A fuzzy PID control method for suppressing the rebound of a rope-tethered system

Abstract

This invention discloses a fuzzy PID control method for suppressing the rebound of a tethered towed system, belonging to the field of spacecraft dynamics and control. The implementation method involves: constructing a simplified model of the tethered towed system; introducing fuzzy control into the PID control; and calculating the control force to be applied to the tether by observing the error and rate of change between the distance between the tether and the space debris and the desired distance. This control force is then applied to the tether to actively control the tethered towed system, bringing the distance between the tether and the space debris closer to the desired state, thus suppressing the rebound of the tethered towed system. This invention can calculate the control force to be applied to the tether simply by observing the error and rate of change between the distance between the tether and the space debris and the desired distance, offering advantages such as simple control method, low computational load, high operability, and strong robustness. This invention can suppress the rebound of the tethered towed system, ensuring its safe and stable operation.

Description

Technical Field

[0001] This invention relates to an active control method for tethered dragging, and to a fuzzy PID control method for suppressing the rebound of a tethered dragging system. It is applicable to the process of dragging and removing space debris from its orbit and belongs to the field of spacecraft dynamics and control. Background Technology

[0002] According to data from the European Space Agency, since the launch of Sputnik 1, the first artificial Earth satellite, on October 4, 1957, as of early 2023, humanity has conducted approximately 6,370 spacecraft launches (including launch failures), sending about 15,070 spacecraft into orbit. Currently, only about 7,200 spacecraft are operational in orbit, with the majority becoming space debris. The sheer volume of space debris not only means the continuous occupation of limited orbital resources, but more dangerously, it also increases the risk of collisions between space debris and spacecraft. Even if no more launches are conducted in the future, the current level of space debris will continue to increase due to collisions. Therefore, passively clearing debris using methods such as atmospheric drag or limiting debris generation during future space activities is insufficient to maintain the stability of the space environment. Active space debris removal missions are now imperative.

[0003] Active space debris removal involves artificially removing space debris from its orbit. Generally, space debris in Low Earth Orbit (LEO) is lowered to re-enter the atmosphere and disintegrate. For debris in higher orbits, such as Geostationary Earth Orbit (GEO), it is directed into a designated graveyard orbit. Among various active removal technologies, tethered removal is considered one of the safest and most feasible due to its advantages such as lightweight, small footprint, large operating range, low cost, and high reliability. In a tethered removal system, a spacecraft acting as a tugboat tows space debris via a flexible tether, transferring them along with the debris to achieve the goal of space debris removal.

[0004] While tethered towing for space debris removal offers numerous advantages, the flexible nature of the tether also introduces a series of problems. For example, during the orbital transfer of space debris by tugboats, the tugboat's thrusters may repeatedly activate and deactivate. This can cause the space debris to tend to move towards the tugboat, a phenomenon known as springback. This springback can lead to collisions between the tugboat and the space debris, threatening the safety and normal operation of the system. Therefore, to ensure the safety and stability of the system during towing, active control measures are needed to suppress springback in tethered towing systems. Summary of the Invention

[0005] To address the potential rebound phenomenon in tethered towing systems during towing, this invention primarily aims to provide a fuzzy PID control method to suppress rebound in tethered towing systems. A simplified model of the tethered towing system is constructed, and fuzzy control is introduced into PID control. A control law is designed, which calculates the control force to be applied to the tugboat by observing the error and rate of change between the distance between the tugboat and the space debris and the desired distance. This control force is then applied to the tugboat to actively control the tethered towing system, bringing the distance between the tugboat and the space debris closer to the desired state, thereby suppressing the rebound phenomenon. This invention calculates the control force to be applied to the tugboat simply by observing the error and rate of change between the distance between the tugboat and the space debris and the desired distance, offering advantages such as simple control method, low computational load, high operability, and strong robustness. This invention effectively suppresses the rebound phenomenon in tethered towing systems, ensuring the safe and stable operation of the towing system.

[0006] The objective of this invention is achieved through the following technical solution:

[0007] This invention discloses a fuzzy PID control method for suppressing the rebound of a rope-driven towing system, comprising the following steps:

[0008] Step 1: Ignoring the oscillation of the tethered towing system, establish the relevant coordinate systems for the simplified model of the tethered towing system. The reference coordinate system is the coordinate system of the center of mass orbit of the tethered towing system. The tethered towing system includes a tugboat with active control capability, the towed space debris, and the tether connecting the two. The tugboat and space debris are considered as the center of mass, and the tether is considered as a massless, damped, tension-only, compression-free half-spring. The dynamic model of the tethered towing system is obtained using Newton's method.

