Quantitative control method and device for preset time output feedback of double inverted pendulum system

Abstract

The invention discloses a quantitative control method and device for preset time output feedback of a double inverted pendulum system, and relates to the field of automation, and the method adopts a fuzzy logic system and a fuzzy state observer which are respectively used for processing unknown nonlinear dynamic characteristics of the system and estimating an unmeasurable state. In the design process of the controller, a second-order command filter and a backstepping technology are combined, a state quantization mechanism is introduced, and a novel self-adaptive quantization control method is provided. According to the method, the problem of discontinuity of virtual control signals can be effectively solved, and meanwhile control singularity is avoided. By introducing the preset time stability criterion, it is proved that the closed-loop system can achieve stable convergence within the preset time. A simulation result verifies the effectiveness of the control method, which indicates that the method can ensure that the output state of the double inverted pendulum system is converged to an expected precision range within a preset time, and the response speed and the control precision of the system are improved.

Description

Technical Field

[0001] The present invention relates to the field of automation, and more particularly to a preset time output feedback quantization control method and device for a double inverted pendulum system. Background Art

[0002] The double inverted pendulum system is a typical nonlinear, unstable dynamic system. Its control objective is to maintain the pendulum in an upright equilibrium state through external control forces. Double inverted pendulum systems are widely used in fields such as automatic control, robotic balance control, spacecraft attitude adjustment, and unmanned driving. In these applications, control methods for double inverted pendulum systems can improve the system's dynamic response speed, reduce control errors, and enhance the system's robustness, enabling stable operation in complex environments.

[0003] In recent years, with the rapid development of theories such as intelligent control, fuzzy logic systems, and adaptive control, control technology for double inverted pendulum systems has gradually developed towards high precision, strong real-time performance, and strong anti-interference capabilities. Among these, features such as preset time control, state quantization control, and observer-based intelligent control have made double inverted pendulum control methods a key development direction in the field of automatic control for applications requiring high precision and high dynamic response.

[0004] Currently, a variety of control algorithms and technologies have been used to control double inverted pendulum systems. Mainstream control methods include classic PID (Proportional-Integral-Derivative Controller) control, fuzzy control, sliding mode control, and adaptive control. However, existing technologies still have the following problems:

[0005] First, traditional control methods have poor robustness when dealing with complex nonlinear systems, external disturbances, and unmodeled dynamics, making it difficult to ensure that the system achieves stable convergence within a finite time. Existing control methods (such as classic PID control and sliding mode control) usually rely on accurate mathematical models of the system. However, in actual applications, due to the uncertainty of system parameters, the complexity of nonlinear dynamics, and interference from the external environment, the control performance of these methods may drop significantly, and may even cause the system to oscillate or become unstable. In addition, in scenarios requiring fast response and high-precision control, existing methods find it difficult to ensure that all system states converge to the desired range within a finite time, thus limiting their application in high-dynamic control tasks.

[0006] Second, existing control methods often rely on high-precision state measurements and frequent data transmission, which increases the communication burden and may cause network congestion, which in turn affects control accuracy and real-time performance. Furthermore, in multivariable coupled systems, it may also cause control singularities. Many traditional control algorithms require continuous and accurate state feedback. However, in practical applications, limited by sensor accuracy, data transmission bandwidth, and computing resources, this high-frequency data acquisition and transmission can cause network delays and even data loss, seriously affecting the system's control performance. Furthermore, in strongly coupled multivariable systems, some control methods may encounter singularities during the solution process. This means that under certain conditions, the control law becomes infeasible or approaches infinity, resulting in system failure or a severe degradation of control performance. These problems severely limit the applicability of traditional control methods in complex environments. Summary of the Invention

[0007] In order to solve the above problems, embodiments of the present invention provide a method and device for quantitative control of a double inverted pendulum system with preset time output feedback.

[0008] An embodiment of the present invention provides a method for quantitative control of a double inverted pendulum system with preset time output feedback, which includes the following steps in each control cycle:

[0009] According to the actual value of the first state variable of the subsystem included in the double inverted pendulum system, the estimated value of the second state variable of the subsystem, the expected output value of the subsystem and the dynamic equation of the second-order low-pass filter, an error in the actual value of the first state variable of the subsystem and an error in the estimated value of the second state variable of the subsystem are obtained respectively;

[0010] Determining a preset time quantized controller for the subsystem based on a preset time quantized controller equation according to an error in an actual value of a quantized first state variable of the subsystem, an error in an estimated value of a quantized second state variable of the subsystem, and a rate of change of a quantized filtered signal;

[0011] Based on the error in the actual value of the first state variable of the quantized subsystem, the error in the estimated value of the second state variable of the quantized subsystem, the estimated vector of the first unknown parameter vector related to the state variable of the subsystem, the estimated vector of the second unknown parameter vector related to the subsystem, and the fuzzy basis function of the state variable, the adaptive law of the state variable of the subsystem is obtained and the estimated value of the state variable of the subsystem is updated.

