this is the equation for an ideal PID

m(k) = m(k-1) + q0*e(k) - q1*e(k-1) + q2*e(k-2)

where
;q0= Kc*(1+T/ti+td/T)
;q1=Kc*(1+2*td/T)
;q2=Kc*td/T

T = sample time

for Kc, ti, td you must first obtain a first order plant that you wish to control there are many methods like zieger-nichols, etc

then you must obtain the integral cryteria. there is for ideal PID, etc. if you choose ideal PID then you must decide wheater your controller will work better with changes of reference or perturbations. after choosing one you choose again if you want a PID or a PID..

choose one more time for ISE, ITAE or IAE


it is just too much information to post here, try reading a book of control, then post your questions here. i can not solve your problem. it's too big if you don't know anything