To provide best control, the PID must be restructured to correctly handle continuous measurement updates that are communicated much slower than 4 times the process response time. The PID also must be able to work with the non-periodic measurement updates that are provided when window trigger mode is configured. The PIDPlus capability included in DeltaV v11 is specifically designed to address control using wireless measurements. The implementation of the PIDPlus in DeltaV v11 is shown below.
The filter output used in the positive feedback network is calculated in the following manner when a new measurement is received.
FN = New filter output
FN-1 = Filter output last execution = filter output after last new measurement
ON-1 = Controller Output last execution
ΔT = Elapsed time since a new value was communicated
Control execution is set much faster than measurement update. This permits immediate action on setpoint change and update in the faceplate. PIDPlus tuning is based on the process dynamic (e.g. RESET= process time constant plus dead time); PIDPlus reset automatically compensates for variations in the measurement update rate. No change in PID tuning is required for varying update rate.
To further enhance the response for continuous changes in setpoint, the implementation of the PIDPlus may be modified as shown below.
Figure 4 – PIDPlus in DeltaV v12
This PIDPlus implementation is standard in DeltaV v12 and allows the reset calculation to automatically compensate for setpoint change and measurement update rate. When either PIDPlus implantation is used, there is no need to modify tuning as sample rate changes; i.e., reset is based strictly on the process response dynamics.
The derivative component of the PIDPlus is also modified to account for the fact that a new measurement value is not available each execution of the PID. The changes in the derivative calculation are shown below.
Figure 5 – Derivative Calculation in PIDPlus
The derivative contribution is only updated when a new measurement becomes available. Also, the calculation is based on the elapsed time since a new value was communicated.
Control Performance Comparison
When the PIDPlus is used with a wireless transmitter in a control application, the performance will be comparable to that achieved using a wired transmitter with a wired transmitter. To demonstrate this, the module shown below was created in DeltaV that allows the control using PIDPlus using a wireless communication to be compared to the control achieved using PID and a wired transmitter.
Figure 6 - Wireless test environment
The simulated processes controlled by the PIDPlus and PID were identical and designed to use the same unmeasured disturbances. Also, using a module parameter, the setpoint value to the PID and PIDPlus can be changed at the same time. Using this capability, tests were conducted in which changes were made in the setpoint and unmeasured disturbance. The PID and PIDPlus control response is shown in the following trend.
For the test shown above, the communications window trigger mode was utilized with a maximum update period of 10 seconds and a trigger value of 1%. As shown, the control performance using wireless was comparable to that achieved using a PID and wired transmitter executing once per second. However, by using window trigger mode, the wireless communications used by the PIDPlus were 96% less than the number of new measurement values provided by the wired transmitter to the PID. The impact of non-periodic measurement updates on control performance as measured by integral of absolute error (IAE) is minimized through the use of PIDPlus for wireless communication as summarized below.
Figure 7 - Wired vs. wireless control performance
Table 1 Control Performance Wired vs. Wireless
The reliability of WirelessHART device communication has been well established. Even so, in the event of loss communication, the expected control behavior is of interest. The simulation environment was used to compare the behavior of the PIDPlus for loss of communications to a PID with a wired transmitter where the measurement value is frozen for a period of time. The response observed when the measurement was lost during a setpoint change is shown below.
Figure 8 - Response for measurement loss – during recovery for a setpoint change
The response observed when the measurement is lost after a process disturbance is shown below.