[0111] In order to facilitate the understanding of those skilled in the art, the present invention will be further described below in conjunction with the embodiments and the drawings, and the content mentioned in the embodiments does not limit the present invention.
[0112] Reference figure 1 As shown, the non-linear compensation method of a micro-volume remote-controlled hydrostatic actuator of the present invention is based on a micro-double-cylinder volume control system, which includes: a control cylinder and an actuator, both of which pass through a slender hose Connection; includes the following steps:
[0113] Step 1: Establish the system dynamics equation;
[0114] Such as figure 2 As shown, the control cylinder acts as a control element driven by the servo unit and is connected to the actuator cylinder through a slender hose, which is a dual-cylinder control strategy;
[0115] Assumptions: 1. Compared with the external load, the mass of the moving parts in the cylinder can be ignored; 2. In the short-time driving process, the leakage of the cylinder is not one of the main factors under the low oil pressure working pressure; 3. Because There is neither throttling loss nor static friction in the system, so the nature of hot oil does not need to be considered;
[0116] The system dynamics balance equation is:
[0117]
[0118]
[0119]
[0120] The friction equation of the actuator is:
[0121]
[0122] Where V h1 It is the increase in pressurized volume of the combination of oil compression and hose expansion between the two rodless chambers; V h2 Is the increase in pressurized volume combined with oil compression and hose expansion between two rod chambers; m is the load mass; f v Is the total friction including static friction and viscous friction in the cylinder; f s Is the maximum static friction force; μ visc Is the coefficient of viscous friction; X pi , X po Respectively the displacement of the control cylinder and the actuator; P 1 , P 2 They are the pressure in the rodless chamber of the control cylinder and the actuator cylinder; A P1 , A P2 They are the effective area of the rodless chamber and the rod chamber of the control cylinder; A A1 , A A2 Respectively the effective area of the rodless chamber and rod chamber of the actuator; F t Is the load loaded on the actuator;
[0123] Liquid volume C is defined as the ratio of flow rate to pressure change rate, and the following formula is given:
[0124]
[0125] Where q 2 , Q 1 They are the flow into and out of the hose.
[0126] Step 2: Convert the dynamic equation to the state space model to complete its mathematical model construction, as follows:
[0127] In order to describe the behavior of the system in the state space model, the equations combining formulas (1) to (4) give:
[0128]
[0129] The state variables of the system are given by:
[0130]
[0131] Then combine equations (5) to (7) to obtain the state space model of the system:
[0132]
[0133] In order to use the reverse push strategy, the system belongs to a strict feedback form; the new variables are determined by Definition, where α=A A2 /A A1; Therefore, the new Substituting formula (8) into the new system state space model is:
[0134]
[0135] In the formula, F is the sum of external force and friction; f(x) and g(x) are functions of x and C, and C varies with the state of the system.
[0136] Step 3: Finally, design the dual-loop controller layout based on DOB (disturbance observer) to identify external loads and RBF (radial basis function) neural network to identify the nonlinear characteristics of the hose, and use the Lyapunov function to determine the system's performance during the design process stability
[0137] 31) Reference image 3 , Design the algorithm of interference observer:
[0138] To quantify the uncertain force, x 2 The expanded state observer is designed as:
[0139]
[0140] Where d is x respectively 2 And F estimated value; χ is the stability correction term of the entire closed-loop system;
[0141] x 2 The estimation errors of and F are respectively defined by the following equations:
[0142]
[0143]
[0144] The law of adaptation is:
[0145]
[0146] Where k 11 , K 12 Is a normal number; χ b It is another correction factor to ensure the stability of the closed-loop system, and its further inference can be seen clearly next;
[0147] The Lyapunov function is defined as:
[0148]
[0149] The derivative of is:
[0150]
[0151] According to equations (13) to (17), V 1 The time derivative of:
[0152]
[0153] Completed the design of interference observer algorithm;
[0154] 32) Algorithm design of position tracking controller:
[0155] By using the following backstep control design method, the position tracking error is defined as:
[0156] e=x 1 -x d (17)
[0157] The sliding surface design is:
[0158]
[0159] Where c 1 Is a normal number; combine the time derivative of s with equations (9) and (17) to get:
[0160]
[0161] β is right The virtual controller is defined as:
[0162]
[0163] Where c 2 It is a normal number; the load pressure error is defined by the following formula:
[0164]
[0165] Combine equations (20) and (21) with (19), and rewrite the time derivative of s as:
[0166]
[0167] The updated Lyapunov function is:
[0168]
[0169] Where k 2 Is a normal number;
[0170] Then combine equations (16) and (20) to get V 2 The time derivative of:
[0171]
[0172] Two correction terms χ b , Χ:
[0173]
[0174] The χ in equation (24) b , Χ is substituted into (25), the new for:
[0175]
[0176] then, The time derivative of:
[0177]
[0178] Now, the Lyapunov function is:
[0179]
[0180] Combine equations (26) and (27) with (28), V 3 The time derivative of is:
[0181]
[0182] u control law becomes:
[0183]
[0184] According to the general function of neural network:
[0185]
[0186]
[0187] Among them, x is the vector of the network input layer, ||·|| represents the Euclidean norm, c j Is the center vector, b j Is the width, h=[h j ] T Describe the output of the RBF mapping function, W * And V * The actual output between the hidden layer and the output layer, and with Is the estimated output between the hidden layer and the output layer.
