# Self-Anti-Disturbance Control of a Hydraulic System Subjected to Variable Static Loads
## 3 Simulation Analysis of Optimal Control Strategy
### Simulation Analysis of SAD Control  
To further improve the control effect of the control system, on the basis of the SAD control algorithm, the classical PID was comprehensively optimized, the optimal scheme of the overall performance of the system was proposed, and the SAD controller was analyzed and designed in combination with the specific structure. The designed block diagram of the proposed SAD third-order controller in this paper is shown in Figure 8.  
The SAD controller consists of three modules, the control parameter Following Differentiator (TD), the error feedback Extended State Controller (ESC), and the EHS Control Law (CL). Based on the system state space expression, the controlled object was set to be third-order, where the TD was third-order, and the ESC was fourth-order. Seeking to improve the dynamics of this control system, we used state feedback to configure the desired poles. If the zero-point configuration of the control system can be realized, the dynamic performance of the control system can be improved. However, the zero-point configuration needs to use the differential signal. The previous differential signal cannot filter out noise, nor is it used for zero-point configuration, while the following differential signal can filter out the noise well, and the differential signal is zero-point configuration. The TD follows a given signal and obtains its differential equation. The transition process is arranged by the TD to prevent the overshoot caused by the sudden change in the given signal, so that the controlled objects approach the target smoothly, thereby improving the stability of the control system. By eliminating the poles of the system with the configured zeros, the system can be viewed as a control system close to unity. This sets the string level object to the following expression. \[y=\frac{1}{p_{1}(s)}\frac{1}{p_{2}(s)}u \tag{21}\]  
Assuming that \(p_{2}(s)\) is known, the virtual control volume is  
\[U(t)=\frac{1}{p_{2}(s)}u \tag{22}\]  
The above expression (21) can be written as  
\[y=\frac{1}{p_{1}(s)}U(t) \tag{23}\]  
Once the virtual control quantity \(U(t)\) is clarified, the actual control quantity acts as  
\[u=p_{2}(s)U(t) \tag{24}\]  
where \(p_{1}(s)\) and \(p_{2}(s)\) are polynomials. Figure 8: Designed block diagram of the proposed SAD third-order controller. The virtual control volume \(U(t)\) is determined by applying a improved controller design of Self-Turbulent Flow (STF) algorithm approach to the control subsystem \(y=U(t)/P_{1}(s)\), which allows for a certain range of uncertainties to exist. Assuming that the mathematical model of the controlled object contains zeros and poles, its general form is described as  
\[y=\frac{q(s)}{p(s)}u \tag{25}\]  
We set the virtual control quantity \(U(t)=q(s)u\); then, the system becomes \(y=U(t)/P(s)\), and the actual control quantity becomes \(u=U(t)/q(s)\). If the controlled object conforms to the minimum phase system, the \(q(s)\) belongs to a stable polynomial and is known. The SAD controller can be used to determine the virtual control quantity \(U(t)\), and the actual control quantity \(u(t)\) can be obtained by solving the system \(u=U(t)/q(s)\), with \(U(t)\) as the input. Through the above analysis, the zero-pole diagram of the controlled object was derived using Matlab, as shown in Figure 9.  
As can be seen in Figure 9, the system model had no zeros and poles in the positive part of the complex plane and was considered as a minimum phase system. In this case, the virtual control variable \(U(t)\) was determined by the active disturbance rejection controller, and \(U(t)\) was used as the input to solve the system \(u=U(t)/q(s)\) to obtain the actual control variable. The transfer function of the control system is known to satisfy the cubic polynomial \(p_{3}(s)=s_{3}+a_{3}s_{2}+a_{2}s+a_{1}\). The parameters \(a_{1}\), \(a_{2}\), and \(a_{3}\) are known, and the STF algorithm of the third-order TD differentiator is written as  
\[\left\{