[0012] An embodiment of the present invention provides a double inverted pendulum system preset time output feedback quantization control device, which includes in each control cycle:

[0013] an obtaining unit, configured to obtain an error in the actual value of the first state variable of the subsystem and an error in the estimated value of the second state variable of the subsystem according to the actual value of the first state variable of the subsystem included in the double inverted pendulum system, the estimated value of the second state variable of the subsystem, the expected output value of the subsystem, and a second-order low-pass filter dynamic equation;

[0014] a determining unit configured to determine a preset time quantized controller for the subsystem based on a preset time quantized controller equation according to an error in an actual value of a quantized first state variable of the subsystem, an error in an estimated value of a quantized second state variable of the subsystem, and a rate of change of a quantized filtered signal;

[0015] An updating unit is configured to obtain an adaptive law for the state variables of the subsystem and update the estimated values of the state variables of the subsystem based on an error in an actual value of the first state variable of the quantized subsystem, an error in an estimated value of the second state variable of the quantized subsystem, an estimated vector of a first unknown parameter vector related to the state variables of the subsystem, an estimated vector of a second unknown parameter vector related to the subsystem, and a fuzzy basis function of the state variables.

[0016] An embodiment of the present invention provides a computer device, comprising a memory and a processor, wherein the memory stores a computer program, and when the computer program is executed by the processor, the processor executes any one of the above-mentioned methods for preset time output feedback quantization control of a double inverted pendulum system.

[0017] An embodiment of the present invention provides a computer-readable storage medium storing a computer program. When the computer program is executed by a processor, the processor executes any one of the above-mentioned methods for output feedback quantization control of a double inverted pendulum system with preset time.

[0018] The embodiments of the present invention provide a method and device for quantitative control of a double inverted pendulum system with preset time output feedback, which has the following beneficial effects:

[0019] First, by introducing a preset time stability criterion, it ensures that all state variables of the double inverted pendulum system converge stably to the desired accuracy range within a preset time. Compared to traditional asymptotically stable control methods, the method provided by the embodiments of the present invention overcomes the limitation that the convergence time depends on initial conditions and control parameters. It can complete the control task within the set time, achieving strict time constraints, thereby improving the system's dynamic performance and response speed. This feature is of great significance in scenarios requiring high precision and fast response.

[0020] Second, a state quantization mechanism is adopted to quantize the state information during the control process, which effectively reduces the amount of data transmission, reduces the demand for communication bandwidth, and at the same time reduces the problem of control performance degradation caused by quantization errors. In addition, the method provided by the embodiment of the present invention, which combines a fuzzy logic system and a fuzzy state observer, effectively compensates for the unknown nonlinear dynamics of the system and estimates the unmeasurable state, thereby improving the system's anti-interference ability and adaptability, so that it can still maintain stable and reliable operation in complex environments with modeling uncertainty and external disturbances. This feature is particularly important in applications such as resource-constrained distributed control systems and multi-machine collaborative control.

[0021] Third, it avoids control singularities and improves the feasibility of the system. Traditional backstepping control may cause control singularity problems in some applications, affecting the feasibility and stability of the controller. The method provided in the embodiment of the present invention, by combining a second-order command filter, constructs a control law without relying on state derivatives, effectively avoiding the "differential explosion" problem of the backstepping method. In addition, the introduction of the filter further smoothes the control signal, reduces the impact on the actuator, and enhances the practical application value of the system.

[0022] Fourth, the adaptability of the system is improved and its adaptability to complex environments is enhanced. Since the double inverted pendulum system has strong nonlinearity and instability, it may face complex external interference and modeling uncertainty in practical applications. The method provided by the embodiment of the present invention, by introducing an adaptive quantization control scheme, can compensate for the quantization error while dynamically adjusting the control gain, thereby adapting to the control requirements in different environments. In addition, the designed control scheme can ensure that the system converges stably within a preset time under different initial conditions and changes in system parameters, providing technical support for the intelligent control and high-precision execution of the double inverted pendulum system. BRIEF DESCRIPTION OF THE DRAWINGS

[0023] In order to more clearly illustrate the embodiments of the present invention or the technical solutions in the prior art, the following briefly introduces the drawings required for use in the embodiments or the description of the prior art. Obviously, the drawings described below are only some embodiments of the present invention. For ordinary technicians in this field, other drawings can be obtained based on these drawings without paying any creative work.

