Modern Control Engineering

Consider the system shown in Figure 10–43(a). Let us examine the transfer function between pointAand point B. Notice that Figure ...

Section 10–9 / Robust Control Systems 811 K (f) w u z y P G w u y K WmI (e) y z + + (^) m T BA (c) G K (^) m (d) y uB zw A ...

Robust Performance. Consider the system shown in Figure 10–44. Suppose that we want the output y(t)to follow the input r(t)as cl ...

Section 10–9 / Robust Control Systems 813 K (b) w u z y P G w u y K WmI WsI (a) y z 2 z 1 z ++ Figure 10–45 (a) Generalized pl ...

Note that can be determined as follows: Since z(s)=P 11 w(s)+P 12 u(s) y(s)=P 21 w(s)+P 22 u(s) u(s)=K(s)y(s) we obtain y(s)=P 2 ...

If we define (10–130) then Inequality (10–129) can be written as Referring to Equation (10–128), rewritten as notice that if we ...

If both the robust stability and robust performance conditions are required, the control sys- tem must satisfy the condition giv ...

The reason to use generalized plants, rather than individual block diagrams of con- trol systems, is that a number of control sy ...

This means that there are qlinearly independent column vectors in the controllability matrix. Let us define such qlinearly indep ...

Example Problems and Solutions 819 Hence, Equation (10–137) may be written as follows: Define Then Equation (10–137) can be writ ...

Thus, Hence, Next, referring to Equation (10–138), we have (10–139) Referring to Equation (10–136), notice that vector Bcan be w ...

Show that wherea 1 ,a 2 ,p,anare the coefficients of the characteristic polynomial Solution.Let us consider the case where n=3.W ...

822 Chapter 10 / Control Systems Design in State Space and where the ai’s are coefficients of the characteristic polynomial Defi ...

Example Problems and Solutions 823 The right-hand side of Equation (10–144) is Clearly, Equation (10–144) holds true. Thus, we h ...

824 Chapter 10 / Control Systems Design in State Space we have Define where Then and Define Then the state equation becomes Sinc ...

Example Problems and Solutions 825 The characteristic equation of the system is The eigenvalues of matrix Aare–1and–2. It is des ...

826 Chapter 10 / Control Systems Design in State Space A–10–6. A regulator system has a plant Define state variables as By use o ...

Example Problems and Solutions 827 A–10–7. Consider a completely observable system Define the observability matrix as N: Show th ...

828 Chapter 10 / Control Systems Design in State Space The right-hand side of Equation (10–148) is (10–150) The Cayley–Hamilton ...

Example Problems and Solutions 829 Show that where the bk’s (k=0, 1, 2,p,n)are those coefficients appearing in the numerator of ...