[0009] To describe a simplified model of a rope-tethered system that ignores system oscillation, a coordinate system f is established based on the center of mass orbit of the rope-tethered system. c (O c x c ), origin O c Located at the system's centroid; x c The axis points in the direction of the space debris.

[0010] The tethered towing system comprises a tugboat with active control capability, a space debris being towed, and a tether connecting the two. The tugboat and space debris are considered as centers of mass, and the tether is considered as a massless, damped, tension-only semi-spring. Ignoring system oscillation, the simplified model of the tethered towing system is only affected by the tether tension and the tugboat thrust. Therefore, the positional changes of the tugboat and space debris relative to the origin of the tethered towing system's center of mass orbital coordinate system satisfy the following:

[0011]

[0012]

[0013] Where, m s and m d These are the masses of the tugboat and the space debris, respectively, r s and r d These are the distances F represents between the tugboat and the origin of the orbital coordinate system of the center of mass of the tethered towing system. s T is the magnitude of the thrust output by the tugboat's thruster, and T is the magnitude of the mooring rope tension.

[0014] Treating the distance between the tugboat and the space debris as the actual length of the mooring rope, let l = r s +r s The tension T of the tethered rope satisfies:

[0015]

[0016] Where, k t and c t These are the stiffness coefficient and damping coefficient of the tether, respectively; l0 is the original length of the tether; and δ is the step function, which is 0 when l < l0 and 1 when l ≥ l0. By combining equations (1) and (2) regarding the position changes of the tugboat and space debris relative to the origin of the center-of-mass orbital coordinate system of the tethered towing system, the dynamic model of the system is obtained:

[0017]

[0018] Step 2: Compare the actual rope length l with the desired rope length l d The difference is taken as error e, and the error e and the rate of change of error are compared. As input, a fuzzy PID controller is designed, and the output control force suppresses the rebound phenomenon of the rope-driven towing system. The fuzzy PID controller is designed based on classical PID control, controlling three PID control parameters, namely the proportional control parameter k. P Integral control parameter k I and differential control parameter k D Control is performed. The inputs to the classic PID control section are e and... The output control force suppresses the rebound phenomenon of the rope-driven towing system, and three control parameters are controlled by the fuzzy controller. The inputs of the fuzzy controller are e and The output consists of three PID control parameters k. P k I and k D The fuzzy controller design incorporates the input quantity e, described by real values, and... The fuzzy set is fuzzified into a corresponding fuzzy set described by language; a fuzzy rule base is established, and the required output fuzzy set is obtained by combining the fuzzy inference engine using the Mamdani inference algorithm; the output fuzzy set is then converted into real values ​​using a centroid defuzzifier; the obtained real values ​​correspond to the increments of the three control parameters respectively, so the three control parameters after control are obtained based on the obtained real values, thus obtaining the fuzzy PID controller.

[0019] Step 2.1: Compare the actual rope length l from Step 1 with the desired rope length l d The difference is taken as error e, and the error e and the rate of change of error are compared. As input, a fuzzy PID controller is designed, and the output control force suppresses the rebound phenomenon of the rope-driven drag system.

[0020] First, compare the actual rope length l with the expected rope length l d The difference is taken as error e, and the error e and the rate of change of error are compared. As input, a fuzzy PID controller is designed, and the output control force suppresses the rebound phenomenon of the rope-driven towing system. The error satisfies e = ll. d Since there is no relative motion between the tugboat and the space debris in the desired state, the velocities and accelerations of the tugboat and the space debris are equal in magnitude and in the same direction. According to the dynamic model in step one, the desired rope length satisfies the following equation (5):

[0021]

[0022] The error e and the rate of change of the error As input, a fuzzy PID controller is designed, and the output control force suppresses the rebound phenomenon of the rope-driven towing system. The control force satisfies the following:

[0023]

[0024] Among them, F c For control force, and satisfying F c =F s -F e , where F e This refers to the thrust output by the tugboat during maneuvering. k represents the three control parameters in the classic PID control section. P k I and k D Then, the fuzzy controller part was designed.

[0025] Step 2.2: The fuzzy PID controller is designed based on the classical PID control described in Step 2.1, with the fuzzy controller controlling the three PID control parameters, namely the proportional control parameter k. P Integral control parameter k I and differential control parameter kD Control is performed. The inputs to the classic PID control section are e and... The output control force suppresses the rebound phenomenon of the rope-driven towing system, and three control parameters are controlled by the fuzzy controller. The inputs of the fuzzy controller are e and The output consists of three PID control parameters k. P k I and k D The fuzzy controller design incorporates the input quantity e, described by real values, and... It is then fuzzified into a corresponding fuzzy set of linguistic descriptions.