[0024] Figure 1 A schematic flow chart of a preset time output feedback quantization control method for a double inverted pendulum system provided by an embodiment of the present invention;

[0025] Figure 2 A schematic diagram of kinematic analysis of a double inverted pendulum model provided in an embodiment of the present invention;

[0026] FIG3 is a schematic diagram of a trajectory tracking performance curve of a double inverted pendulum system provided by an embodiment of the present invention;

[0027] FIG4 is a schematic diagram of a trajectory tracking error curve of a double inverted pendulum system provided by an embodiment of the present invention under different design parameters;

[0028] FIG5 is a schematic diagram of state variables and their quantization process of a double inverted pendulum system provided by an embodiment of the present invention;

[0029] FIG6 is a schematic diagram of a comparison curve between state variables and estimated values of a double inverted pendulum system provided by an embodiment of the present invention;

[0030] Figure 7 A schematic diagram of a control input response curve of a double inverted pendulum system provided in an embodiment of the present invention;

[0031] Figure 8 A schematic structural diagram of a preset time output feedback quantization control device for a double inverted pendulum system provided by an embodiment of the present invention. DETAILED DESCRIPTION

[0032] The following will clearly and completely describe the technical solutions in the embodiments of the present invention in conjunction with the accompanying drawings. Obviously, the described embodiments are only part of the embodiments of the present invention, not all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without making creative efforts are within the scope of protection of the present invention.

[0033] Figure 1 The present invention provides a double inverted pendulum system preset time output feedback quantization control method flow chart, the following is Figure 1 Taking the double inverted pendulum system as an example, the preset time output feedback quantization control method provided by the embodiment of the present invention is described in detail. Figure 1 As shown, the method includes the following steps:

[0034] Step 101, obtaining an error in the actual value of the first state variable of the subsystem and an error in the estimated value of the second state variable of the subsystem according to the actual value of the first state variable of the subsystem, the estimated value of the second state variable of the subsystem, the expected output value of the subsystem, and a second-order low-pass filter dynamic equation;

[0035] Step 102, determining a preset time quantized controller for the subsystem based on a preset time quantized controller equation according to an error in an actual value of the quantized first state variable of the subsystem, an error in an estimated value of the quantized second state variable of the subsystem, and a rate of change of the quantized filtered signal;

[0036] Step 103, based on the error of the actual value of the first state variable of the quantized subsystem, the error of the estimated value of the second state variable of the quantized subsystem, the estimated vector of the first unknown parameter vector related to the state variable of the subsystem, the estimated vector of the second unknown parameter vector related to the subsystem, the fuzzy basis function of the state variable, the adaptive law of the state variable of the subsystem and the update of the estimated value of the state variable of the subsystem.

[0037] It should be noted that the preset time output feedback quantization control method for a double inverted pendulum system provided in an embodiment of the present invention is executed by an inverted pendulum system with a state quantization mechanism. Its core control process revolves around the steps of establishing a double inverted pendulum system model, introducing a fuzzy logic system and algorithm, and designing a fuzzy state observer and parameters to achieve stable control of the double inverted pendulum system.

[0038] In an embodiment of the present invention, the overall architecture and key steps of the preset time output feedback quantitative control method for a double inverted pendulum system are first explained from a macro perspective, that is, a general introduction to the entire control technology. This process focuses on the main technical means and modules relied upon to achieve stable control, and does not involve specific time advancement and execution sequence details; then, from a micro perspective, a series of operation steps experienced by the preset time output feedback quantitative control method for a double inverted pendulum system within a specific execution cycle are described in detail in chronological order. This process emphasizes the sequence of each step and how to specifically use various technologies and algorithms to adjust the system state within the cycle.

[0039] Before step 101, the overall architecture and key steps of the preset time output feedback quantitative control method for the double inverted pendulum system are first explained from a macro perspective, specifically including steps 10 to 15.

