Grafik Aliran Sinyal dan Blok Diagram KALBIN SALIM, M.Eng Jurusan Teknik Elektro Universitas Kepulauan Riau
Blok Diagram dasar sistem kontrol C(s) R(s) G(s) The block diagram technique has been developed not only to show the interrelationship between the constituents of a control system but also to do algebraic manipulations through their reduction procedure
Penjumlahan pada suatu titik dengan blok diagram C(s) + - X(s) Y(s) Z(s) C(s) = X(s) – Y(s) + Z(s)
Implementasi blok diagram pada rangkaian listrik ei eo Ingat: KCL dan KVL
Persamaan transformasi laplace 𝑖= 𝑒 𝑖 − 𝑒 𝑜 𝑅 dan 𝑒 𝑜 =𝐿 𝑑𝑖 𝑑𝑡 Persamaan transformasi laplace 𝐼(𝑠)= 𝐸 𝑖 (𝑠)− 𝑒 𝑜 (𝑠) 𝑅 𝐸 𝑜 𝑠 =𝑠𝐿 𝐼(𝑠) Blok diagram + - Ei(s) Eo(s) I(s) I(s) E(s) 1/R sL
Gabungan kedua blok diagram - + Ei(s) I(s) I(s) Eo(s) 1/R sL
Contoh 2. R1 C1 Vi (t) Vo(t) R1 C2 i1 i2 v1 v1 𝑖 2 = 𝑣 1 − 𝑣 0 𝑅 2 𝑖 2 = 𝑣 1 − 𝑣 0 𝑅 2 𝑣 0 = 𝑖 2 𝑑𝑡 𝐶 2 𝑖 1 = 𝑣 𝑖 − 𝑣 1 𝑅 1 𝑣 1 = 𝑖 1 − 𝑖 2 𝑑𝑡 𝐶 1
Persamaan transformasi laplace menjadi: 𝑖 1 (𝑠)= 𝑣 𝑖 (𝑠)− 𝑣 1 (𝑠) 𝑅 1 𝑣 1 (𝑠)= 𝑖 1 (𝑠) − 𝑖 2 (𝑠) 𝑠 𝐶 1 𝑖 2 (𝑠)= 𝑣 1 (𝑠) − 𝑣 0 (𝑠) 𝑅 2 𝑣 0 (𝑠)= 𝑖 2 (𝑠) 𝑠 𝐶 2 (i) (iii) (ii) (iv)
Blok diagram: - + Vi(s) V1(s) I(s) I(s) - + i2(s) - + Vi(s) V1(s) 1/s C1 (i dan ii)
- + i2(s) - + Vi(s) i1(s) - + V0(s) i2(s) V1(s) - + Vi(s) - + i1(s) - 1/R1 1/s C1 1/R2 (i - iii) - + Vi(s) - + i1(s) - + V1(s) V0(s) - + i2(s) 1/ s C1 1/ S C2 1/R1 1/R2 (i - iv)
Latihan 1. Tentukan Persamaan laplace - + R(s) B(s) E(s) C(s) I(s) G(s) R(S): reference input C(S): control out B(S): feedback signal E(S): signal actual control actions G(S): forward transfer function H(S): feedback transfer function T(S): close loop tranfer function H(s) Penyelesaian menjadi: R(s) C(s) G(s) / 1+G(s) H(s)
Latihan 2. Tentukan Persamaan laplace G3(s) + - + R(s) C(s) G1(s) G2(s) H(s) R(s) C(s) ???
Thanks a lot