Modern Control Engineering

830 Chapter 10 / Control Systems Design in State Space The left-hand side of Equation (10–154) is The right-hand side of Equatio ...

Example Problems and Solutions 831 where The transfer function G(s)for the system defined by Equations (10–155) and (10–156) is ...

832 Chapter 10 / Control Systems Design in State Space where The rank of the observability matrix N, is 2. Hence, the system is ...

Example Problems and Solutions 833 or (10–158) Equations (10–157) and (10–158) are in the observable canonical form. A–10–10. Fo ...

834 Chapter 10 / Control Systems Design in State Space Taking the conjugate transpose of both sides of Equation (10–146), we hav ...

Example Problems and Solutions 835 The closed-loop poles of the observed-state feedback control system with a minimum-order obse ...

836 Chapter 10 / Control Systems Design in State Space we find that the rank of isn+1.Thus, the system defined by Equation (10–1 ...

Example Problems and Solutions 837 Then, the state-space equations become Define The state feedback gain matrix Kand observer ga ...

we have (10–170) Note that where Then, Equation (10–170) can be written as (10–171) Since, from Equation (10–94), we have (10–17 ...

Example Problems and Solutions 839 MATLAB Program 10–27 % Response to initial condition A = [0 0 1 0;0 0 0 1;-36 36 -0.6 0.6;18 ...

840 Chapter 10 / Control Systems Design in State Space (b) for the minimum-order observer: Also, compare the bandwidths of both ...

Example Problems and Solutions 841 MATLAB Program 10–29 % Response to initial condition ---- full-order observer A = [0 1;0 -2]; ...

842 Chapter 10 / Control Systems Design in State Space MATLAB Program 10–31 % Obtaining Ke ---- minimum-order observer Aab = [1] ...

Example Problems and Solutions 843 MATLAB Program 10–32 % Response to intial condition ---- minimum-order observer A = [0 1;0 -2 ...

844 Chapter 10 / Control Systems Design in State Space e 02468 0 0.2 0.4 0.6 0.8 1 t (sec) x^1 x^2 0.6 0.8 1 1.2 0.4 0.2 0 02468 ...

Example Problems and Solutions 845 The observer controller is clearly a lead compensator. The Bode diagrams of System 1 (closed- ...

846 Chapter 10 / Control Systems Design in State Space Noting that Ais a stable matrix and, therefore, we obtain Let us put Note ...

Example Problems and Solutions 847 Consider only the case where the initial condition is Choose the undamped natural frequency t ...

848 Chapter 10 / Control Systems Design in State Space Solving for the matrix P, we obtain The performance index is then (10–177 ...

Example Problems and Solutions 849 where Referring to Equation (10–51), the error equation for the system is given by where and ...