[0040] In step 10, based on Figure 2 The double inverted pendulum system shown in formula (1) is constructed as follows:

[0041]

[0042] Among them, x 1,1 represents the angle between the pendulum 1 and the vertical direction, that is, the angular position of the pendulum 1; x 2,1 represents the angle between the pendulum 2 and the vertical direction, that is, the angular position of the pendulum 2; x 1,2 represents the angular velocity of pendulum 1; x 2,2 represents the angular velocity of the pendulum 2; 1,1 represents the first external disturbance to which the pendulum 1 is subjected; Λ 2,1 represents the first external disturbance to the pendulum 2; Λ 1,2 represents the second external disturbance to the pendulum 1; Λ 2,2represents the second external disturbance to pendulum 2; represents the angular position x of the pendulum 1 1,1 The first-order derivative with respect to time comprehensively reflects the angular velocity x of the pendulum 1 1,2 and external disturbance Λ 1,1 The impact of changes in angular position; represents the angular position x of the pendulum 2 2,1 The first-order derivative with respect to time comprehensively reflects the angular velocity x of the pendulum 2 2,2 and external disturbance Λ 2,1 The impact of changes in angular position; represents the angular velocity x of pendulum 1 1,2 The rate of change over time, i.e. the angular acceleration of pendulum 1; represents the angular velocity x of pendulum 2 2,2 The rate of change with time is the angular acceleration of pendulum 2; u1 represents the torque applied to pendulum 1, and u2 represents the torque applied to pendulum 2. u1 and u2 are the inputs of the control system, which are used to change the motion state of the corresponding pendulum; M1 represents the mass of pendulum 1, and M2 represents the mass of pendulum 2; J1 represents the moment of inertia of pendulum 1, and J2 represents the moment of inertia of pendulum 2; r represents the height of the pendulum; T represents the spring constant of the connecting spring; L represents the natural length of the spring; A represents the distance between the centers of rotation of the two inverted pendulums; and g represents the acceleration due to gravity.

[0043] Furthermore, the double inverted pendulum system model shown in formula (1) is rewritten as a state space expression. The pendulum 1 and pendulum 2 in the double inverted pendulum model are transformed into the first subsystem and the second subsystem of the double inverted pendulum system respectively. The angular position x of the pendulum 1 in the double inverted pendulum model is 1,1 , the angular position x of pendulum 2 2,1 , the angular velocity x of pendulum 1 1,2 , the angular velocity x of pendulum 2 2,2 are transformed into the first state variable x of the first subsystem in the double inverted pendulum system 1,1 , the second state variable x of the first subsystem 1,2 , the first state variable x of the second subsystem 2,1 , the second state variable x of the second subsystem 2,2 , transform the inputs u1 and u2 of the control system in the double inverted pendulum system model into the controllers of the two subsystems respectively, and then obtain the following state space expression:

[0044]

[0045] Furthermore, the specific definitions of some functions and disturbance terms in formula (2) are:

[0046]

[0047] Among them, x represents the state variable of the double inverted pendulum system. Through the state variable of the double inverted pendulum system, we can fully understand the operating state of the system at a certain moment. x=[x1,x2] T =[x 1,1 ,x 1,2 ,x 2,1 ,x 2,2 ] T ; x1 represents the state variable of the first subsystem, x1=[x 1,1 ,x 1,2 ] T ; x2 represents the state variable of the second subsystem, x2=[x 2,1 ,x 2,2 ] T y represents the output of the entire double inverted pendulum system, y=[y1,y2] T ; y1 represents the output of the first subsystem, y2 represents the output of the second subsystem; t represents time; u1 represents the preset time quantitative controller of the first subsystem, u2 represents the preset time quantitative controller of the second subsystem, u1 and u2 are used to adjust and change the operating state of the corresponding subsystem; f 1,1 (x), f 1,2 (x), f 2,1 (x) and f 2,2 (x) represents the unknown smooth nonlinear function of the state variable x of the double inverted pendulum system; δ 1,1 (y), δ 1,2 (y), δ 2,1 (y) and δ 2,2 (y) represents the function of the output y of the double inverted pendulum system, which is the interaction term between the first subsystem and the second subsystem, reflecting the influence of the interaction between the outputs of different subsystems on the relevant state variables in the corresponding subsystems; and It represents the function of time t, which corresponds to the bounded external disturbance of the relevant state variables in the first subsystem and the second subsystem.

[0048] In step 11, given the unknown nonlinear functions in the double inverted pendulum system, a fuzzy logic system is introduced for approximation. Based on fuzzy set theory, it uses fuzzy rules and reasoning to map imprecise inputs to outputs, effectively addressing the system's uncertainty and nonlinearity, providing strong support for system control.

