We have probably heard of the benefits of a signal character in compensating for the gain nonlinearity of a control valve flow characteristic and the pH measurement. What we often don’t recognize is how the use of signal characterizers enables a more accurate loop dynamics identification and adaptation, restores a process time constant and reduces deadtime and limit cycle amplitude. Here we look at how these benefits arise and the “ins and outs” for a successful signal characterizer implementation.
We live in a nonlinear world. With knowledge of operating point nonlinearities we can employ a signal characterizer based on simple tests and configuration to dramatically improve the performance of a PID controller and model predictive controller by better model identification, computation and adaptation and by a larger time constant to dead time ratio.
Signal characterizers in industrial control systems use a piecewise linear fit. While a polynomial fit or neural network might be thought to be advantageous to make the fit a curve, the piecewise fit is safer and simpler to implement. Polynomial fits and neural networks can have reversals of slopes that reverse the process gain especially for extrapolation beyond the test range. A reversal of process gain can cause instability. The piecewise linear fit is a well proven technique in process control. Sufficient resolution in areas of particular nonlinearity and interest can be achieved by the spacing of the X,Y data points and if necessary by cascading the output of a primary signal characterizer to the input of a secondary signal characterizer to zoom in on an operating region.
The most common application of signal characterizers is for compensating for the nonlinear flow characteristic of a control valve. Here a change in flow divided by the change in signal is the valve gain. The plot of valve flow versus signal must be for the installed flow characteristic. The installed flow characteristic can drastically differ from the inherent flow characteristic particularly as we attempt to save energy by allocating less pressure drop to the valve (decreasing ratio of valve drop to system drop). We need to make the calculation of the installed flow characteristics based on piping system design and operating conditions. Fouling of inline equipment (e.g., filters, strainers, and heat exchanger tubes) makes the installed flow characteristic change with time generally in the direction of reducing the valve drop to system drop ratio. Given we have identified the installed flow characteristic, what are the benefits?
Besides the obvious gain from a more linear valve gain (pun intended) the characterizer can reduce the deadtime from valve deadband on the flat portion of installed characteristic by making the change in signal to the valve greater. Also, the characterizer eliminates the need to tune the controller for the steepest part of the installed characteristic. The higher controller gain enables a higher rate of change of controller output that gets through the deadband quicker reducing deadtime in general. The amplitude of a limit cycle from deadband is also reduced since this amplitude is inversely proportional to controller gain. The amplitude of a limit cycle from a resolution limit is proportional to the open loop gain that is the product of the valve gain, process gain and measurement gain. Consequently, the amplitude from a resolution limit will be reduced for the steep part of the flow characteristic (high valve gain).
The valve response time becomes more consistent and more of an identifiable function of actuator and positioner design and tuning. While the discussion here is for control valves, a signal characterizer is also beneficial for a variable frequency drive (VFD) when ratio of static head to system drop becomes appreciable (e.g., greater than 0.2) that results in a steep drop in flow at low speeds resulting in what for control valves is described as a quick open characteristic. The change in flow with speed is only linear at low flows if the static head and speed slip are negligible. The degree of static head and the inverter design determine the actual rangeability, with the greatest rangeability achieved for negligible static head and least slip by a pulse width modulated inverter with built-in cascade control of speed to torque.
The valve or VFD signal characterizer is inserted on the controller output. Since the signal characterizer is computing a nonlinearity using the first input (IN_1) and first output (OUT_1) that is the reverse of the valve nonlinearity, the X data points are flow and the Y data points are valve or VFD signal. The flow can be in flow engineering units or simply 0-100% of maximum valve capacity.
To provide a bumpless download, the "back calculate" (BKCAL) signal that is the valve signal must be converted back to flow since the controller output is now in terms of flow. To achieve this conversion, the BKCAL of the analog output (AO) block process variable (PV) is connected to the second input (IN_2) of the signal characterizer. The inverse function (e.g., SWAP2 = True) is chosen and the second output (OUT_2) is wired as the BKCAL input to the PID block. If the control valve is slow compared to the rate of change of PID controller output or directional move suppression is needed (e.g., fast opening and slow closing surge valve), a fast readback of actual valve position can be used as the BKCAL signal that is connected to the characterizer IN_2. External reset feedback (e.g., dynamic reset limit) is then enabled in the PID.
