Figure 5. Jacket responded faster to cooling than heating as shown with reactor loop in manual and jacket loop in cascade mode.
means the process temperature PV responds consistently regardless of the size, direction or history of the controller output changes. In the jacket loop, achieving linearity requires selecting appropriate control valves and minimizing nonlinearities in the control strategy, e.g., dead zones in the split range logic. Figure 5 shows another example of nonlinearity: on the heating step, after the initial overshoot, recovery to 50° C was extremely slow due to the control-valve flow characteristic. Sometimes the limiting nonlinearity is in the utilities supplying the jacket, e.g., a steam-header pressure control loop. In the reactor loop, linearity means getting symmetrical set-point responses from the jacket. If the cooling and heating responses of the jacket are asymmetrical (as in Figure 5 or for steam versus cold water), consider a gain scheduling controller to compensate. This doesn’t require any special coding because it can be easily configured by drag-drop-and-tune in modern control systems.Linear
Dead time is the time measured from an output change before anything happens on the PV. It’s inherently destabilizing in a feedback control loop. In the jacket, one cause of dead time is transport delay or the time required for a new fluid mixture to pass from the control valve to the measuring element. Minimize this dead time by appropriate sensor location and by installing a circulating pump as shown in Figure 1. Also, the effect of filters added in the transmitter or the controller may look like dead time to the PID algorithm. In the reactor loop, we minimize dead time by getting the fastest linear response of the jacket loop, including allowing one overshoot on the jacket set-point response.
Process dynamics is a model of the shape and size of the PV response to output changes, which we need to optimally tune the controller. For most loops this can’t be calculated before construction and is most conveniently determined from step tests with the controller in manual. The process dynamics can be manually calculated from trend charts or time series data acquired from an OPC server or, in some cases, automatically by software running in the DCS. The two simplest types of process dynamics are:
- self-regulating processes (those that eventually settle at a new value during manual step tests); and
- integrating processes (those that ramp at various slopes during manual step tests).
The tests to measure these process dynamics also will reveal the nonlinearities in the process.
With a PID controller the type of process determines how to compensate for the process dynamics. For purely self-regulating processes we mainly use integral action in the controller. For purely integrating processes we mainly use proportional action. Derivative action normally isn’t needed in the jacket controller but may be appropriate in the reactor controller.
The Lambda tuning method is one way of choosing the PID parameters to tune for the speed required, without oscillation. For process dynamics that are purely self-regulating or integrating, simple algebraic tuning rules developed for continuous processes  have proven applicable to batch processes. These rules can be taught to engineers, technicians and operators as a time domain method — without the use of Bode plots or transfer functions. We must observe the rule of cascade by tuning the jacket (slave) control loop first and faster than the reactor (master) control loop. The Lambda tuning method provides explicitly for tuning by the cascade rule because we can set the response time (λ) of each control loop as: