Control with hysteresis

The temperature resulting from this type of on-off control will be fluctuating around the setpoint. The frequency and amplitude of the temperature fluctuations will be determined by the thermal lag of the particular machine. A problem of on-off control is the possible effect of process disturbances and electrical noise Interference, which can cause the output to cycle rapidly as the temperature crosses the setpoint. This condition can be detrimental to most final control elements such as contactors. To prevent this, an on-off differential or hysteresis is added to the controller function. This function requires that the temperature exceed the setpoint by a certain amount (half the differential) before the output will turn on again. Hysteresis will prevent the output from chattering if the peak-to-peak noise is less than the hysteresis. The amount of hysteresis determines the minimum temperature variation possible. However, process characteristics will add to this differential. Figure 4.23 shows a time-temperature diagram for an on-off controller with hysteresis. 

Time/power-temperature diagram for on-off control with hysteresis... 

Trip Valves The trip valve is part of a system that is used where a specific valve action (i.e., fail up, Fail down, or lock in last position) is required when pneumatic supply pressure to the control valve falls befow a preset level. Trip systems are used primarily on springless piston ac tuators requiring fail-open or fail-closed acrion. An air storage or Volume tank and a check v ve are used with the trip valve to provide power to stroke the valve when supply pressure is lost. Trip valves are designed with hysteresis around the trip point to avoid instabihty when the trip pressure and the reset pressure settings are too close to the same value. 

The control of a stirred tank reactor with hysteresis in the control element-I Phase space analysis (with J.C. Hyun). Chem. Eng. Sci 27, 1341-1359 (1972). 

Hu L, Serpe MJ (2013) Controlling the response of color tunable poly (N-isopropylacrylamide) microgel-based etalons with hysteresis. Chem Commun 49 2649... 

Fig. 7.29 Hysteresis of the multi-stacked actuator controlled with different controllers. Reprinted from [Chuc et al. (2011)] with permission from IEEE, Copyright 2011.

Krejci, P. Kuhnen, K. Inverse Control of Systems with Hysteresis and Creep. 

Wang X, Alici G, Tan X (2014) Modeling and inverse feedforward control for conducting polymer actuators with hysteresis. Smart Mater Struct 23 025015. doi 10.1088/0964-1726/23/2/025015 Xiang X, Alici G, Mutlu R, Li W (2014) How the type of input function affects the dynamic response of conducting polymer actuators. Smart Mater Stmct 23 105008. doi 10.1088/0964-1726/23/10/105008... 

When driven by a sine wave, a valve with hysteresis produces both phase shift and distortion. The former characteristic classifies it as a dynamic element, while the latter distinguishes it as being nonlinear. Controller output and stem position are plotted vs. time for a sinusoidal forcing function in Fig. 5.5. 

Differential gap is hysteresis in an on-off controller. A signal must change by an amount equal to the gap H in order to change the state of the output. The input output characteristic of an on-off controller with differential gap appears in Fig. 5.8. 

The gas pressure loop is perhaps the easiest type of process loop to control. Owing to the low gain in the process, a high controller gain will result in good control with very little offset and very little possibility of instability. It is perhaps the only loop in the fluid processing industry that is very close to being unconditionally stable. As with the level control loop, a valve positioner can be used to improve loop response for a valve with hysteresis. 

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