Chaper 5 Digial PID conrol algorihm Hesheng Wang Deparmen of Auomaion,SJTU 216,3
Ouline Absrac Quasi-coninuous PID conrol algorihm Improvemen of sandard PID algorihm Choosing parameer of PID regulaor Brief summary
Ouline The PID( Proporional - Inegral - Differenial ) regulaor conrol depending on he proporional, inegral and differenial of he deviaion PID regulaion is he mos maure and he mos widely used echnology of coninuous sysem. The subsance of is regulaion is based on he deviaion of he inpu value, a funcion of he proporional, inegral and differenial operaor, The resul of he calculaion for he oupu o conrol. In pracical applicaions, depending on he circumsances, he srucure of he PID conrol can be flexibly changed.
Ouline (2) The advanage of PID maure echnology Easily familiar wih and maser Do no need o creae a mahemaical model Good conrol performance
Ouline (3) To realize PID conrol Analog: elecronic circui regulaor, he measured signal compared wih a given value, hen he difference afer PID circui operaion is sen o he acuaor, change he amoun of inpu o achieve he purpose of regulaion. Digial: using a compuer, he resul of he calculaion is convered o he analog oupu o conrol he acuaors. The regulaor design issues. ---------. Terminal conroller design problem ---. Disurbance Conrolu x Conrolu x x f
algorihm Analog PID regulaor Plan
algorihm(2) Proporional regulaor u K P e u u K e u P e() oupu uy Scale facor inpu deviaion basis of conrol inpu Proporional acion: rapid response error, bu does no eliminae he seady sae error, easily lead o insabiliy if i is oo large KP e()
algorihm(3) e() Proporional inegral regulaor 1 u KP e edu T I T I Inegral ime consan Inegral acion: eliminae saic error, bu may cause overshoo easily, or even oscillaion uy e() uy y2 y1=kp e() K1 KP e()
algorihm(4) proporional and differenial regulaor de u KPeTD u d T D Derivaive ime consan Derivaive acion: reduce he overshoo, o overcome he oscillaion Improve sabiliy, o improve he sysem dynamic characerisics u u
algorihm(5) Proporional inegral differenial regulaor 1 de u KPe ed T D u TI d u e() y KP KD e() KP K1 e() KP e()
algorihm(6) Digial PID conrol algorihm -PID conrol law wih he numerical approximaion -Numerical approximaion: he summaion insead of inegraion, wih he Backward difference insead of differenial analog PID discreized ino he differenial equaion - Two forms: Posiional, incremenal
algorihm(7) The posiional PID conrol algorihm o e ()dt e k j d() e ek ek 1 d T k T TD uk KP[ ek ej ( ek ek )] u T T I j j 1 Posiional conrol algorihm provides acuaor posiion u k, cumulaive e k
algorihm(8) Incremenal PID conrol algorihm T T u K e e e e u k D k P[ k j ( k k1)] TI j T T T u K e e e e u k 1 k1 D P[ k1 j ( k1 k2)] TI j T T T u u u K [ e e e ( e 2 e e )] D k k k 1 P k k 1 k k k 1 k 2 TI T The incremen uk is feedback o he acuaor jus need o keep 3 previous deviaion values
algorihm(9) Posiional and incremenal PID conrol algorihm comparison Posiional PID algorihm plan PID incremenal algorihm Sepper moor plan
algorihm(1) Incremenal algorihm do no need o accumulae - have low inference from he calculaion error and accuracy; posiional algorihms use he accumulaed value of deviaion -> have a bigger cumulaive error. conrol is swiched from manual o auomaic he posiional algorihm mus firs se he compuer oupu value as he iniial value u( impac of he swich); incremenal algorihm is independen of he original value (no impac)..
algorihm(11) PID posiion program The posiional PID conrol algorihm programming - Ideas: k u K e K e K ( e e 1) k P k I j D k k j wk ( ) yk ( ) P ( k) K e P P k k P( k) Ke K e P( k 1) I I j I k I j PD( k) KD( ek ek 1) K K T / T, K K T / T I p I D p D P (k) is convered ino a double-bye ineger reurn
algorihm(12) Enrance Take w y1 Incremenal PID conrol algorihm programming u d e d e d e k k 1 k1 2 k2 Iniializaion placed adjus he parameers d, d1, d2, and he se value w, and iniial value seing error e i =e i 1 = e i 2 = Form Deviaion e=w-y1 Take d d1 d2 Calculae Reurn