[0049] Specifically, the fuzzy logic system can be expressed as:

[0050]

[0051] Where y(x) represents the output of the fuzzy logic system, which is a function of x and is used to approximate the unknown nonlinear function in the double inverted pendulum system. N represents the number of fuzzy rules, l represents the lth fuzzy rule, n represents the number of input variables, representing the dimension of the input information processed by the fuzzy logic system, h represents the number of input variables, and x represents the number of fuzzy rules. h represents the hth input variable, Represents the input variable x h On the hth fuzzy set under the lth fuzzy rule The membership function is used to measure x h belong the extent of Indicates that under the lth fuzzy rule, the output variable y makes the membership function Get the y value when the maximum value is obtained, Represents the fuzzy set G under the lth fuzzy rule of the output variable y l The membership function is used to measure whether y belongs to G l degree.

[0052] Furthermore, the fuzzy basis function is set as follows:

[0053]

[0054] Among them, φ l Represents the fuzzy basis function. The numerator of the function reflects the overall adaptability of the input variable to the rule under the first fuzzy rule, and the denominator plays a normalization role, so that φ l It has a specific numerical range and properties, which facilitates subsequent calculation and analysis.

[0055] In the embodiment of the present invention, after the parameter vector is introduced, the fuzzy logic system shown in formula (4) can be transformed into:

[0056] y(x)=ξ T φ(x) (6)

[0057] Where ξ represents the parameter vector, ξ=[ξ1,ξ2,…,ξ N ] T ,ξ l Represents the parameters related to the lth fuzzy rule, l=1,2,…,N. φ(x) represents the parameters of each fuzzy basis function φ l The vector formed by it comprehensively reflects the adaptation of the input x under different fuzzy rules, φ(x)=[φ1,φ2,…,φ N ] T .

[0058] Through the parameterized form, the unknown nonlinear function in the double inverted pendulum system can be effectively approximated.

[0059] In step 12, a fuzzy state observer is designed to estimate the unmeasurable state of the system. The fuzzy state observer uses the relevant parameters of the fuzzy logic system and the observer gain parameter, combined with the error between the system output and the estimated output, to estimate the system state. This allows the system to obtain more comprehensive state information, improving the accuracy and reliability of control. The fuzzy state observer is shown below:

[0060]

[0061] In formula (7), represents the rate of change of the estimated value of the sth state variable of the ith subsystem, represents the estimated value of the second state variable of the first subsystem, represents the estimated value of the second state variable of the second subsystem, u1 represents the preset time quantization controller of the first subsystem, u2 represents the preset time quantization controller of the second subsystem, express The transpose of the estimated vector, represents the first unknown parameter vector associated with the sth state variable of the ith subsystem, represents the fuzzy basis function about the estimated value of the state variable, Represents the estimated value of the state variable of the double inverted pendulum system, which is the observer's estimated description of the state of the entire system. y i represents the output of the i-th subsystem in the double inverted pendulum system, represents the output y of the i-th subsystem i The estimated value of g i,s Represents the gain parameter of the observer, which is used to adjust the performance of the observer, i=1,2, s=1,2.

[0062] In step 13, in an embodiment of the present invention, a uniform quantizer is used to quantize the state variables or their observed values to reduce the amount of data transmission. In practical applications, the quantization process will produce quantization errors. However, by properly designing parameters such as the quantization interval length, the errors can be controlled within a certain range, thereby meeting the control accuracy requirements while reducing the communication burden. The uniform quantizer is shown below:

[0063]

[0064] Among them, τ represents the state variable or its observed value, q(τ) represents the quantized value, σ>0 indicates the length of the quantization interval, which determines the accuracy of quantization.k Represents the quantized value, and P1=σ, P k+1 =P k +σ,z τ represents the quantization error, z τ =τ-τ q ,satisfy

[0065] In step 14, constructing a dynamic surface is crucial for improving control performance in a double inverted pendulum control system. To address the discontinuity of the virtual control signal, a second-order low-pass filter is introduced to construct the dynamic surface. By defining the filter's dynamic equation and related variables, the virtual control signal is smoothed, reducing signal fluctuations. This allows for more stable control of the subsystem state and enhances system control performance. The following describes the construction of the dynamic surface and its related definitions.

