Opening minds about controllers, part 2

Cases where it’s better or easier to use model predictive control instead of PID.

By Greg McMillan & Stan Weiner

Greg: In part 1, we started with a discussion of how to tune your PID with Mark Darby, principal at CMiD Solutions and part-time lecturer at the University of Houston, who also greatly expanded my horizon on model predictive control (MPC) in our column, “Model predictive control—past, present and future.” Here we discuss in more detail with Mark what MPC can do that PID could not do as well or as easily. Experts like Greg Shinskey and his protégé Sigifredo Nino can get extraordinarily more out a PID than the average user, particularly for challenging multivariable applications, as seen in “Distilled analysis of interaction” ISA Mentor Program resources, such as Michel Ruel, can also achieve much more with PID than most practitioners as seen in Michel’s many articles, starting for me with “Show me the money, part 1."

Stan: What trends do you see in the use of advanced process control? 

Mark: We continue to see widespread use of MPC, although with a variable success rate across the industry. Continuing enhancements from the technology suppliers have been in the areas of closed-loop plant testing and model identification. With the current shortages of knowledgeable staff, which will only get worse with the retiring of baby boomers, we are starting to see technology suppliers enhancing their MPC products to help guide inexperienced users to the right decisions. Embedded MPC capability in the DCS is allowing MPC to be used instead of customized advanced regulatory approaches for smaller applications. Real-time optimization (RTO) has not lived up to its promise. Only a few large companies have the skills to develop and maintain large RTO applications with the traditional general rigorous use of open equations to find and attain steady-state optimums. What we see are more small, targeted and simplified approaches to RTO.

Greg: Monsanto was intimidated by the need to develop several hundred thousand open equations for a large nylon intermediates plant with large amounts of recycle, and operational problems and modeling challenges in terms of solids and high ion concentrations leading to many non-ideal relationships. Since then, we have had a dozen or so small MPC applications that have paid off handsomely. The ability to try out a small MPC built into the DCS without the need for a special license or interface has led to more and more applications. These newer MPC provide much tighter control than the previous PID because of the ability to address compound responses and to identify and include disturbance variables in the model. The existing PID loop tuning was challenging due to  slow, complex response, and the dynamic compensation of a feedforward missing due to  software that could not readily compute the required lead-lag and deadtime.

Mark: I think it’s helpfulto think in terms of two varieties of MPC applications: 1) the process unit applications, consisting of several unit operations, with an objective of production maximization or energy minimization and 2) A standalone or targeted application that is addressing a challenging control problem with complex dynamics and/or interactions.

Stan: Why does MPC do better than PID on processes with complex responses often due to disturbance variables and recycle effects?

Mark: Leaving aside the multivariable advantages, MPC, with its flexible model form, can better control complex process responses than PID, due to its limited structure. Note that this assumes the identification software can identify sufficiently accurate higher-order models. Higher-order effects include inverse response, lead effect, and compound response caused by an embedded recycle in the process. The MPC will explicitly consider a prediction of the model over the prediction horizon, and will include the predictive effect of all manipulated variables plus the contribution from disturbance variables. Consider, for example, MPC control of an inverse response, with a predictive horizon that extends to steady state. The MPC will anticipate the inverse response and not correct in the wrong direction as a PID would.

Greg: For a simple combination of an early first- or second-order exponential response followed by a slow integrator, like we would see in a temperature loop on a heat exchanger in a recirculation on a vessel, we could tune the PID for the early response. We could also include the vessel temperature (heat exchanger input temperature) as a feedforward variable, but this understanding is generally missing. Secondary lags can be compensated to a large degree by derivative action. A lag can be added to the controlled variable via a filter to compensate for a small lead. What we cannot handle very well with a PID is an irregular response, like inverse response in boiler drum level control, and must rely more on a feedforward, such as steam flow in three-element control.

Stan: What are the pros and cons of making the MPC bigger to include more than a single unit operation?

