PID controller is a widely used controller in the field of industrial control, its full name is Proportional-Integral-Derivative Controller (Proportional-Integral-Derivative Controller). It is a linear controller, through the proportional (P), integral (I) and differential (D) three parameters of the adjustment, to achieve accurate control of the system output.
First, the basic principle of PID controller
Proportional control (P control)
Proportional control is the most basic control method in PID controller. Its core idea is to compare the deviation between the output value of the system and the desired value, and then adjust the control amount according to the size of the deviation. The formula for proportional control is:
u(t) = Kp * e(t)
Where u(t) denotes the control quantity, Kp denotes the proportionality coefficient and e(t) denotes the deviation.
The advantage of proportional control is fast response, but the disadvantage is the existence of steady state error, i.e., when the system reaches steady state, there is still some deviation between the output value and the desired value.
Integral control (I control)
Integral control was introduced to eliminate the steady state error in proportional control. Its core idea is to integrate the accumulated value of deviation over time and then adjust the control quantity according to the integral value. The formula for integral control is:
u(t) = u(t-1) + Ki * ∫e(t)dt
where Ki denotes the integral coefficient and ∫e(t)dt denotes the integral value of the deviation.
The advantage of integral control is that it eliminates the steady state error, but the disadvantage is that it may cause overshoots and oscillations in the system.
Differential control (D control)
Differential control was introduced to improve the stability and response speed of the system. Its core idea is to predict the trend of deviation and then adjust the control quantity according to the trend. The formula for differential control is:
u(t) = u(t-1) + Kd * de(t)/dt
where Kd denotes the differential coefficient and de(t)/dt denotes the rate of change of the deviation.
The advantage of differential control is that it can improve the stability and response speed of the system, but the disadvantage is that it is sensitive to noise and may lead to fluctuations in the control quantity.
Second, the design method of PID controller
Determine the control objective
Before designing a PID controller, you first need to define the control objective, that is, what kind of state you want the system output to achieve. The control objective can be the steady state error, overshoot, rise time, etc.
Establish mathematical model
According to the working principle of the actual system, establish a mathematical model. The mathematical model can be linear or nonlinear. For linear systems, transfer functions, state spaces and other methods can be used for modeling; for nonlinear systems, neural networks, fuzzy control and other methods can be used for modeling.
Determine the PID parameters
According to the control objective and mathematical model, determine the proportional coefficient Kp, integral coefficient Ki and differential coefficient Kd of the PID controller. commonly used parameter tuning methods are:
(1) Empirical method: according to experience, select the appropriate proportional coefficient, integral coefficient and differential coefficient.
(2) Trial and error method: by constantly adjusting the PID parameters and observing the system response, until a satisfactory control effect is achieved.
(3) Optimization method: use optimization algorithms (such as genetic algorithm, particle swarm algorithm, etc.) to optimize the PID parameters to obtain the best control effect.
Simulation verification
After determining the PID parameters, it is necessary to carry out simulation verification. Simulation verification can be carried out using software such as MATLAB, Simulink, etc. Through simulation verification, the performance of the PID controller can be checked to see if it meets the control objectives.
Practical application
After the simulation verification is passed, the PID controller is applied to the actual system. In the process of practical application, the PID parameters may need to be fine-tuned to adapt to the changes in the actual working conditions.
Third, the application of PID controller
PID controller has been widely used in the field of industrial control due to its simple, practical, easy to implement and other characteristics. Common application areas include:
Temperature control: such as boilers, air conditioners, chemical reactors.
Flow control: such as water pumps, compressors, pipeline transportation.
Pressure control: such as hydraulic systems, pneumatic systems, etc.
Speed control: such as motors, conveyor belts, etc.
Position control: such as robots, cranes, etc.
Chemical reaction process control: such as chemical reactors, fermentation tanks.
Fourth, the advantages and disadvantages of PID controller
Advantages
(1) simple structure: PID controller consists of proportional, integral, differential three parts, simple structure, easy to understand and realize.
(2) easy to adjust the parameters: PID controller parameters (Kp, Ki, Kd) can be adjusted according to the control objective, has good flexibility.
(3) Wide range of application: PID controllers are applicable to a variety of linear and nonlinear systems, with good universality.
(4) Low realization cost: PID controller has low realization cost and can be applied to various industrial control systems.
Disadvantages
(1) Sensitive to noise: differential control is sensitive to noise, which may lead to fluctuations in the control volume.
(2) Difficulty in parameter adjustment: for complex systems, the adjustment of PID parameters may be difficult, requiring many tests and adjustments.
(3) Inability to deal with nonlinear systems: for nonlinear systems, the performance of PID controllers cannot deal with nonlinear systems.