A PAM-driven double-joint CM angular position tracking control system and algorithm

Abstract

This invention discloses a PAM-driven dual-section CM angular position tracking control system and algorithm, belonging to the technical field of CM angular position control systems. It addresses the problems of model uncertainty and computational burden, as well as unpredictable residual sets, inherent in multi-input multi-output and nonlinear CM angular position control systems, caused by neural networks, fuzzy logic systems, adaptive techniques, and iterative learning. A simple state feedback controller is designed. This controller integrates the adjustment function with error transformation technology, eliminating the need for adaptive mechanisms, neural networks, fuzzy logic systems, and iterative learning algorithms. It also avoids limitations on the initial value of the tracking error, ensuring not only pre-set transient and steady-state tracking performance but also continuous control signal without abrupt increases. The controller designed in this invention can effectively realize PAM-driven dual-section CM angular position tracking control.

Description

Technical Field

[0001] This invention belongs to the technical field of CM angular position control systems, specifically relating to a PAM-driven dual-section CM angular position tracking control system and algorithm. Background Technology

[0002] The compliance of the CM itself and the strong nonlinearity of its actuation mechanism present significant challenges to modeling. Unlike traditional RMs, although CMs do not have defined link and joint variables, their end-effector pose can be altered by changing the deformation of various parts of the CM. Therefore, tracking and controlling the angular position of the CM is of great importance in the practical application of CMs.

[0003] The CC approximation method is widely used in establishing kinematic models of CM systems, which can approximately express the posture of each segment of the robotic arm in three-dimensional space. Furthermore, by connecting the various CC interfaces, the spatial posture of multiple CM segments can be expressed, thus obtaining the PCC model. For the angular position control problem of multi-segment CMs, due to the complexity of the CM system, establishing an accurate mathematical model is almost impossible; therefore, it can be regarded as a multi-input multi-output nonlinear system with model uncertainty. Therefore, robust controllers are widely used. Control strategies are developed by utilizing the powerful approximation capabilities of neural networks and fuzzy logic systems for unknown nonlinear functions (dependent on system state); adaptive mechanisms are introduced into the controller to observe unknown constant parameters in the system; and iterative learning algorithms are used to identify unknown time-varying parameters of the system. However, in the above control algorithms, the large number of parameters learned online increases the computational load and is not easy to use in engineering. At the same time, the above algorithms guarantee that the error signal converges to a certain residual set, although this set can be adjusted, it cannot be predicted. Summary of the Invention

[0004] In order to solve the problems of model uncertainty and algorithm computation burden and unpredictable residual set caused by neural networks, fuzzy logic systems, adaptive technology and iterative learning in multi-input multi-output and nonlinear CM angular position control systems, this invention provides a PAM-driven dual-section CM angular position tracking control system and algorithm.

[0005] The technical solution adopted in this invention is:

[0006] A PAM-driven dual-segment CM angular position tracking control system, characterized in that: it includes a first-segment robotic arm trajectory generator. Section 2 Robotic Arm Trajectory Generator and a dual-section CM angular position tracking control closed-loop system;

[0007] The dual-section CM angular position tracking control closed-loop system includes a first-section robotic arm feedback controller. Section 2 Robotic Arm Feedback Controller Section 1 Robotic Arm Model and Section 2 Robotic Arm Model ,

[0008] The structure of the robotic arm angular position tracking control system in the first section is as follows: the trajectory generator Generate the desired motion trajectory of the first robotic arm The closed-loop system of the first robotic arm is based on the actual motion trajectory of the first robotic arm. Subtracting the expected motion trajectory of the first robotic arm, we obtain the position error of the first robotic arm. The position error After feedback controller Get control signal The control signal Model applied to the first robotic arm The actual motion trajectory of the first robotic arm is obtained. ;

[0009] The structure of the robotic arm angular position tracking control system in Section 2 is similar to that in Section 1.

[0010] Section 1 Robotic Arm Feedback Controller Second section robotic arm feedback controller The feedback controller includes a performance function, a regulation function, an error transformation method, and a final control law.