[0026] The range of variation is essentially a set U consisting of all continuous or discrete objects {u}, called the universe of discourse, where u is an element of U. Without loss of generality, assume that e and... The ranges of variation are [-u e ,u e ] and [-u ce ,u ce ], then their corresponding domains are U e =[-u e ,u e ] and U ce =[-u ce ,u ce Using seven languages—Negative Large (NB), Negative Medium (NM), Negative Small (NS), Zero (ZO), Positive Small (PS), Positive Medium (PM), and Positive Large (PB)—to describe each domain, we obtain the corresponding fuzzy set A. For *∈{e,ce}, we have the fuzzy set A. * ={(u * ,μ A* (u * ))|u * ∈U *} is an ordered pair, where μ A* (u * ) is called a fuzzy set A * The membership function, to represent u * In A * The degree of membership is defined, with values ​​ranging from [0,1]. The design yields the input e and... The corresponding fuzzy set A e and A ce This achieves the fuzzification of input quantities.

[0027] Step 2.3: Establish the relationship between the input and output quantities, both described by the language used in Step 2.1, which is called the fuzzy rule base. To improve the performance of the PID controller, the control parameter k of the PID controller needs to be adjusted. P k I and kD Since fuzzy control is performed separately for each of the three parameters, it is necessary to design fuzzy rules for each parameter based on their individual characteristics and impact on the performance of the PID controller, forming a fuzzy rule base for matching. The fuzzy set A from step 2.1 is then used... e and A ce As input, a fuzzy rule base is used in conjunction with a fuzzy inference engine employing the Mamdani inference algorithm to obtain the desired output fuzzy set.

[0028] (1)k P Fuzzy rule design

[0029] In a PID controller, k P Determines the system's response speed. Increasing k P The value of k can improve the system's response speed and reduce steady-state deviation, but P An excessively large value of k can also cause system overshoot or even instability. Therefore, when e is large, k P The value of k should be large to improve the response speed, while after e decreases... P The value of k should be gradually decreased to avoid excessive overshoot while ensuring response speed; and when the system gradually stabilizes after further decreasing e, k should be increased again. P The value is used to improve control precision. Therefore, k is defined. P The fuzzy rules are shown in Table 1:

[0030] Table 1 k P Fuzzy rules

[0031]

[0032] k can be obtained by referring to Table 1. P The fuzzy rules in the table are as follows: the first column describes the universe of discourse for deviation *e*, the first row describes the universe of discourse for the rate of change of deviation *ec*, and the remaining parts are the outputs under the various rules. Taking the output in the second column of the third row as an example, the corresponding rule is: "if *e* is NM and *ec* is NB, then *U* is PB." That is, if deviation *e* is NM and the rate of change of deviation *ec* is NB, then the output is PB. Therefore, according to the rule interpretation method described above, there are 49 similar rules in Table 1.

[0033] (2)k I Fuzzy rule design

[0034] In a PID controller, k I It affects the system's steady-state deviation. Increasing k I This can reduce the system's steady-state deviation, but it can also cause integral saturation, thereby increasing the system overshoot. Therefore, in the initial stage of the control process, k IThe value should be small or even zero to avoid saturation of the integral. Then, as e gradually decreases, k can be gradually increased. I Value. Therefore, define k. I The fuzzy rules are shown in Table 2:

[0035] Table 2 k I Fuzzy rules

[0036]

[0037] (3)k D Fuzzy rule design

[0038] In a PID controller, k D The value of k affects the dynamic characteristics of the system. D When the value is too large, it indicates premature adjustment, which will increase the system's settling time; k D When the value is too small, it indicates lag adjustment, which will increase the system overshoot. Based on experience, when e is large, k... D A larger value for k results in a smaller system overshoot; subsequently, due to the system's regulation characteristics affecting k... D The value is sensitive to changes, therefore, k D The value should be appropriately reduced and should remain unchanged; when e is small, k should be decreased. D Value, to compensate k D The increased settling time when the value is large. Therefore, k is defined. D The fuzzy rules are shown in Table 3:

[0039] Table 3 k D Fuzzy rules

[0040]

[0041] By combining the designed fuzzy rule base with a fuzzy inference engine using the Mamdani inference algorithm, the desired output fuzzy set can be obtained.

[0042] Step 2.4: Use the centroid defuzzifier to convert the output fuzzy set from Step 2 into real values. The obtained real values ​​correspond to the increments of the three control parameters. Therefore, based on the obtained real value increments and the initial values ​​of the parameters, the three control parameters after control are obtained.

