A thorough understanding of feedforward control in one article

Preface

Control methods can be mainly divided into two categories: feedback control and feedforward control. Usually, our attention is focused on feedback control because feedback control can stabilize the system and meet some robustness requirements and saturation limits at the same time. However, when the control system has large disturbances or needs to improve fast tracking performance, feedforward control is also indispensable, especially in industrial processes.

Feedforward control is common in human systems such as walking, playing basketball, and driving a car.

When you are walking on the street and see an obstacle 5 meters ahead:

• Feedback control: Continue walking forward for 5 meters. After hitting an obstacle, the body will receive pain feedback and then go around it.

• Feed-forward control: You move around obstacles instead of continuing to move forward until you hit them.

In this case, the human eye obtains prior information (Prior Knowledge), and then performs feedforward control (replans its own walking path), avoiding the extra time and energy consumed by replanning the path after walking to an obstacle (feedback control).

Based on this, the advantages of feedforward control can be simply summarized as follows:

1. Faster system response: Before transmitting the input signal, feedforward control predicts the output result of the controlled object according to the physical model, which can compensate for the predicted interference in the system in advance, thereby reducing the response delay of the system.

2. Can better handle nonlinear systems: Feedforward control can predict the disturbance caused by nonlinear systems and compensate for it in advance in the input control quantity, thereby improving the response accuracy and stability of the control system.

3. More robust to system model uncertainty: The feedforward control predictive control quantity is based on the model of the controlled object and can be applied to situations where the model has errors, friction or other non-ideal conditions.

Although the feedforward system can detect (or predict) disturbances and take action in advance, the feedforward controller is usually designed based on the inverse function of the transfer function of the controlled system, and is overly dependent on prior information. Therefore, it has a low tolerance for model errors. When non-ideal factors exist, the model and parameters need to be accurately adjusted, otherwise the results may be inconsistent with expectations. It is also easy to involve system stability issues and cannot adjust system performance, as shown in Figure (b). Therefore, feedforward control systems usually require some specific types of feedback control as a supplement, as shown in Figure (c).

Since it is impossible to obtain an absolutely accurate ideal model in the actual process, the feedforward control designed using the inverse function alone has poor stability, which makes the actual research meaningless. Therefore, this paper does not study this type of feedforward control method, but only studies the feedforward control method based on a stable feedback control system.

Academically, poor stability and feasibility are enough to sentence the method of using feedforward control alone to death. However, in the actual industrial process, relying on the workers' own experience, feedforward control alone is more common. However, such an approach is actually no longer considered "automation."

There are two main types of feedforward controllers, depending on the control objectives:

• Feedforward control with the goal of suppressing disturbances (anti-disturbance feedforward controller): It is often used in chemical and thermal control processes. When disturbances enter the system, they can be detected and eliminated immediately.

• Feedforward control with the goal of precise tracking (tracking feedforward controller): helps the system improve the tracking performance, especially the rapidity of tracking, without changing the original closed-loop structure.

Disturbance-Rejection Feedforward Controller

The figure below clearly shows how a feedforward controller eliminates the effects of disturbances in a feedforward-feedback control system. As soon as the disturbance signal enters the system, the feedforward controller eliminates it immediately, and the disturbance has no effect on the control loop and the system output. In contrast, a control loop with only a feedback controller will propagate the disturbance through all control paths, causing an error signal to form and drive the feedback controller response. In addition, the long lag time on the disturbance propagation path has an unwanted effect on the system output performance, which may cause overshoot and oscillation of the controlled variable. To avoid these effects, it is worth considering a feedforward controller.

The controllability of the feedback controller is evaluated by the ratio of the system lag time to the process model time constant. If this ratio is equal to or greater than 1, the feedback control usually cannot eliminate the impact caused by the measurement disturbance. In this case, a feedforward control strategy needs to be introduced, otherwise the feedback controller alone cannot complete the disturbance suppression. In addition, in industrial production, economic benefits are also a key point in deciding whether to use a feedforward controller.

The closed-loop transfer function from disturbance to output is:

In addition, the following explanations should be given about the anti-disturbance feedforward controller:

(1) When designing a feedforward controller, it is necessary to measure the process disturbance in advance or online.

(2) The effectiveness of the feedforward controller depends mainly on the accuracy of the controlled process model. If there are uncertainties in the process model, the feedback controller will mainly deal with these problems. However, this will increase the burden on the feedback controller.

(3) Although feedforward control may be physically difficult to implement in an ideal situation, in this case, the approximate method can provide an effective solution.

Tracking Feedforward Controller

Calculate the system transfer function from the above figure:

Case Study - Feedforward Controller Can Be Implemented

Consider the chemical composition control system shown in the figure, where the disturbance acts on the preconditioning tank and the output is at Tank 3, using a PI controller.

Assume the transfer function of the preprocessing box is

Case Study - Feedforward Controller is Not Realizable