – not completely observable

19 Principles of duality