Meditating on Disturbance Dynamics

Managing Control Loops Requires a Deep Understanding of Setpoint, Load Path and Noise

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By F. Greg Shinskey

There are three classes of disturbance that enter control loops from the outside: setpoint changes, load variations and noise. Flow loops must principally respond to setpoint changes, load disturbances being common only where multiple users draw from a common pump or compressor. Most of the other loops in a continuous plant operate at a constant setpoint, yet are often tested and tuned by introducing setpoint changes. Control loops respond differently to changes in setpoint and load, the difference being determined entirely by the dynamic elements in the path of the disturbing variable. Unless some filtering is intentionally introduced, there are otherwise no dynamics in the setpoint path. The load path, however, always contains dynamics, because load variables are similar to manipulated variables, being flow rates of mass and energy entering or leaving the process. The only type of disturbance impacting on the controlled variable directly is noise, and it has a frequency content by definition beyond the bandwidth of the loop. With no dynamics, a setpoint change is a poor substitute for a load upset in determining the performance and tuning of a controller whose purpose is to regulate.

Most single control loops can be represented by the diagram of Fig. 1, where the load variable enters the process at the same point as the manipulated flow. This is the case when controlling the composition of a blend of ingredients whose individual streams enter the mixing vessel at the same point. The common dynamic elements represented by gp are the time constant and dead time of the (imperfectly) mixed vessel. This representation also applies when controlling liquid level, where the manipulated flow is one of the streams entering or leaving the vessel and the load is the algebraic sum of all the other flows. However in a level loop, the common dominant dynamic element in gp is an integrator, and there is no steady-state gain Kp.

Fluid Process Dynamics
Figure 1. Most fluid processes have common dynamics.

Figure 2 represents the more general case where the load and manipulated variables may enter the process at different points, with steady-state and dynamic gains for the load input Kq and gq potentially differing from those for the manipulated variable, Km and gm.

Fluid Process Dynamics General Case
Figure 2. A more general case has independent dynamics.

Internal Model Control

An example of the misunderstanding of the load problem by the academic community has been their development of the internal model control concept (IMC). As represented in Fig. 3, the load input is shown with steady-state and dynamic gains, although in academic papers, these are usually omitted. Internal model control is designed to achieve a particular setpoint response: If the gains in the controller and model match those in the process, as indicated in the diagram, then the controlled variable responds to a setpoint change with only the filter dynamics gf. The process usually contains some dead time, however, which cannot be inverted in the controller; consequently, the controller dynamic gain parameter gm* differs from the process and model dynamic gain gm in lacking that dead time. The residual dead time will then appear in the setpoint response.

IMC loop
Figure 3. Feedback in an IMC loop is principally the load.

Any value of load other than zero will cause the value of the estimated controlled variable ce to differ from its measured value c. Therefore, the feedback signal to the controller is actually an indication of the load, including both its steady-state and dynamic gains. The summing junction at the controller input then compares the setpoint against the current load effect—a comparison of apples and oranges. The resulting difference is not an error or deviation in the normal sense applied to feedback controllers, and, therefore, can be a source of confusion among users of IMC.

Proponents of IMC sometimes refer to the feedback signal as normally being zero, when in fact this could only apply to a zero-load process: a batch process under no-flow conditions, which is a relatively rare situation in process control. But this indicates the degree of misunderstanding about load regulation that persists.

Dynamic load response is also commonly misrepresented. If load dynamic gain gq is omitted from consideration, then the response of the IMC loop to a step in load is the same as for a setpoint change, in that the controller responds directly to it, with only the filter in the way. However, solution of the block-diagram algebra for the load response is


Even if the model and controller parameters match the process perfectly, and there is no filtering, the load response is affected by load dynamics gq. The controlled variable will respond to a load step by deviating from the setpoint in a trajectory determined by gq until the dead time in the loop elapses, followed by a return to setpoint along an exponential curve whose time constant is the dominant lag in the load path, as shown in Fig.4.

Step load-response
Figure 4. Step load-response curves where the process lag is twice the dead time.

The load response for a first-order process with dead time produced by an IMC controller (without filtering) is compared with the best-possible response, for the case where the time constant in the load path τq is 2 times the dead time τd in the control loop (See my book, Process Control Systems, 4th ed., McGraw-Hill, New York, 1996, pp. 130-132). The integrated error IE under the IMC curve for this example is 2.5 times as great as under the best-possible response curve, and it increases exponentially with the ratio τqd ,

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