1. Chapter 8 Model Based Control Using Wireless Transmitter

2. General Process Representation  A process model may be used to estimate the control parameter between measurement updates provided by a wireless transmitter. The Kalman Filter and Smith Predictor are used to illustrate how a process model is used to predict the process output and the modifications that are required when applying these techniques in wireless control.  Both approaches are based on the construction of a process model. For example, many industrial process units are characterized by one manipulated input, U(t), and one measured process output, X(t),

3. Rudolf Kálmán at the White House  The basis for the Kalman Filter is a paper published in 1960 by Rudolf Kálmán, “A New Approach to Linear Filtering and Prediction Problems.”  The Kalman Filter uses a dynamic model, measured control input(s) and process measurement(s) to estimate the process output. A wide variety of applications have successfully utilized Kalman filtering.  On October 7, 2009, U.S. President Barack Obama honored Kálmán in an awards ceremony at the White House, where he presented him with the National Medal of Science, the highest honor the United States can give for scientific achievement

4. Application of Kalman Filter with PID  When a process is characterized by process or measurement noise, a Kalman Filter may be applied as an observer to estimate the process state from the process output measurement. The impact of process or measurement noise on a control application may be reduced by using the estimated process state for control

5. Kalman Gain Calculation for Noisy Process  The Kalman gain, Kj, determines the portion of the residual used in the Kalman Filter model to compensate for inaccuracies in a, b, or h and to account for the process or measurement noise.  An optimal linear estimator may be achieved by dynamically calculating the Kalman gain in a recursive manner. However, The Kalman gain may be assumed to be a constant if the process is noise-free or the measurement and process noise covariance is constant.

6. Impact of Noise with Non-zero Mean  When the measurement or process noise mean value is not zero, an offset is observed between the measurement and the estimate of the state for values of K<1/h. For instance, the introduction of an unmeasured disturbance with non-zero mean creates a noticeable offset between the measured and the predicted process output.

7. Kalman Filter – Accounting for Measurement or Process Noise with Non-zero Mean  The offset caused by noise having a non-zero mean value may be eliminated by modifying the Kalman Filter as illustrated below, where the filter may be, for example, a first order filter with a time constant approximately equal to the process response time; that is, process deadtime plus process time constant

8. Application of Smith Predictor with PID The Smith Predictor was invented in 1957 by Otto J. M. Smith. When a process is characterized by significant process deadtime, a Smith Predictor may be used to estimate the process output measurement without process deadtime and to correct for any model error based on a comparison of the output measurement to the process model that includes deadtime.

9. Modifying the Kalman Filter for Wireless Measurement  The design of a Kalman Filter is based on the assumption that a new process output measurement is available each time the algorithm is executed. Thus, it is necessary to modify the Kalman Filter to allow correct control operation when a wireless transmitter is used for the process measurement. The modified Kalman Filter with the PID controller for a wireless measurement

10. Kalman Filter Modification for Wireless Measurement and Noise with Non-zero Mean  When the mean of the process noise is not equal to zero, then for values of Kj<1/h an offset is observed between the measurement and the estimate of the state. This offset may be eliminated by modifying the Kalman Filter as illustrated where the filter is, for example, a first order filter with a time constant approximately equal to the process response time

11. Smith Predictor Modifications for Wireless Measurement  The Smith Predictor may be modified to work with a wireless measurement as illustrated. The Smith Predictor may be executed on a periodic basis that is much faster than the rate at which the measurement is transmitted. However, the residual value that is used to correct the model without deadtime, effectively correcting the PV applied on the controller input, is updated only when a new measurement value is transmitted.

12. Modified Kalman Filter or Smith Predictor Using Standard PID  The Kalman Filter and the Smith Predictor modified for use with a wireless measurement may be used with the standard PID in closed loop control applications. For example, a PID function block and modified Kalman Filter or Smith Predictor may be used to address control using a wireless transmitter

13. Wireless Control as a Function Block  Using a modified Kalman Filter observer or Smith Predictor, the control can be implemented as one function block to show the measurement value to the operator as illustrated

14. PID Control – Wireless vs. Wired  In the following examples, the impact of wireless measurement updates on control performance was minimized through the use of the modified PI algorithm for wireless communication. The difference in control performance is shown below in terms of Integral Absolute Error (IAE) for periodic measurement updates vs. non-periodic updates.

