How to tame unruly ramp function behavior

By Martin Emond, TopControl Inc.

RAMPING BLOCK devices are widespread in most PLCs as a built-in feature these days. The same goes for DCSs in the process field. This involves either ramping the setpoint from one operating point to another production rate, or limiting the rate of change of the controller output through the use of a ramp.

Most of the time, when people use a ramp device, they attempt to: 

1. Avoid overshooting during a setpoint change
2. Respect equipment constraints such as electrical (over-current), thermal or mechanical stress or
3. Make a smoother transition from one operating point to another.

For any of these three approaches, we’ll see that lead/lag filter is a better alternative to properly handle potential problems. 

Avoid Overshoot During Setpoint Change
Wherever the ramp is located--either at the controller output or at the setpoint--there certainly will be an overshoot for a non-self-regulating process and a high potential of overshoot for a self-regulating process (higher potential for a lag-dominant process model) according to the tuning’s aggressiveness. This is what we see by looking at G2(s), G3(s) and G5(s): all of them are overshot (See Figure 1 below).

	FIGURE 1: READY, SET, OVERSHOOT
	These performances are based on a simulation for a self-regulating and non-self-regulating process model. A ramped setpoint versus a step-changed setpoint going through a lead/lag filter has been applied. (Click image to enlarge.)

On the other hand, G1(s), which was step-changed through a lead/lag filter, not only is overshoot, but it reached the new setpoint faster with exactly the same tuning. Consequently, the ramp will postpone the setpoint response and make it overshoot. Thus, the first statement that leads people to use ramp happens to be unjustified for both self-regulating and non-self-regulating process types.

What is this lead/lag filter? This function often is available as a built-in device in most DCSs and PLCs on the market. It is a ratio between 0 and 1 of two time constants. One of them is the numerator and acts as the leader. The leader corresponds to the instantaneous portion of the step change applied to the controller. For instance, if the ratio is 0.7, then 70% of the step is instant or abrupt change and the other 30% goes through a first-order filter, which also is called lag.

The denominator is the lag, which is actually the time constant of a first-order filter. Generally, this filter time constant will match the tuning value of the integral action in the controller. This type of mechanism offers the best of the two worlds: no overshoot during setpoint change and fast load rejection.

Because of this lead/lag filter, tuning can be optimized for load disturbances without having any overshoot at all during a setpoint change. Furthermore, the load rejection will remain the fastest it can be during a load disturbance. Without a lead/lag filter, most people naturally tend to relax the tuning to avoid overshooting too much on a set-point change, or to use a ramp and get an overshoot of different magnitude depending on the tuning’s aggressiveness.

With a lead/lag filter, the excitation signal sent to the PID controller has a sharp break at the beginning, then the rest of the pattern is very smooth. In fact, it has the same shape as a first-order response. When using the ramp pattern, there are two abrupt changes: there is one at the beginning and a second one at the end when it reaches the new setpoint. The idea of a lead/lag function is to make a steep change at the beginning, when it is far away from the final value, then reduce the speed for the final approach. A two-degrees of freedom PID controller (Integral only on SP change) will produce similar results.

The settling time can be improved by a factor of two without overshoot when using a lead/lag filter. Settling time is defined as the time that has passed for both the process Value and controller Output to reach steady state and remain within the range of normal process noise.

The settling time is cut by a factor of two when using a lead/lag filter, as opposed to using a ramp applied on the set point or using a ramp limiter applied at the controller output, where this latter acts as a slew rate limiter.

In addition to lengthening the settling time by 100%, the ramp caused (in this example) an overshoot of 10%. If the aggressiveness of the tuning and the slope of the ramp are reduced to lessen the overshoot as close as possible to the minimum, then the settling time could be increased by a factor as high as four--a considerable amount. Consequently, with a ramp, the reduction of the overshoot during a set point change implies a significant increase of the settling time. On the other hand, the lead/lag filter does not create overshoot for either self-regulating or non-self-regulating processes.