[0011] A PAM-driven dual-joint CM angular position tracking control algorithm includes the following steps:

[0012] S1. The dynamic equations of the CM system are derived using the Euler-Lagrange form based on the assumption of a single lumped mass.

[0013] S2. Based on the system described in S1, select the system output as the control target. Tracking a given reference signal That is, the system outputs an angular position that tracks a given reference angular position trajectory;

[0014] S3. Apply pre-constraints to the upper bounds of the transient and steady-state performance of the system output;

[0015] S4. Design a feedback controller based on the conditions in S3.

[0016] Compared with the prior art, the present invention has the following advantages:

[0017] This invention achieves precise output tracking by introducing an error transformation strategy to adjust the tracking error. Utilizing the designed adjustment function and design process, the limitation of needing to reselect controller parameters when the system restarts under new initial conditions is eliminated. Furthermore, the designed feedback controller does not employ adaptive mechanisms, neural networks, fuzzy logic systems, or disturbance observers to identify unknowns, avoiding the need for real-time updates of numerous online learning parameters. In addition, the designed feedback controller does not require calculating or introducing filters to observe the derivative of the virtual control signal; therefore, the designed feedback controller has a simple structure. Attached Figure Description

[0018] Figure 1 This is a schematic diagram of the control system of the present invention;

[0019] Figure 2 This is a diagram showing the angular position tracking of the first section of the robotic arm using the present controller and the MFAC controller in this invention (the present controller is on the left, and the model-free adaptive controller is on the right).

[0020] Figure 3 This is a diagram showing the angular position tracking of the second section of the robotic arm using the presented controller and the MFAC controller in this invention (the presented controller is on the left, and the model-free adaptive controller is on the right).

[0021] Figure 4 This is a tracking error diagram of the first section of the robotic arm using the presented controller and the model-free adaptive controller in this invention (the presented controller is on the left, and the model-free adaptive controller is on the right).

[0022] Figure 5 This is a tracking error diagram of the first section of the robotic arm using the presented controller and the model-free adaptive controller in this invention (the presented controller is on the left, and the model-free adaptive controller is on the right). Detailed Implementation

[0023] To better understand the purpose, structure, and function of this invention, the invention will be described in further detail below with reference to the accompanying drawings.

[0024] This invention addresses the angular position tracking control problem of a PAM-driven two-section CM from the perspective of multi-input multi-output nonlinear systems, under conditions of unknown virtual control coefficient matrix, unknown nonlinearity, and unknown mismatched disturbances. It designs a simple state feedback controller. This feedback controller integrates the adjustment function with error transformation technology, eliminating the need for adaptive mechanisms, neural networks, fuzzy logic systems, or iterative learning algorithms. It also avoids limitations on the initial value of the tracking error, ensuring not only the pre-set transient and steady-state tracking performance but also continuous control signal without abrupt increases. The controller designed in this invention can effectively achieve angular position tracking control of a PAM-driven two-section CM.

[0025] A PAM-driven dual-segment CM angular position tracking control system, including a first-segment robotic arm trajectory generator. Section 2 Robotic Arm Trajectory Generator and a dual-section CM angular position tracking control closed-loop system;

[0026] The dual-section CM angular position tracking control closed-loop system includes a first-section robotic arm feedback controller. Section 2 Robotic Arm Feedback Controller Section 1 Robotic Arm Model and the second section robotic arm model ,

[0027] The structure of the robotic arm angular position tracking control system in the first section is as follows: the trajectory generator Generate the desired motion trajectory of the first robotic arm The closed-loop system of the first robotic arm is based on the actual motion trajectory of the first robotic arm. Subtract the expected motion trajectory of the first robotic arm The position error of the first robotic arm was obtained. The position error After feedback controller Get control signal The control signal Model applied to the first robotic arm The actual motion trajectory of the first robotic arm is obtained. ;

[0028] The structure of the robotic arm angular position tracking control system in Section 2 is similar to that in Section 1.

[0029] Section 1 Robotic Arm Feedback Controller Second section robotic arm feedback controller This includes the designed performance function, adjustment function, error transformation method, and final control law.