[0188] In formula (30), with Represented by the RBF neural network as:
[0189]
[0190] The estimation error is defined as:
[0191]
[0192]
[0193] Combining equations (31) with (34) and (35), and V 3 The time derivative of is transformed into:
[0194]
[0195] The final Lyapunov function is:
[0196]
[0197] among them,
[0198] The final adaptive law is:
[0199]
[0200] Combine (37) with (36) and (38), the time derivative of L is expressed as:
[0201]
[0202] Due to ε f And ε g (The approximate error of the RBF neural network) is small enough, so the robust system D≥|ε f +ε g u|, then Therefore, the RBF-DOB position tracking controller is designed according to the stability of the closed-loop system.
[0203] In summary, a micro-capacity remote-controlled hydrostatic actuator nonlinear compensation strategy can make the system get a stable output. In order to verify the displacement tracking performance of the RBF-DOB controller designed in the present invention, a traditional PID controller and an SMC controller are used to compare different situations. The parameters of PID controller and SMC controller are determined by many simulations and comparisons of different values. The PID controller parameters are selected from a large number of simulation results, and the standard is the minimum overshoot and the shortest adjustment time. The design of the SMC controller complies with legal regulations, and uses appropriate constant approach coefficient and exponential approach coefficient to ensure minimum displacement oscillation and fast response speed. Some parameters of the RBF-DOB system are shown in Table 1. The advantages of the present invention will be explained below in conjunction with the simulation results. Table 1 is as follows:
[0204] Table 1
[0205]
[0206] Combine Figure 4 with Figure 5 , Under a constant external force step signal, from 5mm to 20mm at 2s, and then back to 10mm at 4s, an external load of 500N is applied to the actuator. Figure 4 It can be seen that the system using PID control and SMC control exhibits longer delay time and larger error than RBF-DOB control under this signal. Figure 5 It shows that because the proportional term cannot be too large, the PID control in the system cannot make the output high enough, which slows down the modulation of the target displacement. The system with SMC and RBF-DOB control provides higher and faster control signals, and can quickly stabilize the actuator in the desired position. However, the SMC control causes significant signal jitter during the adjustment, while the system with RBF-BOD control has a faster and more stable control signal output.
[0207] Combine Image 6 with Figure 7 , Under constant external force sinusoidal signal, given signal displacement X d =0.005sinπt+0.02(m) and load force F t =500N. Image 6 It shows that the SMC control produces a displacement tracking error of up to 5mm under the rising signal. The system using PID control can achieve the same amplitude as the signal, but the delay is 0.2s. At the same time, RBF-DOB control has excellent system tracking performance. Figure 7 As shown, it is described that among the three controllers, only the RBF-DOB controller produces a speed output of up to 0.55m/s, which allows the actuator to quickly track the signal input. However, when the moving cylinder reaches the position specified by the signal, the SMC generates a severe jitter signal, so it is not suitable for engineering situations.
[0208] Combine Figure 8 with Picture 9 Under the constant displacement step signal, the step external force signal with a constant displacement command is applied to the actuator. In 2 seconds, the external force drops from 600N to 400N, and then reaches 500N in 4 seconds. Figure 8 Shows the comparison of different actuator displacements using the above three methods. The system adopting PID controller or SMC has steady-state error. Compared with the other two strategies, the RBF-DOB controller can improve the control accuracy. in Picture 9 Among them, the poor quality control signal of the SMC makes it difficult to achieve the control target. In comparison, the control signal from the RBF-DOB and PID controller will slightly change. In view of the above analysis, under the constant displacement step signal, the RBF-DOB controller strategy is more suitable for the robust control of the system.
[0209] Combine Picture 10 with Picture 11 , Under constant pressure sinusoidal signal, based on load F t =100sinπt+500(N) and 10mm displacement command. Picture 10 It shows that in the absence of a pressure feedback controller, the system using PID control will produce large displacement turbulence, and the preset maximum error for the external load is 0.3mm. Although the SMC contributes to strong robustness under variable external loads, large displacement errors occur during its initial response. Compared with the above two methods, RBF-DOB control has higher accuracy (error displacement is 0.004mm), and it also has stronger target displacement robustness during its initial response. The output signal of the controller is like Picture 11 As shown, PID control tends to produce a small output signal (the maximum value is 0.1 m/s), which results in a poor control effect. The control signal of SMC is often jittered to ensure robustness when the external load changes rapidly. The RBF-DOB control gives a large signal at the initial time of the displacement response to deal with sudden changes in the load, and generates a small and fast control signal for smoothing the load. Obviously, RBF-DOB control is more suitable for engineering practice.
[0210] The control method of Lyapunov theory used in the present invention can realize a stable system. Compared with the traditional PID and SMC control, the RBF-DOB control system has higher accuracy and better dynamic performance. In terms of anti-interference ability, the micro hydraulic drive system using RBF-DOB controller is better than the micro hydraulic drive system using PID controller. Although the robustness is better than the proposed method, SMC easily induces control signals with a large amount of jitter, and is not suitable for servo motor control in the system. In contrast, the RBF-DOB control with strong robustness and qualified output meets engineering needs. The control strategy proposed by the present invention significantly improves the influence caused by uncertain system parameters and different load states, and improves the displacement control accuracy of the miniature and high-pressure system connected by the hose.
[0211] There are many specific applications of the present invention. The above are only the preferred embodiments of the present invention. It should be pointed out that for those of ordinary skill in the art, several improvements can be made without departing from the principle of the present invention. Improvements should also be regarded as the protection scope of the present invention.
