# Comparison of Single Control Loop Performance Monitoring Methods
## 4 Discussion  
The current state of control performance monitoring methods was explored, and different model-free CPM methods were chosen for a demonstration case with the aim of providing easily adaptable methodologies for control loop performance monitoring in industrial applications. Some of these methods are widely used in control loop design and tuning, and this work further adapts these methods in a dynamic control performance monitoring application. A simulated environment was used to obtain a representative dataset for testing, with the possibility of including different faults in different time periods in the simulation. Among the studied methods, histogram intersection well identified the control error residual difference from the reference data. Increased error from poor control results in an abnormal distribution. However, the metric is heavily dependent on the conditions from which reference data were obtained. Naturally causing drift and other changes in the process can cause the metric to shift from an optimal area, even though the process may perform adequately. As such, multiple metrics should be monitored for verifying the results of other metrics and observing the actual state of the process. One option to facilitate this is to take the approach used in the OCE method, which uses a product of several indices to assess the overall controller performance. For example, the histogram intersection is naturally scaled to values between 0 and 1, thus being an appropriate candidate for such a combined CPM index. With respect to the second case with varying fault intensities, the _KL_, _HI_, and _ED_ methods performed rather poorly. The metrics mostly stayed at levels of normal operation with the original method parameters. Adjusting the parameters for these methods allowed accurate identification of the fault with the valve stiction values above 0.0031, as seen in Table 2. However, robustness was compromised, with the methods only falling slightly below the normal operation levels (for example, the median stayed above 0.96 for histogram intersection in the highest valve stiction cases). The metrics could identify some of the lowest fault intensities with decent accuracy but missed the identification of some of the highest intensities. Amplitude Index performed poorly in the second case; however, the metric has utilization potential in different fault cases. The integral methods _ITAE_ and _ISE_ performed well, with _ISE_ identifying 61.4% and _ITAE_ 69% of the varying fault intensities. This can be explained by the nature of the implemented fault, which caused residual setpoint error that integrating methods can identify well. Additionally, due to the nature of the simulation, the chosen sliding window has a large and very homogenous number of step changes. In practice, setpoint changes can happen infrequently and at random time intervals. As such, applicability of the methods should be considered when implementing CPM tools. This paper focused on a single control loop case to build on a solid foundation for further research. Multiple-input multiple-output control could prove an interesting topic in the future. The setpoint changes utilized in the demonstrations were chosen to be rather short, while industrial applications may run in the same state for weeks at a time. Additionally, only one process was utilized for the simulations. Differences in process dynamics may cause differences in the behavior of the control performance monitoring metrics. Thus, the performance of the methods should also be studied for different types of