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Abstract
Flow control is an essential element in many industrial processes, and the proportional-integral-derivative (PID) controller is one of the most widely used control algorithms. However, in many cases, the performance of the PID controller is affected by non-linearities and disturbances in the system. In this paper, a non-linear compensation technique based on PID auto-tuning is proposed to improve the flow control performance. The proposed method can effectively eliminate the non-linearity in the system and improve the control accuracy. The simulation results demonstrate the effectiveness of the proposed method.
Introduction
Flow control is an essential element in many industrial processes, such as chemical reactors, heat exchangers, and distillation columns. The performance of the flow control system depends on the accuracy of the control algorithm. The PID controller is one of the most widely used control algorithms due to its simple structure and ease of implementation. However, the performance of the PID controller is affected by non-linearities and disturbances in the system. In this paper, a non-linear compensation technique based on PID self-tuning is proposed to improve the flow control performance.
PID Controller
The PID controller is an algorithm that calculates the control signal based on the error between the desired value and the measured value. The PID controller consists of three components: proportional, integral, and derivative. The proportional component is proportional to the error, the integral component is proportional to the accumulated error, and the derivative component is proportional to the rate of change of the error. The mathematical expression of the PID controller is as follows:
u(t) = Kp e(t) + Ki ∫e(t)dt + Kd de(t)/dt
Where u(t) is the control signal, e(t) is the error, and Kp, Ki, and Kd are the proportional, integral, and derivative gain, respectively.
PID Auto-tuning
The PID controller performance depends on the selection of the gain values. The process of determining the optimal gain values is called PID auto-tuning is a technique that automatically adjusts the gain values based on the system response. There are several auto-tuning methods such as Ziegler-Nichols, Tyreus-Luyben, and Chien-Hrones-Reswick.
Flow Control with Non-linearities
In many industrial processes, the flow control system is affected by non-linearities such as valve backlash, friction, and hysteresis. These non-linearities can cause performance degradation in the flow control system. The non-linearities can be eliminated by using non-linear compensation techniques.
Non-linear Compensation Based on PID Auto-tuning
The proposed method is a non-linear compensation technique based on PID auto-tuning. The method consists of the following steps:
Step 1: Perform conventional PID tuning to obtain the initial gain values.
Step 2: Introduce a non-linear element in the system (such as backlash, friction, and hysteresis).
Step 3: Measure the system response and obtain the transfer function.
Step 4: Use the transfer function to identify the non-linearities in the system.
Step 5: Determine the non-linear gain values using the identified non-linearities.
Step 6: Modify the PID controller gain values using the non-linear gain values.
Step 7: Verify the system performance using simulation.
Simulation Results
The proposed method was verified using a simulation study. The simulation model is shown in Figure 1. The model consists of a pump, a valve, a flowmeter, and a non-linear element. The non-linear element was introduced in the form of valve friction. The system was controlled using a PID controller with conventional tuning and non-linear compensation based on PID auto-tuning.
The simulation results are shown in Figure 2. The blue line represents the response of the system with conventional PID tuning, and the red line represents the response of the system with non-linear compensation based on PID auto-tuning. The results show that the proposed method effectively eliminates the non-linearity in the system and improves the control accuracy.
Conclusion
In this paper, a non-linear compensation technique based on PID auto-tuning was proposed to improve the flow control performance. The proposed method can effectively eliminate non-linearity in the system and improve the control accuracy. The simulation results demonstrate the effectiveness of the proposed method. The proposed method can be used in various industrial processes to improve the performance of the flow control system.