Since 1942, the Ziegler-Nichols "Closed-Loop Method and Equation," developed by John G. Ziegler and Nathaniel B. Nichols, has been the de facto industry standard for temperature and process control. This method also is commonly known as the proportional integral and derivative (PID) method and is the primary -- and many times only -- control methodology currently taught in many colleges and universities throughout the world.
Utilizing this strategy typically measure the deviation of a measured process value (PV) from the desired set value (SV) of the control and subsequently make changes to the control output to minimize or eliminate this deviation. The proportional term (Pb) controls the output action proportional to the current measured deviation; the integral term (I) accounts for the accumulated error; and the derivative term (D) corrects for the rate of change of the deviation. The sum of these three terms is utilized to provide the amount of control action required to minimize the measured process value deviation from set value and can be expressed mathematically as:
Control engineers can calculate the optimal PID values for their processes in many ways. The most common and perhaps easiest way is to use the self-tuning or autotuning algorithms that are available as standard features in almost all industrial controls on the market today, including single-loop controls, distributed control systems and even some industrial computers.
These features calculate PID values for the control either by providing a step change to the output or by observing the process dynamics near set value. This method allows the control to observe the amplitude and period of oscillation of a process by measuring the input change to a predetermined output change. These parameters then can be utilized to calculate the PID parameters.
However, be warned that not all self-tuning algorithms are created equal, with many using different variations of the PID algorithm such as parallel- or series-type calculations and others being optimized only for specific applications. In addition, most only calculate the PID values once and may not be ideal for processes that exhibit different process dynamics under certain conditions or times.
Under most conditions, the feedback PID method incorporated into a discrete control is ideal for optimal process or temperature control. How-ever, some processes may exhibit characteristics make this method inadequate for accurate and stable temperature control. These characteristics include:
If needed, the control engineer may even modify the process by repositioning actuators or sensors, or by using inferential control by changing the final control object. These changes may help to minimize or even eliminate time-delay or other transport phenomena but normally will not compensate for any process nonlinearities or interactivity among process variables. When time delay is present, many control engineers will simply detune their control devices in such a way to compensate for it, which normally will result in sluggish process control or exhibit a poor control response to any significant load disturbance.
Because most PID tuning algorithms, including Ziegler-Nichols and Cohen-Coon, are based on a one-quarter decay ratio, an engineer should only use standard PID tuning if the quotient of time-delay over time constant is less than one. There are several modifications to feedback control that can be implemented to provide more precise control without going to a completely model-based or decoupled control. These include adaptive tuning, feedforward control and cascade control.
Adaptive Tuning. Sometimes referred to as continuous tuning, adaptive tuning allows the control feedback to read the responses that the control is seeing based on current PID parameters and output response, and adjust PID parameters accordingly. Adaptive tuning also can be useful in processes that cannot encounter the process disturbance required by many self-tuning controls. However, most adaptive tuning algorithms are not able to differentiate a load disturbance from an intrinsic change in the process dynamics, which may result in inaccurate tuning parameters being calculated by the tuning algorithm.
Feedforward Control. This strategy utilizes changes in extraneous variables in conjunction with feedback control to provide more stable control. For example, the ambient plant temperature or feedwater temperature may affect the temperature control operation in a steam boiler. If the temperature control is aware of what these values are in the plant, the control can make changes to the output control action in an effort to compensate for these externalities. The feedforward signal will have its own feedforward gain and action that will be added or subtracted to the gain in the boiler control. This value will correct the output of the temperature control in such a manner that it will change to anticipate the disturbance that may have affected optimal operation of the control.
Cascade Control. This type of control is similar to feedforward except that two complete PID loops exist rather than a modification to the existing single-loop control. The two control loops include a primary and a secondary control with the primary control determining the set value of the secondary control. The primary control is the actual temperature or process variable desired to control (in my previous example, this would be the boiler temperature), and the secondary control will control and account for any additional disturbance that may occur.
In the boiler example, the internal pressure of the boiler will affect the temperature of the boiler because temperature and pressure are directly proportional (remember the ideal gas equation, PV = nRT). With the secondary control controlling the pressure in the boiler, the disturbance to the process dynamics caused by a pressure change will not affect the primary boiler temperature control.
Advanced ControlSometimes, no matter how hard you try, the discrete feedback PID control will just not work for some applications. When this is the case, a more advanced control strategy can be implemented to ensure that the process operates at peak efficiency.
Although feedback control utilizing standard PID algorithms is simple and many times the most cost-effective control method, these more advanced control techniques must be utilized to achieve maximum return on investment in many processes. Typically, these processes include batch or interactive, multivariable processes.
Model-predictive control (MPC) has been adopted in industry as the most effective solution to large, multivariable-constrained control problems. MPC controllers use empirical data identified from test data and require a significant amount of engineering and programming time to implement effectively. MPC is just like it sounds: It utilizes data from past experiences to calculate future control responses. The variable interactions and transfer functions are placed in an array and output actions are based on these values. MPC has been shown to outperform standard and adaptive PID algorithms in many single-input single-output (SISO) linear processes, but care should be taken to recognize the costs and time associated with implementing such a system.
A good example of a process that may be best suited for MPC is an oxygen reactor in a pulp mill. To operate an oxygen reactor, a number of variables must be controlled for optimal pulp production. The amount of sodium hydroxide, pulp temperature and amount of oxygen all can be controlled variables while the wood lignin content, inlet/outlet temperature, pH out, and reactor temperature are response variables to the control. All of the variables in such a control loop are interrelated, and the acid/base reaction exhibits a nonlinear control response. In addition, transfer lag may be common in an application such as this if the tank agitator is undersized or if the process sensors are slow acting or mounted in a less-than-ideal location in the reactor vessel. Finally, the reaction may be slightly exothermic.
An application such as this would be almost impossible for a single-loop feedback PID control to control, but a more accurate model-based approach may meet a cost-benefit analysis based on ongoing improvements in process yields. Other applications exhibiting similar types of behavior that MPC may be best suited for include distillation columns, hydrogen catalytic crackers, pulp digesters and other chemical processes.