[0043] The output fuzzy set is then transformed into a sharp quantity using a centroid defuzzifier. Since the output fuzzy set is also described using seven terms: negative large (NB), negative medium (NM), negative small (NS), zero (ZO), positive small (PS), positive medium (PM), and positive large (PB), the membership degree during defuzzification is given using the aforementioned fuzzification method. The obtained sharp quantity corresponds to the increment of three control parameters; therefore, the parameters actually output to the PID controller are expressed as follows:

[0044] k * =k *0 +λ×Δk * (7)

[0045] Where *∈{P,I,D}, k *0 The control parameters before modification, Δk * λ represents the increment of the control parameters given by the fuzzy controller, where λ is the amplification factor.

[0046] Step 3: Observe the error and rate of change between the distance between the tugboat and the space debris and the desired distance. Using the fuzzy PID controller designed in Step 2, calculate the control force that should be applied to the tugboat. Apply the control force to the tugboat to actively control the rope towing system, so that the distance between the tugboat and the space debris approaches the desired state, thereby suppressing the rebound phenomenon of the rope towing system.

[0047] Beneficial effects:

[0048] 1. This invention discloses a fuzzy PID control method for suppressing the rebound of a tethered towed system. For a simplified model of the tethered towed system, fuzzy control is introduced into PID control. A control law is designed, which calculates the control force to be applied to the tether by observing the error and rate of change between the distance between the tether and the space debris and the desired distance. The control force is then applied to the tether to actively control the system, making the distance between the tether and the space debris approach the desired state, thereby suppressing the rebound of the tethered towed system.

[0049] 2. The present invention discloses a fuzzy PID control method for suppressing the rebound of a rope-driven towing system. Fuzzy control theory is introduced into PID control to adjust the PID control parameters. Compared with the classic PID control method, it has the advantages of simple control method, low computational load, high operability and strong robustness.

[0050] 3. The present invention discloses a fuzzy PID control method for suppressing the rebound of a tethered towing system. Combining fuzzy theory and PID control, the input is simple. The control force that should be applied to the tugboat can be calculated by observing the error and rate of change between the distance between the tugboat and the space debris and the desired distance. Attached Figure Description

[0051] Figure 1 A flowchart of a fuzzy PID control method for suppressing the rebound of a rope-driven towing system;

[0052] Figure 2 To input the membership function, Figure 2 a) is the membership function of the error e. Figure 2 b) is the rate of change of error. Membership function;

[0053] Figure 3 To input the membership function, Figure 3 a) is k P The membership function corresponding to the output quantity Figure 3 b) is k I The membership function corresponding to the output quantity Figure 3 c) is k D Membership function corresponding to the output quantity;

[0054] Figure 4 A comparison of the distance changes between the tugboat and space debris under fuzzy PID control, classical PID control, and no control action designed using the method described above;

[0055] Figure 5 A comparison of the output control force of the controller designed using the method, the classic PID control, and the controller without control action. Detailed Implementation

[0056] To better illustrate the purpose and advantages of this invention, the following description, in conjunction with the accompanying drawings and simulation examples, further explains the content of this invention.

[0057] Example 1:

[0058] The main parameters of a fuzzy PID control method for suppressing the rebound of a rope-tethered system are shown in Table 4.

[0059] Table 4. Main parameters of the rope-tethered towing system

[0060]

[0061] To verify the feasibility and beneficial effects of the fuzzy PID control method for suppressing rebound in a rope-driven towing system disclosed in this invention, the technical solution of this invention is clearly and thoroughly described below in a case study, as shown in the flowchart below. Figure 1 As shown.

[0062] like Figure 1 As shown in the figure, this example discloses a fuzzy PID control method for suppressing the rebound of a rope-tethered system. The specific implementation steps are as follows:

[0063] Step 1: Ignoring system oscillation, establish the relevant coordinate systems for the simplified model of the tethered towing system. The reference coordinate system is the coordinate system of the center of mass orbit of the tethered towing system. The tethered towing system includes a tugboat with active control capability, the towed space debris, and the tether connecting the two. The tugboat and space debris are considered as the center of mass, and the tether is considered as a massless, damped, tension-only, compression-free half-spring. The dynamic model of the tethered towing system is obtained using Newton's method.

[0064] Step 2: Compare the actual rope length |l| from Step 1 with the desired rope length l d The difference is taken as error e, and the error e and the rate of change of error are compared. As input, a fuzzy PID controller is designed, and the output control force suppresses the rebound phenomenon of the rope-driven towing system. The fuzzy PID controller is designed based on classical PID control, controlling three PID control parameters, namely the proportional control parameter k. P Integral control parameter k I and differential control parameter k D Control is performed. The inputs to the classic PID control section are e and... The output control force suppresses the rebound phenomenon of the rope-driven towing system, and three control parameters are controlled by the fuzzy controller. The inputs of the fuzzy controller are e and The output consists of three PID control parameters k. P k I and k D The fuzzy controller design first involves converting the input quantity e, described by real values, into... The fuzzy set is first fuzzified into a corresponding fuzzy set described by language. Then, a fuzzy rule base is established, and a fuzzy inference engine using the Mamdani inference algorithm is used to obtain the required output fuzzy set. The centroid defuzzifier is then used to convert the output fuzzy set into real values. Finally, the obtained real values ​​correspond to the increments of the three control parameters, and thus the three control parameters after control are obtained based on the obtained real values. At this point, the design of the fuzzy PID controller is complete.

