## 2 The Pressure Control Configurations Design
### The PID Control Mechanism with a Backward-Propagation Neural Network  
The principle of traditional PID controllers, especially the control principle of digital PID, is deeply studied and analyzed. The digital PID is divided into position PID and incremental PID. It can be seen that the control output of position PID is related to the calculation results of each step and the previous results need to be accumulated. However, it has a great influence on the subsequent calculation results and the calculation amount is large when the previous calculation results have errors. However, the control output of each step for incremental PID is only related to the calculation results of the previous step. The previous disoperation has little effect on the subsequent calculation results and the calculation amount is smaller than that of the position PID control. The incremental PID is picked in this paper. The incremental ubiquitous PID algorithm (shown in Figure 1) we adopted is as Equations (1) and (2), whereas the \(y_{sp}(t)\) = process value of the controlled variable, \(y(t)\) = setting value of the controlled variable, \(e(t)\) = real-time error, \(u_{0}\) = initial output, \(k_{c}\) = the proportional coefficient, \(\tau_{I}\) = integral time constant, and \(\tau_{d}\) = derivative time constant. As a kind of sampling control, sampling and processing of computer control proceeds at short intervals; thus, continuous PID algorithms cannot be applied in actual control system before discretization. Incremental digital PID algorithms focus on the augmentation of the last controlled variable, which reduces negative effects of the past maloperation. The incremental PID algorithms are depicted as in Equation (3), where \(k\) = the sampling instant. \[u(t) = u_{0}+k_{c}\bigg{[}e(t)+1/\tau_{t}\int_{0}^{t}e\big{(}t^{\prime} \big{)}dt^{\prime}+\tau_{D}de(t)/dt\bigg{]} \tag{1}\] \[e(t)=y_{sp}(t)-y(t)\] (2) \[u(k) = u(k-1)+K_{p}[e(k)-e(k-1)]+K_{i}(k)\] (3) \[+K_{d}[e(k)-2e(k-1)+e(k-2)]\]  
At the same time, aiming at the tuning method of PID parameters, we analyze the structure and principle of neural network control algorithm and take the BP neural network control algorithm as the PID parameter tuning method in this paper, in order to improve the control quality of PID to drum pressure, so as to improve the temperature control accuracy of the Fischer-Tropsch synthesis reactor. The backward-propagation neural network (BPNN) has excellent capacity of self-learning, self-tuning, self-adaptation, and paralleled distributed processing, robustness, and fault tolerance, which can deal with complicated nonlinear control systems. There are three-layer (or more) neurons in the backward-propagation neural network (BPNN, as is Figure 2), including the inter-connected but inner-unconnected input layer, hidden layers, and output layers. The neuron activation values of the input layer are transmitted from the input layer to the output layer through hidden layers, the neurons of output layer capturing the input response; this procedure is referred to as forward information transmitting. If the actual output of the network does not fall within the expected error range, the error in the output is used as feedback sent from the output layer to the input layer in the reverse direction to adjust the connection weights at the neurons/nodes in each layer; this procedure is referred to as backward error correction transmission or backward propagation. With this kind of backward error correction transmission ongoing, the precision of network response to input information continuously rises [30; 31]. The detail of the BPNN self-tuning PID controller is described in Figure 3. After setpoint \(P_{sp}(k)\), process value \(P(k)\) and control deviation \(e(k)\) are entered and BPNN control algorithms are used to self-adjust \(K_{p}\), \(K_{i}\), and \(K_{d}\) online. Self-tuned parameters are assigned to input incremental PID algorithms; hence, drum pressure control with the PID controller is realized.