Modern Control Engineering

850 Chapter 10 / Control Systems Design in State Space where Obtain the unit-step response of the system designed. Solution.A MA ...

MATLAB Program 10–35 gives the unit-step response of the system given by Equation (10–179). The resulting response curves are pr ...

852 Chapter 10 / Control Systems Design in State Space x^1 0246810 t (sec) 0246810 t (sec) 0246810 t (sec) 0246810 t (sec) 02468 ...

Example Problems and Solutions 853 G w u K WaI y z − + K (f) (e) w u z y P G K (^) a (d) u zw −+ (^) a Ta BA (c) G K (^) a (a) u ...

854 Chapter 10 / Control Systems Design in State Space Assume that is stable and its upper bound is known. Assume also that and ...

Problems 855 x.=Ax+Bu y=Cx x 2 x 3 k 2 k 1 k 3 r u x y=x 1 +– +– Figure 10–58 Type 1 servo system. Problems B–10–1.Consider the ...

856 Chapter 10 / Control Systems Design in State Space B–10–9.Consider the inverted-pendulum system shown in Figure 10–59. Assum ...

Problems 857 R(s) Observer U(s) Y(s) +– controller s^2 + 2 s+ 50 s(s+ 4) (s+ 6) Figure 10–60 Control system with observer contro ...

858 Chapter 10 / Control Systems Design in State Space Determine the value of the parameter aso as to minimize the following per ...

A 859 Appendix Appendix A first presents the complex variable and complex function. Then it presents tables of Laplace transform ...

A complex function G(s)is said to be analyticin a region if G(s)and all its deriva- tives exist in that region. The derivative o ...

where It can be seen that, except at s=–1 (that is,s=–1,v=0),G(s)satisfies the Cauchy–Riemann conditions: HenceG(s)=1/(s+1)is an ...

G(s)has zeros at s=–2, s=–10, simple poles at s=0, s=–1, s=–5, and a double pole (multiple pole of order 2) at s=–15. Note that ...

Appendix A / Laplace Transform Tables 863 f(t) F(s) 1 Unit impulse d(t) 1 2 Unit step 1(t) 3 t 4 5 tn (n=1, 2, 3,p) 6 e–at 7 te– ...

864 Appendix A / Laplace Transform Tables 18 19 20 e–atsinvt 21 e–atcosvt 22 23 24 25 1-cosvt 26 vt-sinvt 27 sinvt-vtcosvt 28 29 ...

Appendix A / Laplace Transform Tables 865 1 2 3 4 5 where 6 7 8 9 10 11 12 13 14 15 16 17 18 lCf(t)g(t)D= 1 2 pj 3 c+jq c-jq F(p ...

Finally, we present two frequently used theorems, together with Laplace transforms of the pulse function and impulse function. 8 ...

B 867 Appendix Before we present MATLAB approach to the partial-fraction expansions of transfer functions, we discuss the manual ...

We see that all the expanded terms drop out with the exception of ak. Thus the residue akis found from Note that, since f(t)is a ...

Note that the Laplace transform of the unit-impulse function d(t)is 1 and that the Laplace transform of dd(t)/dtiss. The third t ...