[0065] Step 2.1: Compare the actual rope length |l| from Step 1 with the desired rope length l d The difference is taken as error e, and the error e and the rate of change of error are compared. As input, a fuzzy PID controller is designed, and the output control force suppresses the rebound phenomenon of the rope-driven drag system.

[0066] First, compare the actual rope length |l| with the expected rope length l d The difference is taken as error e, and the error e and the rate of change of error are compared. As input, a fuzzy PID controller is designed, and the output control force suppresses the rebound phenomenon of the rope-driven towing system. The error satisfies e = |l| - l d Since there is no relative motion between the tugboat and the space debris in the desired state, the velocities and accelerations of the tugboat and the space debris are equal in magnitude and in the same direction. According to the dynamic relationship in step one, the desired rope length satisfies the following equation (5):

[0067]

[0068] The error e and the rate of change of the error As input, a fuzzy PID controller is designed, and the output control force suppresses the rebound phenomenon of the rope-driven towing system. The control force satisfies the following:

[0069]

[0070] Among them, F c For control force, and satisfying F c =F s -F e , where F e This refers to the thrust output for the tugboat's maneuvering. The three control parameters k are for controlling the PID control section. P k I and k D Then, the fuzzy controller part was designed.

[0071] Step 2.2: The fuzzy PID controller is designed based on the classical PID control described in Step 2.1, with the fuzzy controller controlling the three PID control parameters, namely the proportional control parameter k. P Integral control parameter k I and differential control parameter k D Control is performed. The inputs to the classic PID control section are e and... The output control force suppresses the rebound phenomenon of the rope-driven towing system, and three control parameters are controlled by the fuzzy controller. The inputs of the fuzzy controller are e and The output consists of three PID control parameters k. P k I and k D The fuzzy controller design first involves converting the input quantity e, described by real values, into... It is then fuzzified into a corresponding fuzzy set of linguistic descriptions.

[0072] Let's assume that e and The ranges of variation are [-12, 12] and [-0.12, 0.12], respectively. Therefore, the universe of discourse U e =[-12,12],U ce =[-0.12,0.12], and fuzzyen it using seven languages: negative large (NB), negative medium (NM), negative small (NS), zero (ZO), positive small (PS), positive medium (PM), and positive large (PB), to obtain the input e and The corresponding fuzzy set A e and A ce The membership degree of its fuzzy subset is as follows: Figure 2 As shown.

[0073] Step 2.3: Establish the relationship between the input and output quantities, both described by the language used in Step 2.1, which is called the fuzzy rule base. To improve the performance of the PID controller, the control parameter k of the PID controller needs to be adjusted. P k I and k D Since fuzzy control is performed separately for each of the three parameters, it is necessary to design fuzzy rules for each parameter based on their individual characteristics and impact on the performance of the PID controller, forming a fuzzy rule base for matching. The fuzzy set A from step 2.1 is then used... e and A ce As input, a fuzzy rule base is used in conjunction with a fuzzy inference engine employing the Mamdani inference algorithm to obtain the desired output fuzzy set.

[0074] (1)k P Fuzzy rule design

[0075] In a PID controller, k P This determines the system's response speed. Increasing k P The value of k can improve the system's response speed and reduce steady-state deviation, but P An excessively large value of k can also cause system overshoot or even instability. Therefore, when e is large, k P The value of k should be large to improve the response speed, while after e decreases... P The value of k should be gradually decreased to avoid excessive overshoot while ensuring response speed; and when the system gradually stabilizes after further decreasing e, k should be increased again. P The value is used to improve control accuracy. Therefore, based on the above parameter design concept, k is defined. P The fuzzy rules are shown in Table 5:

[0076] Table 5 k P Fuzzy rules

[0077]

[0078] (2)k I Fuzzy rule design

[0079] In a PID controller, k I It affects the system's steady-state deviation. Increasing k I This can reduce the system's steady-state deviation, but it can also cause integral saturation, thereby increasing the system overshoot. Therefore, in the initial stage of the control process, k I The value should be small or even zero to avoid saturation of the integral. Then, as e gradually decreases, k can be gradually increased. I Value. Therefore, define k. I The fuzzy rules are shown in Table 6:

