By Farid Golnaraghi, Benjamin C. Kuo

Automated regulate platforms offers engineers with a clean new controls publication that areas precise emphasis on mechatronics. It follows a progressive method through really together with a actual lab. furthermore, readers will locate authoritative assurance of recent layout instruments and examples. present mechatronics purposes construct motivation to profit the fabric. broad use of digital lab software program can be built-in in the course of the chapters. Engineers will achieve a robust comprehend of keep an eye on platforms with the aid of smooth examples and routines.

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**Extra info for Automatic Control Systems**

**Example text**

5 ! 2! 4 ! cos t = − sin t sin t cos t (2) Inverse Laplace transform: −1 1 s 1 s −1 Φ ( s ) = ( sI − A ) = 1 s = s 2 + 1 −1 s −1 φ (t ) = cos t − sin t sin t cos t (b) A= −1 0 0 −2 A = 2 1 0 0 4 A = 3 −1 0 0 − 8 A = 4 −1 0 0 16 (1) Infinite series expansion: 2 3 4 t t t 1 − t + − + +L 0 1 2 2 2 ! 3! 4 ! φ ( t) = I + At + A t + L = 2 3 2! 4t 8t 0 1 − 2t + − +L 2! 3! e −t = 0 e 0 −2 t (2) Inverse Laplace transform: Φ ( s ) = ( sI − A ) = −1 s + 1 0 1 s +1 = s + 2 0 1 s + 2 0 −1 0 e− t −2 t e 0 φ (t ) = 0 (c) A= 0 1 1 0 A = 2 1 0 0 1 A = 3 0 1 1 0 A = 4 1 0 0 1 (1) Infinite series expansion: 3 5 t t t2 t4 1+ + +L t+ + L 1 2 2 e− t + et 2!

Notice that there is a loop with gain −1 after all the s (b) State equations: dx 1 dt = 17 x 2 1 + 1 x 2 dx 2 2 dt = 15 2 x − 1 1 2 x 2 + 1 r R (s ) = 2. 82. These are not functions of K. 4536, pole-zero cancellation occurs. 02s 2 ) = 100 s + 12 s + 70 s + 100 3 2 State diagram by direct decomposition: State equations: x&1 x& = 2 x&3 0 0 −100 x1 0 0 1 x2 + 0 u −70 −12 x3 1 1 0 (b) Characteristic equation of closed-loop system: Roots of characteristic equation: 62 s 3 + 12 s + 70 s + 200 = 0 2 − 5.

1 e (s (s ) T D 30 e (s)+ + 5) (s T (s) D + 2 )( s + 20 −0 . 2 s (s (s + 5) (s ) + 90( s + 2 )U ( s ) + 2 )( s + 20 ) + 0 . 1e 30 e + − 0. 2 s −0 . 2 s −0 . 1e There should not be any incoming branches to a state variable node other than the s −1 −0 . 2 s branch. Thus, we should create a new node as shown in the following state diagram. Notice that there is a loop with gain −1 after all the s (b) State equations: dx 1 dt = 17 x 2 1 + 1 x 2 dx 2 2 dt = 15 2 x − 1 1 2 x 2 + 1 r R (s ) = 2. 82. These are not functions of K.

### Automatic Control Systems by Farid Golnaraghi, Benjamin C. Kuo

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