[0030] A PAM-driven dual-joint CM angular position tracking control algorithm includes the following steps:

[0031] S1. The dynamic equations of the CM system, derived by scholars at the University of Stuttgart, Germany, based on the assumption of a single lumped mass and using the Euler-Lagrange form, are as follows:

[0032]

[0033] in, These represent the angular position, angular velocity, and angular acceleration vectors of CM, respectively. The inertia matrix representing CM; Represents the centripetal Coriolis matrix of CM; This represents the homogeneous matrix of CM, which includes stiffness and damping characteristics as well as the effects of friction and gravity. Represents the generalized interference vector of the CM; This represents the input torque vector of CM; This indicates the number of discrete units in the CM.

[0034] S2. Based on the system described in S1, select the system output as the control target. Tracking a given reference signal That is, the system outputs an angular position that tracks a given reference angular position trajectory.

[0035] Tracking error Described as:

[0036]

[0037] in, and for:

[0038]

[0039]

[0040] S3. Apply pre-constraints to the upper bounds of the transient and steady-state performance of the system output, and give the performance function in the following form:

[0041]

[0042] in, It is a constant. It is a constant. and satisfy . as well as It is a positive constant arbitrarily chosen by the designer.

[0043] Taking this method as an example, the specific steps are as follows:

[0044]

[0045] in, , , To achieve the expected transient and steady-state tracking performance of the system, a simple state feedback controller needs to be designed to ensure that, under any initial conditions, the system output satisfies:

[0046]

[0047]

[0048] S4. Design a feedback controller based on the conditions in S3:

[0049] S41. Design the adjustment function:

[0050]

[0051] in, Indicates design parameters.

[0052] S42. Modify and convert the diagonal position tracking error:

[0053]

[0054] In the formula, This is the modified angular position tracking error.

[0055]

[0056] In the formula, This represents the angular position tracking error after transformation.

[0057] Taking this method as an example, the specific steps are as follows:

[0058]

[0059] In the formula, and This is the modified angular position tracking error.

[0060]

[0061] In the formula, This represents the angular position tracking error after conversion.

[0062] S43. Design of virtual control law:

[0063]

[0064] in, Represents the controller parameters, and satisfies .

[0065] Taking this method as an example, the specific steps are as follows:

[0066]

[0067] in, .

[0068] S44. Modify the angular velocity using the virtual control law designed in S43:

[0069] .

[0070] Taking this method as an example, the specific steps are as follows:

[0071]

[0072] S45. Set the following performance limits:

[0073]

[0074] in, It is a constant. It is a constant. and satisfy . as well as It is a positive constant arbitrarily chosen by the designer.

[0075] Taking this method as an example, the specific steps are as follows:

[0076]

[0077] in, , , .

[0078] S46. Design the final control law, in the form of:

[0079]

[0080] in, Represents the controller parameters, and satisfies ,

[0081]

[0082]

[0083] Elements in the formula and The form is as follows:

[0084]

[0085] .

[0086] Taking this method as an example, the specific steps are as follows:

[0087]

[0088] in, .

[0089]

[0090]

[0091] Elements in the formula , and , The form is as follows:

[0092]

[0093] .

[0094] S47. Conduct a comparative experiment using an existing model-free adaptive controller (MFAC), which is required to operate under identical conditions. The controller parameters are set as follows: , , , , , , , .

[0095] Figures 2-5 To compare the experimental results, the left side shows the results obtained using the presented controller, and the right side shows the results obtained using MFAC.

[0096] Depend on Figure 2 , Figure 3 The comparison shows that the two controllers perform the same in the initial stage, both reaching the specified reference output very quickly from the initial angular position.

[0097] Depend on Figure 4 and Figure 5It can be seen that the designed controller can meet the requirements for tracking the end-effector angular position of the first and second robotic arms, that is, the output tracking error converges to the specified limit within 3 seconds, and the designed controller still ensures that the output tracking error remains within the specified limit as the controller continues to run. In contrast, the existing MFAC cannot pre-specify the output tracking error, and the steady-state error obtained using MFAC is relatively large.

[0098] Table 1 shows the RMSTE of the two controllers under steady-state conditions. The data in Table 1 clearly demonstrates that the designed controller achieves a smaller steady-state error compared to the steady-state error obtained by the MFAC.