[0080] Table 6 kI Fuzzy rules

[0081]

[0082]

[0083] (3)k D Fuzzy rule design

[0084] In a PID controller, k D The value of k affects the dynamic characteristics of the system. D When the value is too large, it indicates premature adjustment, which will increase the system's settling time; k D When the value is too small, it indicates lag adjustment, which will increase the system overshoot. Based on experience, when e is large, k... D A larger value for k results in a smaller system overshoot; subsequently, due to the system's regulation characteristics affecting k... D The value is sensitive to changes, therefore, k D The value should be appropriately reduced and should remain unchanged; when e is small, k should be decreased. D Value, to compensate k D The increased settling time when the value is large. Therefore, k is defined. D The fuzzy rules are shown in Table 7:

[0085] Table 7 k D Fuzzy rules

[0086]

[0087] By combining the designed fuzzy rule base with a fuzzy inference engine using the Mamdani inference algorithm, the desired output fuzzy set can be obtained.

[0088] Step 2.4: Use the centroid defuzzifier to convert the output fuzzy set from Step 2 into real values. The obtained real values ​​correspond to the increments of the three control parameters. Therefore, based on the obtained real value increments and the initial values ​​of the parameters, the three control parameters after control are obtained.

[0089] To obtain clear, usable quantities, a centroid defuzzifier is needed to transform the output fuzzy set into clear quantities. During defuzzification, the membership functions corresponding to the three control parameters are as follows: Figure 3 As shown. Finally, the obtained clear quantity can be represented as the increment of the three control parameters, therefore the actual parameters output to the PID controller can be expressed as:

[0090] k * =k *0 +λ×Δk * (10)

[0091] Where *∈{P,I,D}, k*0 The control parameters before modification, Δk * Let k be the increment of the control parameters given by the fuzzy controller, and λ be the amplification factor. P0 =100, k I0 =10,k D0 =10, λ=5.

[0092] Step 3: Observe the error and rate of change between the distance between the tugboat and the space debris and the desired distance. Using the fuzzy PID controller designed in Step 2, calculate the control force that should be applied to the tugboat. Apply the control force to the tugboat to actively control the rope towing system, so that the distance between the tugboat and the space debris approaches the desired state, thereby suppressing the rebound phenomenon of the rope towing system.

[0093] The results obtained based on the fuzzy PID control method for suppressing the rebound of a rope-tethered drag system disclosed in this embodiment are as follows: Figure 4 and Figure 5 As shown. In comparison, the fuzzy PID control method for suppressing the rebound of a rope-tethered system disclosed in this invention is compared with a method using three control parameters k... P =100, k I =10,k D A comparison is made between a PID control system with a value of 10 and an uncontrolled system. Figure 4 A comparison of the distance variation between the tugboat and space debris obtained by the method of this invention with PID control and an uncontrolled system shows that the distance variation range between the tugboat and space debris is smaller and the desired distance is reached faster in the method of this invention. In the uncontrolled state, the system becomes unstable. Under the other two control strategies, the distance variation range between the tugboat and space debris is [100.055, 99.925] m and [10.23, 99.68] m, respectively; the time to reach the desired distance is 75 s and 250 s, respectively. Under the same conditions, the method of this invention reduces the distance variation range between the tugboat and space debris by approximately 76.4% and the time to reach the desired distance by 70%. The results indicate that control is necessary to suppress the rebound phenomenon, and the method of this invention has better control performance than PID in terms of control overshoot capability and response speed. Figure 5 A comparison of the control force output by the tugboat using the method of the present invention with PID control and an uncontrolled system shows that the control force output by the tugboat in the method of the present invention has a smaller range of variation and reaches the desired distance faster. In the uncontrolled state, the system becomes unstable, while under the other two control strategies, the range of variation of the control force output by the tugboat is [20.19, -5.47]N and [22.34, -18.78]N, respectively. Under the same conditions, the method of the present invention reduces the range of variation of the control force output by the tugboat by approximately 37.6%. The results indicate that the method of the present invention has advantages over PID control in terms of the required range of control force variation.

[0094] The above detailed description is a further explanation of the purpose, technical solution and beneficial effects of the invention. It should be understood that the above description is only a specific implementation example of the present invention and is only used to explain the present invention. It is not intended to limit the scope of protection of the present invention. Any modifications, equivalent substitutions, improvements, etc. made within the spirit and principles of the present invention should be included within the scope of protection of the present invention.