[0066] Specifically, the dynamic equation of the second-order low-pass filter is as follows:

[0067]

[0068] Among them, α i,1 The virtual control signal representing the first state variable of the i-th subsystem, a i,1,1 represents the damping coefficient of the second-order low-pass filter, a i,1,2 represents the natural frequency of the second-order low-pass filter, Indicates α i,1 The filtered signal obtained by filtering satisfies express The first-order derivative with respect to time, which represents the rate of change of the filtered signal, satisfies

[0069] Furthermore, a dynamic surface is constructed as shown below:

[0070]

[0071] Among them, z i,1 is the actual value x of the first state variable of the i-th subsystem of the double inverted pendulum system i,1 and the expected output y i,r The error between i,2 is the estimated value of the second state variable of the i-th subsystem of the double inverted pendulum system With the filtered signal In order to be more concise, the error between z and i,1 represents the error in the actual value of the first state variable of the i-th subsystem, z i,2 represents the error of the estimated value of the second state variable of the i-th subsystem; Represents the filtered signal and αi,1 The error between And there are represents the filtering error of the i-th subsystem.

[0072] In step 15, a Lyapunov function is constructed, using a positive definite matrix to measure the system state error. A virtual control signal is designed, and the hyperbolic tangent function is used to address control singularities. Fuzzy basis functions and related parameters are combined to adjust system performance. Furthermore, an adaptive law is designed to update parameter estimates, enabling the system to better adapt to parameter changes and ensuring stable convergence within a preset time.

[0073] Specifically, the Lyapunov function is as follows:

[0074]

[0075] Among them, V0 represents the basic error energy index, V1 represents the related variable index, V2 represents the comprehensive state index, P1, P2 and represents a positive definite matrix, e i represents the error between the state variable of the ith subsystem and the estimated value of the state variable of the ith subsystem, z i,1 represents the error in the actual value of the first state variable of the i-th subsystem, express and The error between the estimated vectors, represents the second unknown parameter vector associated with the i-th subsystem, express The transpose of the estimated vector, express The estimated vector of express The transpose of the estimated vector, express The estimated vector of represents the first unknown parameter vector associated with the actual value of the first state variable of the i-th subsystem, represents the first unknown parameter vector associated with the estimated value of the second state variable of the second subsystem, represents the filtering error of the i-th subsystem, Represents the filtered signal and α i,1 The error between Represents the rate of change of the filtered signal, T represents transpose, and i=1,2.

[0076] in, represents the second unknown parameter vector associated with the i-th subsystem, express The estimated vector of x i represents the state variable of the i-th subsystem, represents the estimated value of the state variable of the i-th subsystem. In the embodiment of the present invention, by continuously reducing the error, the observer can more accurately estimate the system state and provide reliable state information for subsequent control strategies, thereby improving the control performance and stability of the entire inverted pendulum system.

[0077] Specifically, the virtual control signal is designed as shown below:

[0078]

[0079] Among them, α 1,1 The virtual control signal representing the first state variable of the first subsystem, z 1,1 represents the error in the actual value of the first state variable of the first subsystem, express The transpose of the estimated vector, represents the first unknown parameter vector associated with the actual value of the first state variable of the first subsystem, φ 1,1 (x 1,1 ) represents the fuzzy basis function of the actual value of the first state variable of the first subsystem, represents the rate of change of the desired output of the first subsystem, express The estimated vector of represents the second unknown parameter vector associated with the first subsystem, represents the 1+η power of the error of the actual value of the first state variable of the first subsystem, represents the 1-n power of the error of the actual value of the first state variable of the first subsystem, represents the 2-η power of the error of the actual value of the first state variable of the first subsystem, η represents the design parameter in the virtual control signal, T d Indicates the time it takes for the preset system to achieve stability; α 2,1 The virtual control signal representing the first state variable of the second subsystem, z 2,1 represents the error in the actual value of the first state variable of the second subsystem, express The transpose of the estimated vector, express The transpose of the estimated vector, represents the first unknown parameter vector related to the actual value of the first state variable of the second subsystem, φ 2,1 (x 2,1) represents the fuzzy basis function of the actual value of the first state variable of the second subsystem, represents the rate of change of the desired output of the second subsystem, express The estimated vector of represents the second unknown parameter vector associated with the second subsystem, represents the 1+η power of the error of the actual value of the first state variable of the second subsystem, represents the 1-η power of the error of the actual value of the first state variable of the second subsystem, Represents the 2-η power of the error in the actual value of the first state variable of the second subsystem.

