In the steady state, there is no difference between the load and its lagged value. This is considered operationally desirable, in that the output of the controller and the manipulated flow have the same steady-state value, as in a conventional cascade system.
However, it has a profound defect: After a load change has passed, the feedforward compensation gradually returns to zero, requiring the PID controller to move its output to the new steady-state value dictated by the load. In essence, feedforward correction is only dynamic—there will be a Δm required by the controller, which will have to integrate an error to get there. The IE is, therefore, no different with or without impulse feedforward. The impulse acts to flatten the disturbance, with the result that the same IE is spread out over a longer time. Peak deviation alone is reduced—but there is a better way.
Fig. 5. Three possible methods of applying feedforward control.
In a linear feedforward system, the load variable passes through a dynamic compensator (if required) and then is added to the controller output with a gain adjustment as shown. Again, the gain is set so that the effect of the load change is canceled by the resulting change in setpoint of the manipulated flow. This is the preferred arrangement when the process is linear and its gains are constant.
The best example of its application is that of boiler drum-level control. The level responds equally to the load—steam flow—and the manipulated flow of feedwater. The feedforward gain is thereby constant at 1.0. Linear feedforward control of boiler drum level has been applied as early as 1929, in the "three-element" feedwater system.
In the control of composition or temperature, however, the gain of the controlled variable to load flow is not constant. It varies with both the feed condition and the product composition or temperature setpoint. Feedforward gain can be set to match the process gain initially, but it will be incorrect when feed conditions or product specifications change. For example, the ratio of high-octane blending ingredient to the flow of the main stock varies with the octane rating of that stock and the setpoint of the octane controller.
We see linear feedforward used widely in matrix-based multivariable systems. The process is first tested extensively to estimate all the gains relating load, manipulated and controlled variables, both steady-state and dynamically. The gains are then entered into the control matrix and fine-tuned for performance. But since the process gains change with feed conditions and product slates, after a while they may no longer match the feedforward gains set into the matrix, so control deteriorates—IE following load changes is no longer zero. Accounts of lost performance over time are very common with installed linear multivariable systems.
Composition and temperature measurements are properties of a flowing stream. The heat content of a flowing stream is the product of its flow and its temperature rise above inlet conditions. Similarly, the rate of high-octane blending ingredient needed to reach the blend specification is the product of the main stock flow and the rise in octane number required. Multiplication is a bilinear operation—the output of a multiplier is linear with both of the inputs. Multiplication of variables is an essential function in feedforward control of composition and temperature. Accurate multipliers only became available in pneumatic and electronic instrumentation in 1960, which is when feedforward control began to be applied to heaters and distillation columns.
The bottom system in Fig. 5 multiplies the load variable—feed flow—by the PID output. A very common example of a bilinear feedforward system is the control of stack-gas oxygen by manipulating the air-to-fuel ratio in a combustor. The oxygen-controller output then represents the ratio of the manipulated airflow to the load fuel flow. This ratio is not a constant, but varies with both the heating value of the fuel and the setpoint of the controller in terms of percent oxygen in the stack gas. This setpoint is varied with load in most boilers, and the heating value of the fuel varies widely in mixed-fuel installations. When either of these parameters changes, the oxygen measurement is upset, and the controller must readjust its output to restore a balance. In doing so, it is not only returning the controlled variable to setpoint, it is also recalibrating the feedforward gain to match the new process gain.
The multiplier also serves another purpose: gain-compensating the feedback loop. The gain of a bilinear process varies inversely with flow. For example, a step in the flow of octane enhancer to a blender will have twice the effect on the blend octane at half the production rate as it does at full production. Likewise, a step in steam flow to a heat exchanger will have twice the effect on the temperature of liquid leaving at half flow than it does at full flow. This has led engineers over the years to use equal-percentage valves for temperature control, as the valve gain varies directly with flow delivered. In the bottom diagram of Fig. 5, the feedback-loop gain from the controller passes through the multiplier, whose gain varies with the load variable, the flow through the process.