Claims

1. A fuzzy PID control method for suppressing the rebound of a rope-driven towing system, characterized in that: Includes the following steps, Step 1: Ignore the swaying of the rope-tethered system and establish the relevant coordinate system involved in the simplified model of the rope-tethered system. The coordinate system is the center-of-mass orbit coordinate system of the rope-tethered system. The tethered towing system includes a tugboat with active control capability, a space debris being towed, and a tether connecting the two. The tugboat and the space debris are considered as centers of mass, and the tether is considered as a massless, damped, tension-only, compression-only half-spring. The dynamic model of the tethered towing system is obtained using Newton's method. The implementation method for step one is as follows: To describe a simplified model of a rope-tethered system that ignores system oscillation, a coordinate system for the center of mass of the rope-tethered system is established. ,origin Located at the system's centroid; The axis points in the direction of the space debris; The tethered towing system includes a tugboat with active control capability, a towed space debris, and a tether connecting the two. The tugboat and space debris are considered as centers of mass, and the tether is considered a massless, damped, tension-only semi-spring. Ignoring system oscillation, the simplified model of the tethered towing system is only affected by the tether tension and the tugboat thrust. Therefore, the positional changes of the tugboat and space debris relative to the origin of the tethered towing system's center of mass orbital coordinate system satisfy the following: in, and These are the masses of the tugboat and the space debris, respectively. and These are the distances of the tugboat and the space debris relative to the origin of the orbital coordinate system of the tethered towing system's center of mass. It refers to the magnitude of the thrust output by the tugboat's thruster. It refers to the tension of the rope. Treating the distance between the tugboat and the space debris as the actual length of the mooring rope, tether tension satisfy: in, and These are the stiffness coefficient and damping coefficient of the rope, respectively. It is the original length of the rope. It is a step function, in When it is 0, in Time is 1; the positional variation of the tugboat and space debris relative to the origin of the orbital coordinate system of the center of mass of the tethered towing system. and The dynamic model of the system is obtained as follows: Step 2: Calculate the actual rope length With expected rope length The difference is used as the error. , will the error and the rate of change of error As input, a fuzzy PID controller is designed, and the output control force suppresses the rebound phenomenon of the rope-driven towing system. The fuzzy PID controller is designed based on classical PID control, controlling three PID control parameters, namely proportional control parameters. Integral control parameters and differential control parameters To perform control; the input of the classic PID control section is and The output control force suppresses the rebound phenomenon of the rope-driven towing system, and three control parameters are controlled by the fuzzy controller; the input of the fuzzy controller is... and The output consists of three PID control parameters. , and The fuzzy controller design converts the input quantity described by real values ​​into a fuzzy controller. and The fuzzy set is fuzzified into a corresponding fuzzy set described by language; a fuzzy rule base is established, and the required output fuzzy set is obtained by combining the fuzzy inference engine using the Mamdani inference algorithm; the output fuzzy set is then converted into real values ​​using a centroid defuzzifier; the obtained real values ​​correspond to the increments of the three control parameters respectively, so the three control parameters after control are obtained based on the obtained real values, and the fuzzy PID controller is obtained. Step 3: Observe the error and rate of change between the distance between the tugboat and the space debris and the desired distance. Using the fuzzy PID controller designed in Step 2, calculate the control force that should be applied to the tugboat. Apply the control force to the tugboat to actively control the rope towing system, so that the distance between the tugboat and the space debris approaches the desired state, thereby suppressing the rebound phenomenon of the rope towing system.

2. The fuzzy PID control method for suppressing the rebound of a rope-driven towing system as described in claim 1, characterized in that: The second step is implemented as follows: Step 2.1: Calculate the actual rope length from Step 1. With expected rope length The difference is used as the error. , will the error and the rate of change of error As input, a fuzzy PID controller is designed, and the output control force suppresses the rebound phenomenon of the rope-driven drag system. First, the actual rope length With expected rope length The difference is used as the error. , will the error and the rate of change of error As input, a fuzzy PID controller is designed, and the output control force suppresses the rebound phenomenon of the rope-driven drag system; the error satisfies Since there is no relative motion between the tugboat and the space debris in the desired state, their velocities and accelerations are equal in magnitude and in the same direction. According to the dynamic model in step one, the desired rope length satisfies the following equation. : Error and the rate of change of error As input, a fuzzy PID controller is designed, and the output control force suppresses the rebound phenomenon of the rope-driven towing system. The control force satisfies the following: in, For control force, and satisfying ,in This refers to the magnitude of the thrust output by the tugboat's maneuvering; these are the three control parameters of the classic PID control section. , and Then, the fuzzy controller part was designed; Step 2.2: The fuzzy PID controller is designed based on the classical PID control described in Step 2.1, and controls the three PID control parameters, namely the proportional control parameters. Integral control parameters and differential control parameters To perform control; the input of the classic PID control section is and The output control force suppresses the rebound phenomenon of the rope-driven towing system, and three control parameters are controlled by the fuzzy controller; the input of the fuzzy controller is... and The output consists of three PID control parameters. , and The fuzzy controller design converts the input quantity described by real values ​​into a fuzzy controller. and It is fuzzified into a corresponding fuzzy set of linguistic descriptions; The range of variation is essentially determined by all continuous or discrete objects. The set This set is called the universe of discourse. for One element; without loss of generality, let, and The range of variation are respectively and Then their corresponding domains are respectively and The seven languages ​​NB (Negative Large), NM (Negative Medium), NS (Negative Small), ZO (Zero), PS (Positive Small), PM (Positive Medium), and PB (Positive Large) are used to describe each domain, resulting in the corresponding fuzzy sets. ;for There are fuzzy sets It is an ordered pair, in which Known as fuzzy set The membership function, to represent exist The degree of membership, with a range of values. The design yields the input. and Corresponding fuzzy set and To achieve fuzzification of input quantities; Step 2.3: Establish the relationship between the input and output quantities, both described by the language used in Step 2.1, called the fuzzy rule base; to improve the performance of the PID controller, it is necessary to adjust the control parameters of the PID controller. , and Fuzzy control is performed separately for each of the three parameters. Therefore, it is necessary to design fuzzy rules for each parameter based on their individual characteristics and impact on the performance of the PID controller, forming a fuzzy rule base to match them; and then combine the fuzzy set from step 2.