[0080] Specifically, the adaptive law is set as follows:

[0081]

[0082] in, represents the first adaptive law for the first state variable of the first subsystem, represents the first adaptive law for the second state variable of the first subsystem, represents the first adaptive law for the first state variable of the second subsystem, The first adaptive law representing the second state variable of the second subsystem, represents the error of the actual value of the first state variable of the first subsystem after quantization, represents the error of the estimated value of the second state variable of the first subsystem after quantization, represents the error of the actual value of the first state variable of the second subsystem after quantization, represents the error of the estimated value of the second state variable of the second subsystem after quantization, represents the fuzzy basis function of the actual value of the first state variable of the first subsystem after quantization, represents the fuzzy basis function of the estimated value of the second state variable of the first subsystem after quantization, represents the fuzzy basis function of the actual value of the first state variable of the second subsystem after quantization, represents the fuzzy basis function of the estimated value of the second state variable of the second subsystem after quantization, express The estimated vector of express The estimated vector of express The estimated vector of express The estimated vector of represents the first unknown parameter vector associated with the actual value of the first state variable of the first subsystem, represents the first unknown parameter vector associated with the estimated value of the second state variable of the first subsystem, represents the first unknown parameter vector associated with the actual value of the first state variable of the second subsystem, represents the first unknown parameter vector associated with the estimated value of the second state variable of the second subsystem, represents the second adaptation rate of the first subsystem, express The estimated vector of represents the second unknown parameter vector associated with the first subsystem, represents the second adaptation rate of the second subsystem, express The estimated vector of represents the second unknown parameter vector associated with the second subsystem, represents the design parameters in the adaptive law, i=1,2, s=1,2, η represents the design parameters in the virtual control signal, T d Indicates the time it takes for the preset system to stabilize.

[0083] Specifically, set the preset time quantization controller as shown below:

[0084]

[0085] Wherein, u1 represents the preset time quantization controller of the first subsystem, u2 represents the preset time quantization controller of the second subsystem, represents the error of the actual value of the first state variable of the first subsystem after quantization, represents the error of the estimated value of the second state variable of the first subsystem after quantization, represents the error of the actual value of the first state variable of the second subsystem after quantization, represents the error of the estimated value of the second state variable of the second subsystem after quantization, Indicates α 1,1 The quantized value obtained after quantization processing is obtained by the rate of change of the filtered signal obtained by filtering. Indicates α 1,1 The rate of change of the filtered signal obtained by filtering, α 1,1 a virtual control signal representing a first state variable of the first subsystem, Indicates α 2,1 The quantized value obtained after quantization processing is obtained by the rate of change of the filtered signal obtained by filtering. Indicates α 2,1 The rate of change of the filtered signal obtained by filtering, α 2,1a virtual control signal representing a first state variable of the second subsystem; express The transpose of the estimated vector, represents the first unknown parameter vector associated with the estimated value of the second state variable of the first subsystem, express The transpose of the estimated vector, A first unknown parameter vector representing an estimated value of a second state variable of the second subsystem; represents the fuzzy basis function of the estimated value of the second state variable of the first subsystem after quantization, represents the fuzzy basis function of the estimated value of the second state variable of the second subsystem after quantization, represents the 1+η power of the error of the actual value of the first state variable of the i-th subsystem, represents the 1-η power of the error of the actual value of the first state variable of the i-th subsystem, represents the 2-η power of the error of the actual value of the first state variable of the i-th subsystem, η represents the design parameter in the virtual control signal, T d Indicates the time it takes for the preset system to stabilize.

[0086] Based on the overall architecture and key steps provided by steps 10 to 15 above, the specific process within an execution cycle based on the above overall architecture is described in detail below. Each operation step and calculation method in this specific process is designed based on the technology and algorithm in the above core control process, ensuring that each execution cycle moves towards the goal of achieving stable control of the inverted pendulum system.

[0087] Within a single execution cycle, a double inverted pendulum system with a state quantization mechanism first acquires the state and output of the double inverted pendulum system and calculates the rate of change of the state variables based on the system model. Next, a fuzzy logic system is used to approximate unknown nonlinear functions, and unmeasurable states are estimated using a fuzzy state observer. Subsequently, the state variables and their observed values are quantized, and a virtual control signal is processed using a second-order low-pass filter to calculate the dynamic surface-related error. Finally, a virtual control signal, an adaptive law, and a preset time quantization controller are calculated based on a specific formula. The control signal is applied to the system and the parameter estimates are updated, driving the system state adjustment to achieve stable convergence within a preset time.

[0088] In step 101, according to the actual value x of the first state variable of the subsystem included in the double inverted pendulum system i,1 , the estimated value of the second state variable of the subsystem The expected output value y of the subsystem i,r and the second-order low-pass filter dynamic equation to obtain the error z of the actual value of the first state variable of the subsystem i,1and the error z in the estimated value of the second state variable of the subsystem i,2 ;

[0089] Specifically, the error of the actual value of the first state variable of the subsystem included in the double inverted pendulum system is determined by the following formula:

[0090] z i,1 =x i,1 -y i,r (10-1)

[0091] Among them, z i,1 represents the error in the actual value of the first state variable of the i-th subsystem, x i,1 represents the actual value of the first state variable of the i-th subsystem, y i,r represents the expected output of the i-th subsystem, i=1,2, and r represents the reference.