15. PIDPlus and Wireless Measurement vs. PID with Wired Measurement  The closed loop response of the PIDPlus is illustrated for both setpoint and load disturbances and is shown in the lower trend. The response for a standard PI controller where the wired measurement value is communicated as frequently as the PI control algorithm executes is shown in the upper trend.

16. PID Control with Kalman Filter Using Wireless Measurement vs. PID with Wired Measurement  The test results achieved using a modified Kalman Filter with a PID controller and wireless communication of the process measurement are shown below. The control performance is comparable to a PID and a wired measurement for both setpoint changes and for a large unmeasured process disturbance.

17. PID Control with Smith Predictor and Wireless Measurement vs. PID with Wired Measurement  The test results achieved using a modified Smith Predictor for wireless communication of the process measurement are shown below. The control performance was comparable to a PID and a wired measurement for both setpoint changes and for a large unmeasured process disturbance.

18. Guideline in Using Process Model in Wireless Control  The PIDPlus has been proven to be a reliable means of implementing feedback control using wireless measurement in many applications.  When the process measurement is characterized by significant noise or long transport delay, an alternative approach is to use PID with a Kalman Filter or a Smith Predictor that has been modified to work with non-periodic measurement updates.  The test results shown for the application of a modified Kalman Filter or Smith Predictor with PID were based on ideal conditions.  Further research into the control performance and robustness of these approaches versus the PIDPlus for changes in process gain, dynamics and noise level are needed to fully prove the advantages of the alternative approaches.

19. Exercise: Model Based Wireless Control – Kalman Filter This workshop provides several exercises that can be used to further explore model based control using a wireless measurement. The module used in this workshop allows the control performance of a PID with a wired input to be compared to a Kalman Filter observer with a PID using a wireless input.  Step 1: Open the module containing the Kalman Filter with a wireless measurement vs PID with a wired measurement.  Step 2: Initialize the Performance Index (IAE) and then change the SP parameter of both control loops by 10%. Observe the control response using a plot of the setpoint, control measurements and output.  Step 3: Note the IAE and the number of communications for the wireless and wired control. You should see a significant difference in the number of communications for wired vs wireless control that were required to respond to the setpoint change.  Step 4: Initialize the Performance Index and change the Disturbance input from zero to 10. Observe the response of the PID with wired measurement and the Kalman Filter with PID and wireless measurement to this unmeasured process disturbance.  Step 5: Note the IAE and the number of communications for the wireless and wired control.

20. Process: Model Based Wireless Control – Kalman F ilter A simulation of two identical processes is used to compare control performance of a PID using a Kalman filter with a wireless measurement to PID using a wired measurement.

21. Exercise: Model Based Wireless Control – Smith Predictor This workshop provides several exercises that can be used to further explore model based control using a wireless measurement. The module used in the workshop allows the control performance of a PID with a wired input to be compared to a Smith Predictor with a PID using a wireless input.  Step 1: Open the module containing a Smith Predictor with a wireless measurement and PID with a wired measurement.  Step 2: Initialize the Performance Index (IAE) and then change the SP parameter of both control loops by 10%. Observe the control response using a plot of the setpoint, control measurements and output.  Step 3: Note the IAE and the number of communications for the wireless and wired control. You should see a significant difference in the number of communications for wired vs wireless control that were required to respond to the setpoint change.  Step 4: Initialize the Performance Index and change the Disturbance input from zero to 10. Observe the response of the PID and the Smith Predictor to this unmeasured process disturbance.  Step 5: Note the IAE and the number of communications for the wireless and wired control.

23. Compensation Method Based on Fictitious Setpoint  The setpoint compensation method is a means for compensating for lost communication to a wireless actuator. If back calculated controller input (i.e., actually implemented controller output) is different from calculated controller output, the fictitious setpoint is calculated using PV and actual back calculated controller input. In contrast, the PIDPlus suppresses response degradation by managing integral term calculation based on the communication status. This approach achieves similar goals without the complexity associated with the calculation of a compensating controller output (MV).

24. Process Unit – Single Input-Single Output  The model of a linear process with one manipulated input and one measured process output may be expressed in state variable format for both a self- regulating process and an integrating process.