While the process controller output is now flow, similar to what would be obtained if there was secondary flow loop, operator s and maintenance people can get confused. The actual valve position must be shown on operator graphics and the ability to manually directly change a valve signal given.
The next most common application is for pH control. Here we start with a titration curve obtained from lab titration of a process sample at operating temperature and concentration. The titration curve must have at least 10 data points on the steep part of the curve and in the operating region. A theoretical curve obtained from even the best electrolyte modeling program needs to have the concentration of weak acids and weak bases and conjugate salts adjusted so that the slope (process gain) in the control region of the computed curve matches that of the actual titration curve from the lab titration. Small amounts of carbonic acid absorbed from seemingly insignificant amounts of carbon dioxide in the atmosphere can decrease the slope of a strong acid and strong base system by several orders of magnitude. The use of lab titration curves at actual process conditions is critical.
The abscissa of titration curve should be converted first to a ratio of reagent flow to feed flow for continuous systems and fed-batch systems and the ratio of reagent added to vessel liquid volume for pure batch systems. This translation enables the computation of feedforward gain and reagent valve or VFD capacity, rangeability and deadband requirements. For signal characterization, I prefer to subsequently scale the abscissa as simply a 0-100% reagent demand. Since the signal characterizer is computing a nonlinearity using the first input (IN_1) and first output (OUT_1) that is the reverse of the pH nonlinearity, the X data points are pH and the Y data points are percent reagent demand.
The PID PV scale is now percent reagent demand. Consequently, a pH setpoint must be converted to percent reagent demand by connecting the pH setpoint to the second input (IN_2) and using the second output (OUT_2) of the characterizer as the PID setpoint. Note that in contrast to the valve or VFD signal characterizer, the inverse function is not chosen (e.g., SWAP2 = False). The pH setpoint and pH measurement must be on the operator graphics and be trended for operators, process engineers, control engineers and maintenance technicians. The operator must be able to change the pH setpoint.
Besides the obvious gain from a more linear process gain (pun intended) the characterizer can restore the process time constant. In a worst case scenario per calculation made in my ISA book Advanced pH Measurement and Control - 3rd Edition, a 19 minute time constant would be reduced to a 0.04 minutes for a pH approaching neutrality (7 pH) in a true strong acid and strong base system. The acceleration in pH response can resemble a runaway response to the PID controller further complicating the tuning. Also, the characterizer eliminates the acceleration and need to tune the controller for the steepest part of the titration curve. The higher controller gain enables a higher rate of change of controller output that gets through the electrode resolution limit quicker reducing deadtime. The amplitude of a limit cycle from deadband is also reduced since this amplitude is inversely proportional to controller gain. The amplitude of a limit cycle from a resolution limit is proportional to the open loop gain that is the product of the valve gain, process gain and measurement gain. Consequently, the amplitude from a resolution limit will be reduced for the steep part of the titration curve (high process gain).
Other applications include the linearization of the process gain for level loops where the cross section area of the volume changes (e.g., horizontal tanks and spheres), for conductivity loops where the conductivity versus concentration is a curve and for distillation column temperature loops where the slope of the temperature response as an inference of composition changes with the reflux to feed ratio.
The implementation of input and output signal characterizers generally increases the time constant to deadtime ratio and decreases limit cycle amplitude improving loop performance. The identification of the open loop gain, time constant, and deadtime is less dependent upon the setpoint and the size and direction of the change in controller output. The identification of dynamics becomes more consistent as the result of signal characterizers. The need for good tuning software and adaptive control is not eliminated. Knowledge of the pH titration curve and valve or VFD installed flow characteristic is far from perfect. Flow characteristics will change with system resistance and static head and titration curves will change with feed concentration. Tuning software and adaptive control is needed to identify the many unknowns and non-idealities in industrial systems. Like any process control improvement, the concept and implementation details must be thoroughly developed, the actual configuration completely tested and the operators, engineers, and technicians extensively trained for normal and abnormal valve, process and measurement conditions by the use of high fidelity dynamic simulations in a virtual plant.
For more on the concepts and details on the effects of nonlinearities, deadband and resolution limits on limit cycles, identification and tuning of PID controllers see my Momentum Press book Tuning and Control Loop Performance - 4th Edition.