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# Y cx du 1 2 1 1 1 t v d x x c c y x ax bu bekc3533

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y Cx Du = + [ ] [ ] [ ][ ] ) ( 1 2 1 1 1 t v d x x c c y + = ! x = Ax + Bu

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BEKC3533 – SEM2, 15/16 DR. CHONG SH, FKE, UTEM 3 State-space representation DR CHONG 9 Exercise 2-10 Consider the system described by the coupled differential equations where u 1 and u 2 are inputs, y 1 and y 2 are outputs, k i , i = 1, …, 6 are the system parameters. Obtain the state-space representation of the differential equation. !! y 1 + k 1 ! y 1 + k 2 y 1 = u 1 + k 3 u 2 ! y 2 + k 4 y 2 + k 5 ! y 1 = k 6 u 1 State-Variable Modeling DR CHONG 10 Example 2-9 State-Variable Modeling DR CHONG 11 Example 2-10 State-Variable Modeling DR CHONG 12 Exercise 2-11
BEKC3533 – SEM2, 15/16 DR. CHONG SH, FKE, UTEM 4 Simulation Diagrams § The basic element of the simulation diagram is the integrator. DR CHONG 13 ( ) ( ) y t x t dt = and the Laplace transform of this equation yields 1 Y( ) ( ) s X s s = Simulation Diagrams § We need TWO integrators to construct a simulation diagram of the mechanical system shown on left; DR CHONG 14 y ( t ): displacement !! y ( t ) = B M ! y ( t ) K M y ( t ) + 1 M f ( t ) Converting a Transfer Function to State-Space DR CHONG 15 Example 2-11 Find the state-space representation in phase variable form for the transfer function shown below: ( ) 3 2 ( ) 24 ( ) 9 26 24 C s R s s s s = + + + Converting from State-Space to a Transfer Function DR CHONG 16 y Cx Du = + State and output equations: ( ) 1 ( ) ( ) ( ) Y s T s C sI A B D U s = = + Take the Laplace transform assuming zero initial conditions: ( ) ( ) ( ) ( ) ( ) ( ) sX s

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• Spring '19
• Dr.Saifulza
• y1, Dr Chong

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