Mark: MPC size is dictated by process interactions and the expected constraints. Larger controllers typically arise when the plant-wide objective is maximum production and limiting constraints lie at the back-end of the plant. By expanding the MPC to include a series of unit operations, you can greatly expand the optimization, improve constraint handling, and provide a more coordinated solution. However, the condition of the matrix can become challenging. Fortunately, techniques exist that can detect and repair the ill conditioning.

Greg: I think there is an opportunity in PID control to provide coordination of production rate changes typically seen as a change in a feed rate by an operator. This can be done by simple ratio control strategies that would move the plant in unison as explained in the March/April 2011 InTech article “Feedforward control enables flexible, sustainable manufacturing” (Feedforward control enables flexible, sustainable manufacturing). The setup of ratio control with feedback correction is detailed in the YouTube recording of my March 2017 presentation “Feedforward and Ratio Control” on the ISA Mentor Webinar playlist.

Want more?: Read our full slate of 2017 State of Technology reports

Included in this presentation is the use of feedforward signals to preemptively deal with changes in user steam flow and to decouple headers in a steam pressure control system where the feedforward is added directly to a PID output that goes directly to a linear, fast and precise letdown valve. For many pressure control systems, the use of a secondary flow loop introduces too slow of a response. Consequently, ratio control that depends upon a secondary flow loop is not used. The pressure controller output goes directly to valve(s). The valves generally need a resolution plus deadband less than 0.4%, an 86% response time less than 4 sec., and a linear installed flow characteristic. The requirements for surge control valves are even more dramatic. Signal characterization of the PID output should be used for nonlinear installed flow characteristics in flow, pressure and level control loops. In some cases, the equal percentage installed flow characteristics in composition and temperature loops may help to compensate for changes in the process gain, increasing the rangeability by reducing the effect of backlash and stiction near the closed position and reducing the nonlinearity seen from a low valve drop-to-system drop ratio in a misguided attempt to try to save energy, as discussed in detail in the 5/06/2015 Control Talk Blog, “Best Control Valve Flow Characteristic Tips."

Stan: How well does an MPC handle unmeasured load disturbances?

Mark: The traditional bias correction for unmeasured load disturbances on the process input does not do as well as a PID for lag-dominant processes where the PID gain and rate time settings are large. This limitation can often be mitigated by adding feedforward disturbances or by incorporating DCS PID temperature loops as manipulated variables in the MPC. We can switch to modeling the MPC process as an integrator so that the correction of the slope can provide action similar to what a PID can do. However, due to the way integrators are often treated in MPC, this uses up a degree of freedom (to balance the integrating variable at steady state). Some MPCs include additional options for handling unmeasured disturbances that can address error originating from a load disturbance on the process input.

Greg: A PID can provide deadtime compensation either via a Smith Predictor or the simple insertion of a deadtime block in the external reset feedback, as explained in “Common automation myths debunked."

Mark: A few MPC allow a variable deadtime. In general, though, a change in deadtime requires a reformulation of the matrix, making frequent changes impractical. This would be a nice feature for an MPC to have as it would allow, for example, deadtime to be expressed as a function of throughput.

Stan: Do I see a trend to seek the MPC to directly manipulate a control valve rather than a flow controller to avoid having to deal with incorrect or changes in flow loop tuning?

Mark: Direct manipulation of a control valve is normally done when either typical operation or the optimal steady state is at or near fully open or closed valve position. In these situations, it can make sense to “open” the DCS loop and directly manipulate the controller output. This approach may require signal characterization for linearization and assumes good positioner tuning, minimal stiction and backlash, and an 86% response time that is not significantly dependent on step size. Backlash can be addressed to some degree by using a lead-lag on the valve signal. When stiction or backlash is present, it is advisable to incorporate a minimum move limit in the MPC output. Adaptive approaches that adjust the controller output to PV model have also been applied.

