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Second Order Transfer Functions and PID Control Loop Tuning

Est. Reading: 2 minutes

Second order transfer functions are not very common in chemical plants and oil refineries but they do exist and make up about 5% of all control loops. About 70% of all industrial processes can be characterized by first order transfer functions, 20% by zero order transfer functions and the remaining 10% can be characterized by second order transfer functions, higher order transfer functions and a special category of processes that are open loop unstable transfer functions.

What can you do when a process is second order or even higher order? In most cases, experience shows that you can get by really by just fitting a first order transfer function to a truly second order transfer function process. In doing so there will be some prediction and model error but this is often not too important given there are always unknowns, unmeasured disturbances, sticking control valves (control valves with stiction and deadband), bad sensors and many unknowns.

Second Order Transfer Function PITOPS
Fitting First Order to Second Order Transfer Function PITOPS

Another benefit of approximating second order transfer function dynamics with first order transfer function dynamics is that many PID control loop tuning criteria and heuristics are based on first order processes and first order transfer functions. These include IMC (Internal Model Control) by the famous professor Dr. Manfred Morari who invented the concept of internal model control, Cohen Coon tuning criteria, Lambda tuning and the famous PITOPS from PiControl methods based on IAE (integrated absolute error) criteria, ISE (integrated square error) criteria, ITAE )integrated time absolute error) criteria and PITOPS RO (reduced overshoot).

With PiControl's advanced process control (APC) technology and closed-loop transfer function identification technology, closed-loop system identification technology, it is possible to optimize the PID control loop tuning parameters far superior to the control loop tuning based on heuristics like IMC, Ziegler Nichols, Lambda tuning, Cohen Coon and others. With PiControl's PITOPS, you can optimize PID control loop tuning parameters for specific custom applications matching the real PV process trends, typical noise and disturbances including the impact of production rate changes etc. can be mimicked precisely.

Optimum PID control loop tuning for true second order process
Optimum PID control loop tuning for first order simplification to second order process

The optimized PID tuning for the PID control loops will work better than the currently known popular PID control loop tuning criteria and heuristics. PiControl can help you on your second order transfer function and higher order transfer function PID control loops and then help you optimize single PID control loops, slave PID control loops, master PID control loops (cascade PID control loops) and also all types of APC (advanced process control) loops including feedforward control, constraint override control, inferential control and model based control. Visit www.PiControlSolutions.Com.

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