1. and As input, a fuzzy rule base is used in conjunction with a fuzzy inference engine that uses the Mamdani inference algorithm to obtain the desired output fuzzy set. (1) Fuzzy rule design In a PID controller, Determines the system's response speed; increases The value of can improve the system's response speed and reduce steady-state deviation, but Excessively large values ​​can also cause system overshoot or even instability; therefore, in When it is large, The value should be large to improve response speed, while... After reduction The value should be gradually decreased to avoid excessive overshoot while ensuring response speed; while... When the system gradually stabilizes after further reduction, it should be increased again. Value, to improve control precision; therefore, defined The fuzzy rules are shown in Table 1: Table 1 Fuzzy rules We can obtain this by referring to Table 1. The fuzzy rules, the first column of the table describes the deviation. The domain of discourse, the first line of which describes the rate of change of the deviation. The domain is defined by the given information, and the rest is the output as specified by each rule. For example, the output in the third row, second column corresponds to the following rule: "if..." is NM and is NB, then "is PB." means deviation. It is NM and the rate of change of deviation If it is NB, then output PB; therefore, according to the rule interpretation method, there are 49 similar rules in Table 1. (2) Fuzzy rule design In a PID controller, Affects the steady-state deviation of the system; increases This can reduce the system's steady-state deviation, but it will cause integral saturation, thereby increasing the system overshoot; therefore, in the initial stage of the control process, The value should be small or even set to zero to avoid saturation of the integral. Then, as... Gradually decrease, can gradually increase Value; therefore, definition The fuzzy rules are shown in Table 2: Table 2 Fuzzy rules (3) Fuzzy rule design In a PID controller, The value affects the dynamic characteristics of the system; When the value is too large, it indicates premature adjustment, which will increase the system's adjustment time. When the value is too small, it indicates lag adjustment, which will increase the system overshoot; based on experience, in When it is large, A larger value results in a smaller system overshoot; subsequently, due to the system's regulation characteristics... The value is sensitive to changes, therefore, The value should be appropriately reduced and should remain unchanged; When it is small, it should be reduced. Value, to compensate The increased settling time when the value is large; therefore, the definition is... The fuzzy rules are shown in Table 3: Table 3 Fuzzy rules By combining the designed fuzzy rule base with the fuzzy inference engine using the Mamdani inference algorithm, the desired output fuzzy set can be obtained. Step 2.4: Use the centroid defuzzifier to convert the output fuzzy set from Step 2 into real values. The obtained real values ​​correspond to the increments of the three control parameters. Therefore, based on the obtained real value increments and the initial values ​​of the parameters, the three control parameters after control are obtained. The output fuzzy set is then transformed into a sharp quantity using a centroid defuzzifier. Since the output fuzzy set is also described using seven terms: negative large (NB), negative medium (NM), negative small (NS), zero (ZO), positive small (PS), positive medium (PM), and positive large (PB), the membership degree during defuzzification is given using the aforementioned fuzzification method. The obtained sharp quantity corresponds to the increment of three control parameters; therefore, the parameters actually output to the PID controller are expressed as follows: in #imgpt154# represents the control parameters before modification, #imgpt155# represents the control parameter increment given by the fuzzy controller, and #imgpt156# represents the amplification coefficient, thus obtaining the fuzzy PID controller.

Images