Effect of Disturbance Dynamics Perspective Tips

Much of the differences in approaches to controller algorithms and tuning can be traced back to assumptions made about the type and importance of disturbances. Each method has merits based on the disturbance frequency, location, and time lag. Here we gain an understanding of how to reduce process variability from upsets originating from changes in raw materials, production rates, weather, operating conditions, or other loops.  

The emphasis in control literature is on setpoint response. When the ability to handle disturbances is studied a step disturbance is typically shown as entering the loop at the process output at the point of the measurement. Often sensor and measurement delays and lags, filter time, and PID module execution time are not included. Consequently, the disturbance appears immediately at the PID input. This approach simplifies the mathematical analysis and the dynamic compensation of feedforward signals and shows the advantage of model based algorithms, such as internal model control. The tuning for a step disturbance in the process output is the same as for a setpoint change for a PI on error structure. In contrast the tuning for a step disturbance in the process input (load disturbances) uses more aggressive tuning to minimize peak and integrated errors. We can use this aggressive tuning for load disturbances for setpoint changes by the use of an alternate structure, such as two degrees of freedom (2DOF) or the introduction of a setpoint filter or lead-lag to reduce overshoot without excessive increase the time to reach setpoint. For step disturbances on the process output the lack of options, such as these just mentioned for dealing with setpoint changes, has led to the development of different tuning rules and special algorithms. The rules and algorithms also depend on whether the process has a self-regulating, dead time dominant, near or true integrating, or runaway open loop response. As you can imagine this sets us up for a remarkable spectrum of proposed solutions and a considerable difference of opinions. Often proponents of a particular rule or algorithm are focusing on a specific disturbance location and type of open loop response.

The disturbance most commonly encountered that is of greater interest enters into the process typically upstream of the process dynamics and is a change in flow, typically feed flow.  This disturbance entering the process about the same point as the manipulated flow is termed a load disturbance. Changes in composition or temperature of the feed or manipulated flow are also considered load disturbance but these are usually much slower.

For a given size disturbance, the impact increases with the rate of change of the disturbance. The worst case is the step disturbance seen throughout the literature. Step disturbances result from compressors, fans, or pumps starting or stopping and from relief valves or on-off valves opening or closing. These actions are typically initiated by manual actions, sequences (e.g. batch operations and automated startups and transitions), and safety instrumentation systems. Snubbers (restrictors in the air lines) can be used to slow down the stroke of on-off valves but the adjustment is not as accessible or flexible as the tuning settings and analog output (AO) block setpoint rate limits in a PID. 

Most disturbances are not a step change because flows are typically manipulated by PID with reset action. If a flow loop is used the PID tuning uses more integral action rather than proportional action (e.g. PID gain = 0.2 and reset time = 2 seconds) to deal with the valve nonlinearities. The flow control closed loop time constant (lambda) and thus the disturbance time constant for the process loops affected by the flow change is about 10 sec. If there is no secondary flow loop, the feedback action of primary process composition and temperature loops has even larger closed loop time constants. However, when for the case of setpoint changes rather than load disturbances, there is a large initial step from proportional action and a kick from derivative action for a structure with PID on error.  If a secondary flow loop is not used, the primary PID output changes are immediately passed on as abrupt valve position or speed changes and hence flow changes to affected loops.  For continuous operations there are not many setpoint changes. The disruptive nature of setpoint changes is more an issue for batch operations and automated startups and transitions in product grade or type. Note that for many batch pressure and temperature loops, the time to reach setpoint is more important for reducing batch cycle time than minimizing steps in utility flows. An analog output (AO) block setpoint rate of change limit can be used with external reset feedback to slow down the action of the valve making the upset to utility systems less abrupt.   

Thus, the advantage of a secondary flow loop extends beyond isolating the primary process loop from valve and speed nonlinearities to slowing down the most prevalent fast disturbance being flow and enabling flow feedforward control (e.g. flow ratio control) to deal with the disturbance directly compensating for most of disturbance before it affects other primary process loops.

The fastest reasonable response is a lambda equal to one dead time. Due to unknowns, a lambda equal to two to four times the dead time is used. For a disturbance that ramps due to a near or true integrating process, the open loop error (process variable error if PID is in manual) is replaced by the open loop ramp rate (process variable ramp rate if PID is in manual). The time units of this open loop error are cancelled out by the time units in the integrating process gain in the equations for the integrated error and peak error for closed loop control (PID in automatic or cascade mode).

Slow load disturbances will exhibit longer recovery times (slow protracted approach to go back to setpoint).   An increase in integral action (decrease in reset time) can help the PID deal with the continual increase in the load with time.

Oscillatory disturbances are particularly problematic because a perpetual state of upset is created and the possibility of resonance exists. If the period of the disturbance is near the ultimate period of a loop, closed loop control will increase the amplitude (resonance). The best solution is of course to eliminate the oscillatory disturbance. Most often these oscillatory disturbances are caused by inappropriate tuning, valves with excessive backlash or stiction, batch operations, and on-off control. PID control should replace on-off control (e.g. level measurement and PID control instead of level switches). In terms of tuning, the most common mistake is a reset time that is too small particularly for level loops. For surge tank level control, the transfer of a change in inlet flow from batch operations to manipulated outlet flow can be smoothed to take advantage of available inventory.  For valves, the use of rotary valves designed for tight shutoff with piston actuators is the most frequent culprit. If the disturbance period is significantly less than twice the ultimate period, the amplification can be reduced by tuning the affected PID slower (smaller gain and rate time and greater reset time). Feedforward can provide a preemptive action reducing the need for feedback control and the consequences of slowing down the PID tuning. If the disturbance period is much larger than twice the ultimate period, the tuning solution is to make the PID faster (larger gain and rate time and smaller reset time).  The application of special notch filters is highly dependent upon accurate knowledge of the noise. The careful judicious use of the standard DCS first order filter offers the greatest general utility. 

 

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