### Stiction  
The main cause of static friction or stiction is opposition to the movement of the valve stem. Thus, valve movement is achieved when the pressure applied on the valve to cause movement in the valve stem must overcome the opposing forces obstructing valve movement. When the applied force surpasses the static friction force, a sudden movement in the valve stem can be observed, which is due to the dynamic friction force based on the velocity of the stem movement. Then, because of the velocity, the valve becomes stuck in the new position. The controller starts reducing the input when the actual valve position is more than the required position. Thus, such repeated movements cause stick and slip movements in the valve, representing stiction in the control valve. The stiction behavior of the valve is represented by the following three regions: constant, jump, and movement or motion [34], as shown in Figure 2. The constant is the region where there is a change in controller output, whereas no change is observed in the actual valve position or manipulating variable, represented as region 'KLM', where 'KL' represents the deadband, whereas 'LM' represents the stick band. The jump is the region where a sudden change in the valve stem movement is observed, depicted as 'MN'. Movement or motion is the third region, where the actual valve keeps moving with a very slight variation in the control input, represented as 'NO'. This behavior is observed when the controller input continuously increases, and stick jump operations are also observed when the controller output is reduced, as represented by 'OPQK'. In Figure 2, the green line represents the constant region, the movement of the valve is represented by the red line, and the jump phases are represented by the blue dashed line. The stiction in a valve is nonlinear, thus exhibiting abnormal behavior that affects the valve behavior slowly. It is one of the incipient faults in pneumatic control valves; thus, the detection of stiction is challenging. For this reason, many researchers have worked in the area of modeling stiction to gain sound knowledge of stiction faults and determine their behavior under various conditions. An empirical model that simulates the stiction behavior  
Figure 2: Stiction representation. for various stick band and jump values was detailed in [35]. The enhanced version of the model specified in [35], also known as the Choudhury stiction model, was reported with the inclusion of other parameters in [36]. Another nonlinear model that considers stiction was reported in [37], in which stiction was also detected. The identification of friction faults using a smoothed model was highlighted in [38], and the use of a data-driven fuzzy system was reported in [39]. Some researchers have added their contributions to the stiction detection domain. A technique for identifying stiction in control valves by calculating the cross-correlation between a control signal and a loop output was described in [40]. The signals shifted because of static friction by approximately \(\pi/2\), resulting in an odd cross-correlation function. An even cross-correlation function is produced in the presence of additional disturbances. Therefore, the presence of stiction in control valves is implied by the occurrence of odd cross-correlation functions. This technique was examined utilizing industry statistics regarding oscillation occurrence. Three stiction detection techniques, relay, bicoherence, and cross-correlation, were described in [41] with a comparative inference of better performance on the use of the bicoherence method. The detection of stiction based on the movement of the plot of controller output and valve position was described in [42]. This method is a qualitative approach, and an indicator is used for the detection of stiction. Multiple stiction detection algorithms were utilized in [43], where one of them was selected for the detection of stiction.