What Are Digital PID Controllers?

Since computers and various microcontroller chips have entered the field of control, a computer or microcontroller chip has replaced the analog PID control circuit to form a control system. Not only can the PID control algorithm be implemented by software, but also the logic of the computer and the microcontroller chip can be used. Functions to make PID control more flexible. After the analog PID control law is appropriately transformed, a microcontroller or computer is used as the computing core, and a software program is used to implement PID control and correction, which is digital (software) PID control.

The basic structure of a typical control system includes input, sampling, controller, and controlled object

As shown in the dashed box in Figure 2, the PID controller combines three basic control links: a proportional control link Kp, an integral control link Ki / s, and a differential control link Kd * s. When the controller works, the proportional (P), integral (I), and derivative (D) of the error signal are linearly combined to form a control quantity to control the controlled object, so it is called a PID controller.

These three basic control links have their own characteristics:

(1) P proportional control: proportionally reflects the error signal of the control system. Once the deviation occurs, the controller immediately generates a control effect to reduce the deviation. When the proportional controller changes the signal, it only changes the amplitude of the signal without changing the phase of the signal. The proportional control can increase the open-loop gain of the system, which is the main control part of the system. It should be noted that an excessively large scale factor will cause a relatively large overshoot of the system, and generate oscillations, which will deteriorate the stability.

(2) I integral control: integral control is mainly used to eliminate the static difference and improve the system's indeterminate degree, but it will make the system's oscillations worse, the overshoot will increase, and the dynamic performance will be impaired. Generally, it does not work alone, but it is controlled with PD. Combine. The strength of the integral action depends on the integral time constant Ti. The larger the time constant, the weaker the integral action, and the stronger the contrary.

(3) D differential control: reflects the change trend (rate of change) of the error signal, and can introduce an effective early repair signal into the system before the error signal becomes too large, thereby speeding up the system's operation speed and reducing adjustment time. Differential control can predict the changes of the system, increase the system's damping , increase the phase angle margin, and improve the dynamic performance of the system. However, the differential can greatly amplify the interference. Excessive differential will increase the system oscillation To reduce the system signal-to-noise ratio.

In order to achieve the control purpose and achieve the control targets, it is necessary to select an appropriate control algorithm. Commonly used control methods include feedback control, feedforward control, P control, PD control, PI control, PID control, etc. Among them, PID control is one of the most widely used control methods. The composite control of PID can synthesize the respective characteristics of these several control laws, so that the system can obtain good dynamic and steady-state performance at the same time ^[1]

PID control algorithms can be divided into two types in actual applications: position-type PID control algorithms and incremental PID control algorithms. The control theory is the same in the two, but there will be differences in the implementation after digital quantization, which are introduced separately below.

The digital PID control system is the same as the analog PID control system, and requires parameter tuning to operate normally. The difference is that in addition to setting the proportional band (proportional gain value Kp), the integration time Ti, the differential time Td, and the differential gain Kd, the sampling (control) period T of the system must be determined.

According to the sampling theorem, the sampling period Tmax, because the physical process of the controlled object and the changes in the parameters are more complicated, it is difficult to determine the maximum angular frequency max of the analog signal. The sampling theorem only gives the upper limit of the sampling period theoretically. The selection of the actual sampling period is restricted by many factors.

(1) Requirements for system control quality: Because electric control valves or pneumatic control valves are usually used in process control, their response speed is low. If the sampling period is too short, the actuator is too late to respond and still fails to achieve the control purpose, so The sampling period should not be too short.

(2) The requirements for anti-disturbance and fast response of the control system: The sampling period is required to be short. From the calculation workload, the sampling period is longer. This can control more loops and ensure that each loop has sufficient time. To complete the necessary operations.

(3) Computer cost: The computer cost also hopes that the sampling period is longer, so that the computer's computing speed and data collection rate can also be reduced, thereby reducing hardware costs.

The selection of the sampling period should also consider the time constant Tp and pure delay time of the controlled object. When = 0 or <0.5 Tp, the optional T is between 0.1 Tp and 0.2 Tp; At 0.5Tp, the optional T is equal to or close to .

(4) It must be noted that the selection of the sampling period should be considered in conjunction with the tuning of the PID parameters. Several factors should be considered when selecting the sampling period:

1) The sampling period should be much shorter than the object's disturbance signal period.

2) The sampling period is much smaller than the time constant of the object, otherwise the sampling signal cannot reflect the transient process.

3) Consider the response speed of the actuator. If the response speed of the actuator is slow, too short sampling period will be meaningless.

4) The quality of regulation required by the subject. When the computer's operating speed allows it, the sampling period is short and the regulator is of good quality.

5) Performance-price ratio. From the perspective of control performance, I hope the sampling period is short, but the computer operation

With the development of computer technology, generally a shorter sampling (control) period T can be selected, which is also shorter than the time constant Tp of the controlled object. So the setting process of digital PID control parameters is to first select according to the method of analog PID control parameter setting, and then adjust it appropriately, taking into account the effect of the sampling (control) period on the setting parameters.

Due to the long history of application of analog PID regulators, a variety of parameter tuning methods have been developed, and many materials have been discussed in detail. According to the characteristics of digital control, there are currently several setting methods commonly used.

Digital PID control stable boundary method

This method requires stable boundary experiments. The experimental procedure is to use pure proportional control and set the value r as a step perturbation. Start with a larger proportional band and gradually decrease until the controlled quantity Y appears a critical oscillation position. Note the critical oscillation period Tu and the critical value. The proportional band u is then used to calculate , Ti, and Td according to the empirical formula.

Digital PID control attenuation curve method

The experimental steps are similar to the stable boundary method. First, pure proportional control is used. A given value r is used as a step disturbance. Starting from a larger proportional band , the is gradually reduced until the controlled quantity Y shows a 4: 1 attenuation process. Note the proportional band v at this time and the time Tv between adjacent peaks. Then calculate , Ti and Td according to the empirical formula.

Digital PID control dynamic characteristic method

The above two methods perform parameter tuning directly in a closed-loop system. In the dynamic characteristic method, when the system is in an open loop, the step response curve of the controlled object is first made, and the pure delay time , time constant, and amplification factor K of the object are obtained from the curve. Then calculate , Ti and Td according to the empirical formula.

Digital PID control based on tuning parameter method with minimum deviation integral index

Due to the fast computing speed of the computer, this provides the possibility to tune the PID control parameters using deviation integral indicators. The following three indicators are commonly used: ISE, IAE, ITAE. Under normal circumstances, the ISE indicator has a large overshoot and a fast rise time; the AIE indicator has a moderate overshoot and a slightly faster rise time; the ITAE indicator has a small overshoot and a small adjustment time. With the deviation integral index, a computer can be used to find the best PID control parameters ^[2] .