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Tuning a PID Temperature Controller

Previous: Practical Matters.

In some case one may be able to measure the oven time constants directly and hence calculate the best controller settings. Often an equipment manufacturer will have suggested settings based on their commissioning report - a good reason read the manual first. Sometimes one has no option but to set up, or 'Tune', a system in closed-loop mode by trial and error so here are two straightforward procedures to tune a PID-controlled oven, they will get fairly close to optimum settings in most cases.

CDHW Method

1. Adjust the set-point value, T_s, to a typical value for the envisaged use of the system and turn off the derivative and integral actions by setting their levels to zero. Select a safe value for the maximum power M and increase the proportional gain until the system is just oscillating.
2. Note the period of oscillation then reduce the gain by 30%.
3. Suddenly decreasing or increasing T_s by about 5% should induce underdamped oscillations. Try several values of derivative level and choose a value for that gives a critically damped response. If the controller is calibrated D will need to be approximately one third of the oscillation period noted above.
4. Slowly increase the integral level until oscillation just starts, then reduce this level by a factor of two or three - this should be enough to stop the oscillation. I have found it is a good idea to use the lowest integral level that gives adequate performance.
5. Check the overall performance of system is satisfactory under the conditions it will be used.

This procedure is based on the assumption that a critically damped system is optimal and the fact that stability and noise must be traded for response time. Please bear in mind that the second step may involve large temperature oscillations and so the procedure would not be suitable if these could be dangerous or cause damage, for example in a chemical processing plant.

John Shaw's (Ziegler-Nichols Based) Method

1. Adjust the set-point value, T_s, to a typical value for the envisaged use of the system and turn off the derivative and integral actions by setting their levels to zero. Select a safe value for the maximum power M and set the proportional gain to minimum.
2. Progressively increase the gain until suddenly decreasing or increasing T_s by about 5% induces oscillations that are just self-sustaining.
3. The gain at this stage will be set to the ultimate gain G_u the period of the oscillations is known as the ultimate period t_u. Note the values of each quantity.
4. Set the controller parameters as follows:
• P-Control: P=0.50*G_u, I=0, D=0.
• PI-Control: P=0.45*G_u, I=1.2/t_u, D=0.
• PID-Control: P=0.60*G_u, I=2/t_u, D=t_u/8.
5. Check the overall performance of system is satisfactory under the conditions it will be used.

This procedure was adapted slightly from John Shaw's, description of the Ziegler-Nichols Closed Loop method. It should yield a system that is slightly underdamped; if a less "aggressive" response is desired try reducing P to half the values listed. As was the case with the CDHW method the second step may involve large temperature oscillations and so the procedure would not be suitable if these could be dangerous or cause damage, for example in a nuclear reactor. Strictly speaking, the Ziegler-Nichols method was developed for the traditional series, or interacting design of controller.

Further Reading

• Ron Graham et al., sci.engr.* FAQ on PID Controller Tuning. Includes example code for digital implementations.
• Dave Harrold, Process Controller Tuning Guidelines. Control Engineering Online.
• David St Clair, Controller Tuning and Control Loop Performance. Excellent booklet, avoids mathematics.
• David St Clair, The PID Algorithm. Describes and compares the many variants.
• Vance J. VanDoren, Ziegler-Nichols Methods Facilitate Loop Tuning. Control Engineering Online.