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Sistema ad anello chiuso PD
Controllore PD tau 1 2 := k 1 2 := Ao 1 5 := t:=0 0.1, ..50 Kp1:=20 Td1:=0 Gc1 s( ):=Kp1 1⋅( +s Td1⋅ ) Gf s( ) Ao k 2 ⋅ k2+s tau⋅ ⋅k+s2 := E s( ) 1 s := G1 s( ) Gc1 s( ) Gf s⋅ ( ) 1+Gc1 s( ) Gf s⋅ ( ) simplify 4 4 s⋅ 2+s+5 → := U1 s( ):=E s( ) G1 s⋅ ( ) U1 t( ) U1 s( ) invlaplace 4 5 4⋅ 79e t 8 − ⋅ sin 79 t⋅ 8
⋅ 395 − 4 e t 8 − ⋅ cos 79 t⋅ 8
⋅ 5 − → := Kp2:=20 Td2:=1 Gc2 s( ):=Kp2 1⋅( +s Td2⋅ ) G2 s( ) Gc2 s( ) Gf s⋅ ( ) 1+Gc2 s( ) Gf s⋅ ( ) simplify 4 s⋅( +1) 4 s⋅ 2+5 s⋅ +5 → := U2 s( ):=E s( ) G2 s⋅ ( ) U2 t( ) U2 s( ) invlaplace 4⋅ 55e 5 t⋅ 8 − ⋅ sin 55 t⋅ 8
⋅ 55 4 e 5 t⋅ 8 − ⋅ cos 55 t⋅ 8
⋅ 5 − 4 5 + → := 0 10 20 30 40 50 0 0.5 1 1.5 U1 t( ) U2 t( ) tRiassumendo, il contributo derivativo permette di ridurre le oscillazioni spurie del sistema, evitando che questo oscilli intorno al valore asintotico.
D’altro canto, in presenza di un forte rumore esterno, il contributo derivativo tende ad amplificare l’effetto del rumore producendo una instabilità addizionale del sistema.
