Data Acquisition

Figure 11.2Block diagram of a closed loop control systemOne effective method of calculating the required controller output m(t) for a givencontrol process, is the PID (proportional, integral and derivative) control algorithm,which is the sum of four terms. This is shown in the following two equations for both thereal time continuous and discrete time processes:de ( t )m ( t ) = K p e ( t ) + K i ∫ e ( t ) dt + K d + Biasdtm(t) is the outputK p is the proportional gain constant (l/sec)K i is the integral gain constant (l/sec)K d is the derivative gain constant (sec)e(t) is (SP–PV) [set point – process variable]‘Bias’ is a constant determined from knowledge of the systemk = i[ e ( i ) − e ( i −m ( i ) = Kp e ( i ) + T×Ki ∑ e ( k ) + Kd ×Tk = 01 )]+ Biasm(i) is the output at time of the ith sample (=i*T)K p is the proportional gain constantK i is the integral gain constant (1/sec)K D is the derivative gain constant (sec)T is the time interval for samplingi is the number of samplese(i) is the error at ith sampling intervale(i–1) is the error at (i–1)th previous sampling interval‘Bias’ is the feed-forward or constant-biase(i) is the SetPoint (i) – process variable (i) (measured at the ith sample)The first term (proportional term) of these equations is directly proportional to thecurrent process error. The value of the proportional constant (K p ) determines how hard thesystem reacts to differences between the SetPoint and the actual process variable.Simple proportional control cannot take into account load changes in the process undercontrol. This is handled by the integral term of the PID equation, which sums up the long-