Greg: These requirements on valve response are important in PID control as well, but often are not met due to an emphasis on tight shutoff and low cost, as extensively detailed in “How to specify valves and positioners that do not compromise control” and in the YouTube recording of my May 2017 presentation, “How to Get the Most Out of Control Valves” on the ISA Mentor Webinar playlist.

A big advantage of MPC over PID lies in more extensive and easier optimization. MPC can simultaneous honor the future trajectories of constraints by computing trajectories of the manipulated variables. There is also a sophisticated optimization of operating points by a Linear Program and in some cases a Nonlinear Program. For PID control, you can use valve position control and override control to optimize a particular process condition but the action is sequential and the tuning of the controllers is challenging. The use of setpoint rate limits and external reset feedback can provide directional move suppression to enable a smooth gradual approach to the optimum and a quick getaway for abnormal conditions as discussed in “Don’t overlook the virtues of PID when optimizing processes."

Top 10 advertisements and advisements

(10) Level switches are a cheap, easy solution for level control. Great if you are into upsetting downstream operations by on-off control and don’t need the knowledge of what the level is really doing and whether the switch is messed up literally and figuratively.

(9) Here is a PID tuning technique that achieves minimum Integrated Absolute Error (IAE) to give you the best process performance. Sure, if the process and the operator like oscillations that spread throughout the process and you love to use Power Spectrum Analysis and thrive on the challenge of chasing down the sources of oscillations.

(8) These control valves offer the tightest shutoff and greatest capacity. Fine, if you just need a very high flow and no flow, otherwise the resolution and deadband and limit cycle amplitude as a percent of flow is huge particularly near the seat and what is seen as feedback and readback of valve position is a lie due to backlash and shaft windup.

(7) Use a second smart d/p transmitter with a much lower range for a differential head meter to achieve a rangeability of 15:1. Boy this is a real stretch requiring an incredibly uniform velocity profile, an incredibly small hole for the orifice, constant sensing line fill composition and temperature, steering clear of the transition between laminar and turbulent flow and essentially no measurement noise.

(6) Use a smart vortex meter to achieve a rangeability of 15:1. Possible but you would need an exceptionally fortuitous situation of a constant kinematic viscosity, an incredibly uniform velocity profile and a rare coincidence of meter size maximum velocity matching the process maximum flow velocity.

(5) Adding a temperature to a differential head measurement will give you a mass flow measurement. Sure, if the composition and density never changes.

(4) All you need is steady state simulation. In your dreams or as a chemical engineering student, the process may be in a steady state and at the conditions you see on the Process Flow Diagram (PFD) but in real plants there are upsets and unknowns, variability introduced by just putting a PID in auto, and movement of operating points courtesy of operators, abnormal conditions, startups, transitions, optimization and batch operations.

(3) All you need is a good steady state understanding. Wishful thinking by engineers with predominantly a process rather than a controls mentality ignoring the above and the fact that the tuning settings and the minimum peak and integrated errors for unmeasured disturbances depends most notably on deadtime as discussed in the May 2017 Control Talk Blog “Deadtime, the Simple Easy Key to Better Control” and the April 2017 Control Talk Column “Common automation myths debunked”.

(2) My university control theory courses will prepare me for what I need to know to design, install and maintain control systems. I think I can count on one hand the number of universities in the USA that prepare you for what you need to know on the job in terms of what you need to know applying process control in the process industry.

(1) My new control algorithm for single loop control will do better than the PID for nearly all control applications. Sure, if you are not considering unmeasured load disturbances on the process input, not including process dynamics that can range from deadtime dominant, to balanced, lag dominant, integrating and runaway, don’t use the best tuning settings, don’t include the value of simply inserting a deadtime block in external reset feedback path, and ignore the 1976 landmark paper by A. Bohl and Y. McAvoy “Linear Feedback vs. Time Optimal Control II - The Regulator Problem” in Industrial & Engineering Chemistry Process Design and Development, Vol 15, No. 1.

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