Compensation Using the process field G PF (s) step response

Analysis of step response The following analysis technique are also used using the original recorded values or the identified model created from these recorded values. First it must be concluded if the process field has or hasn't got integral effect. It possible from the reaction curve of the process field. It takes a new steady-state or uniformly changing the amplitude. First it must be concluded if the process field has or hasn't got integral effect. It possible from the reaction curve of the process field. It takes a new steady-state or uniformly changing the amplitude. It should be noted the time constants of the approximation model. It should be noted the time constants of the approximation model. It is possible editing the reaction curve.

Self-adjusting process field PI or PIDT1 compensation European structure

Without integral effect In this case the most commonly used controller type the PI or if the reaction curve starts relatively slowly PIDT1 The 1 can also be used if the process field has got large dead time. The approximation models, whose parameters can be determined without computers the next: HPT1 PTn

The transfer functions PI In case of PIDT1 the transfer function has got four variables. You must be determine the A D differential gain to define the T time constants! PIDT1

The principle of compensation Be plotted the step response of process field. Be plotted the step response of process field. The ratio of the steady-state amplitude of the input (energizing) and output (response) signals is the K P. The ratio of the steady-state amplitude of the input (energizing) and output (response) signals is the K P. You should look for the inflection point of the reaction curve. You should look for the inflection point of the reaction curve. You need to edit the crossover points of beginning and final values of reaction curve with the line which overlaid on the inflection point. You need to edit the crossover points of beginning and final values of reaction curve with the line which overlaid on the inflection point. The intersection can be defined the apparent T u dead time and the apparent T g first order time constant. The intersection can be defined the apparent T u dead time and the apparent T g first order time constant.

HPT1 model from the reaction curve of process field

Edited parameters

Determination of K P, T u and T g The above figures are made MATLAB software. The amplitude of step command of MATLAB is unit, and so the read final value equals the process field gain K P = Determination with editing of T g and T u is quite inaccuracy. Recommendation of Piwinger: IPID PI

Recommendation of Chien-Hrones-Reswick The initial conditions for optimization parameters: The process field is an ideal HPT1; The objective function is the fastest aperiodic transient at setpoint tracking; The optimization is based on the square-integral criterion.

Determination of K C and T I Defined values: K P = 0.72, T g = 10.6 sec., and T u = 0.9 sec. The ratio of the time constants 11.8, and so the recommended compensation is PI. Using the above table: The PI compensation is:

Step response of closed loop Important: It is not an optimal parameter choice!

Chien-Hrones-Reswick recommendations The initial conditions for optimization parameters: The process field is an ideal HPT1; The objective function is the fastest periodically transient with maximum 20% overshoot at setpoint tracking; The optimization is based on the square-integral criterion.

A PI kompenzáló tag: Determination of K C and T I Defined values: K P = 0.72, T g = 10.6 sec., and T u = 0.9 sec. The ratio of the time constants 11.8, and so the recommended compensation is PI. Using the above table:

Step response of closed loop It can be seen that the approximation of process field the objective function is not satisfied.

PTn model

Determination of system parameters

Step response of process field

Determination of n and T Defined values t 10 = 1.95sec, t 30 = 4 sec., és t 70 = 10.1 sec. The process gain K P = 0.72 Based on the table above the PT2 is the closest approximation: n = 2.

Proposed parameters for PTn model The fastest periodically transient with maximum 20% overshoot at setpoint tracking

Proposed parameters for PTn model n = 2, and so you choose PI. In the industrial area you never use a pure P compensation to control a self-tuning process field!

Step response of the closed loop Compare the two models the PTn is the better approximation, if the process field has not got a real dead time.

Process field with integral effect P or PDT1 compensation European structure

Process field with integral effect In this case the most popular compensation is the P or if the response signal without noise than PDT1, but in the later case be applied the PIDT1 too. The approximate models IT1 or HIT1

IT1 model from the reaction curve of process field

Recommendation of Friedlich for IT1 TípusKCKC TITI TDTD P PDT1 Tg PIDT1 3.2Tg0.8Tg The initial conditions for optimization parameters: The process field is an ideal IT1; The objective function is the fastest periodically transient with maximum 20% overshoot at setpoint tracking; The optimization is based on the square-integral criterion.

Step response of the process field The compensation type does not depend on the ratio of the T I and T g.

Parameters of the P, PDT1, and PIDT1 P PDT PIDT It is possible other A D value too.

Step response of closed loop with P compensation The steady-state error is 0; settling time is 11.4 sec.; overshoot is 6.1%

The steady-state error is 0; the settling time is 10.1 sec.; there is not overshoot. Step response of closed loop with PDT1 compensation

Very bad! It is convenient the open-loop transfer function analysis. Step response of closed loop with PIDT1 compensation

The Bode plot of open-loop (G 0 (s)) with PIDT1 compensation It can be seen that increasing the gain of the compensation up to 17.4 a better phase margin value is obtained.

The result of the PIDT1 compensation with the new parameters Better, but it is not good!

Tuning the PDT1 compensation Replace the phase margin value from 95° to 90° the K C increasing by 2.8-fold.

It is good enough! The result of the PIDT1 compensation with the new parameters