[0099] Table 1. Comparison of RMSTE for the two controllers

[0100]

[0101] It will be apparent to those skilled in the art that the present invention is not limited to the details of the exemplary embodiments described above, and that the invention can be implemented in other forms without departing from its spirit or essential characteristics. Therefore, the embodiments should be considered illustrative and non-limiting in all respects, and the scope of the invention is defined by the appended claims rather than the foregoing description. Thus, all variations falling within the meaning and scope of the equivalents of the claims are intended to be included within the present invention. No reference numerals in the claims should be construed as limiting the scope of the claims.

Claims

1. A PAM-driven dual-joint CM angular position tracking control algorithm, wherein the control algorithm is implemented based on a PAM-driven dual-joint CM angular position tracking control system, characterized in that: The control system includes a first-section robotic arm trajectory generator. Section 2 Robotic Arm Trajectory Generator and a dual-section CM angular position tracking control closed-loop system; The dual-section CM angular position tracking control closed-loop system includes a first-section robotic arm feedback controller. Section 2 Robotic Arm Feedback Controller Section 1 Robotic Arm Model and the second section robotic arm model , The structure of the robotic arm angular position tracking control system in the first section is as follows: the trajectory generator Generate the desired motion trajectory of the first robotic arm The closed-loop system of the first robotic arm is based on the actual motion trajectory of the first robotic arm. Subtract the expected motion trajectory of the first robotic arm The position error of the first robotic arm was obtained. The position error After feedback controller Get control signal The control signal Model applied to the first robotic arm The actual motion trajectory of the first robotic arm is obtained. ; The structure of the robotic arm angular position tracking control system in Section 2 is the same as that in Section 1. Section 1 Robotic Arm Feedback Controller Second section robotic arm feedback controller The feedback controller includes a performance function, a regulation function, an error transformation method, and a final control law; The control algorithm includes the following steps: S1. The dynamic equations of the CM system are derived using the Euler-Lagrange form based on the assumption of a single lumped mass. S2. Based on the system described in S1, select the system output as the control target. Tracking a given reference signal That is, the system outputs an angular position that tracks a given reference angular position trajectory; S3. Apply pre-constraints to the upper bounds of the transient and steady-state performance of the system output; In S3, the upper bounds of the transient and steady-state performance of the system output are pre-constrained through the following performance function: in, It is a constant. It is a constant. and satisfy , as well as It is a positive constant arbitrarily chosen by the designer. S4. Design a feedback controller based on the conditions in S3, which is achieved through the following steps: S41. Design the adjustment function; S42. Modify and convert the diagonal position tracking error; S43. Design a virtual control law; S44. Modify the angular velocity using the virtual control law designed in S43; S45. Set performance limits; S46. Design the final control law; S47. Conduct comparative experiments using an existing model-free adaptive controller, which is required to operate under the same conditions.

2. The PAM-driven dual-section CM angular position tracking control algorithm according to claim 1, characterized in that: The adjustment function designed in S41: in, Indicates design parameters.

3. The PAM-driven dual-section CM angular position tracking control algorithm according to claim 2, characterized in that: The diagonal position tracking error in S42 is modified and converted: In the formula, This is the modified angular position tracking error. In the formula, This represents the angular position tracking error after transformation.

4. The PAM-driven dual-section CM angular position tracking control algorithm according to claim 3, characterized in that: The virtual control law designed in S43: in, Represents the controller parameters, and satisfies .

5. The PAM-driven dual-section CM angular position tracking control algorithm according to claim 4, characterized in that: In S44, the virtual control law designed in S43 modifies the angular velocity: 。 6. The PAM-driven dual-section CM angular position tracking control algorithm according to claim 5, characterized in that: The performance limits designed in S45 are as follows: in, It is a constant. It is a constant. and satisfy , as well as It is a positive constant arbitrarily chosen by the designer.

7. The PAM-driven dual-section CM angular position tracking control algorithm according to claim 5, characterized in that: The final control law designed in S46: in, Represents the controller parameters, and satisfies , Elements in the formula and The form is as follows: 。

Images