[0092] Furthermore, according to the error of the actual value of the first state variable of the subsystem included in the double inverted pendulum system, the actual value of the first state variable of the subsystem, the estimated vector of the first unknown parameter vector and the second unknown parameter vector related to the first subsystem, the virtual control signal of the first state variable of the subsystem is determined by the following formula;

[0093]

[0094] Among them, α i,1 The virtual control signal z represents the first state variable of the i-th subsystem. i,1 represents the error in the actual value of the first state variable of the i-th subsystem, express The transpose of the estimated vector, represents the first unknown parameter vector associated with the actual value of the first state variable of the i-th subsystem, φ i,1 (x i,1 ) represents the fuzzy basis function of the actual value of the first state variable of the i-th subsystem, represents the rate of change of the expected output of the i-th subsystem, express The estimated vector of represents the second unknown parameter vector associated with the i-th subsystem, represents the 1+η power of the error of the actual value of the first state variable of the i-th subsystem, represents the 1-η power of the error of the actual value of the first state variable of the i-th subsystem, represents the 2-η power of the error of the actual value of the first state variable of the i-th subsystem, η represents the design parameter in the virtual control signal, T d Indicates the time it takes for the preset system to stabilize.

[0095] It should be noted that when i=1, 2 in formula (12), formula (12) can be transformed into formula (12-1) and formula (12-2).

[0096] After obtaining the virtual control signal of the first state variable of the i-th subsystem, the filtered signal obtained by filtering the virtual control signal of the first state variable of the i-th subsystem can be determined by the dynamic equation of the second-order low-pass filter shown in formulas (9-1) and (9-2) and the virtual control signal of the first state variable of the i-th subsystem. Then, the error of the estimated value of the state variable of the subsystem included in the double inverted pendulum system can be obtained by formula (10-2):

[0097]

[0098] Among them, z i,2 represents the error of the estimated value of the second state variable of the i-th subsystem, represents the estimated value of the second state variable of the i-th subsystem, Indicates α i,1 The filtered signal obtained by filtering is represents the rate of change of the filtered signal, α i,1 A virtual control signal representing the first state variable of the i-th subsystem.

[0099] It should be noted that in the embodiment of the present invention, during the initial period, the first state variables of the subsystems included in the double inverted pendulum system are set values, and the second state variables of the subsystems included in the double inverted pendulum system are also set values. However, during periods other than the initial period, the first state variables of the subsystems included in the double inverted pendulum system are all actual values, while the second state variables of the subsystems included in the double inverted pendulum system are all estimated values. Therefore, in the embodiment of the present invention, the first state variable of a subsystem can also be referred to as the actual value of the first state variable of the subsystem, and the second state variable of a subsystem can also be referred to as the estimated value of the second state variable of the subsystem.

[0100] It should be noted that in the fuzzy state observer shown in formula (7), since y i represents the output of the i-th subsystem in the double inverted pendulum system, represents the output y of the i-th subsystem i The estimated value of Therefore, in this formula, the first state variable of the subsystem may include an estimated value or an actual value. In formula (7), there is no restriction on the value of the first state variable.

[0101] In step 102, a preset time quantized controller of the subsystem is determined based on a preset time quantized controller equation according to an error in an actual value of the quantized first state variable of the subsystem, an error in an estimated value of the quantized second state variable of the subsystem, and quantization of a rate of change of the quantized filtered signal. The preset time quantized controller equation is as follows:

[0102]

[0103] Among them, u i represents the preset time quantization controller of the i-th subsystem, represents the error of the actual value of the first state variable of the ith subsystem after quantization, represents the error of the estimated value of the second state variable of the ith subsystem after quantization, It represents the quantized value obtained after the rate of change of the filtered signal is quantized. Indicates α i,1 The filtered signal obtained by filtering is express The transpose of the estimated vector, represents the first unknown parameter vector associated with the estimated value of the second state variable of the i-th subsystem, represents the fuzzy basis function of the estimated value of the second state variable of the i-th subsystem after quantization, represents the 1+η power of the error of the actual value of the first state variable of the i-th subsystem, represents the 1-η power of the error of the actual value of the first state variable of the i-th subsystem, represents the 2-η power of the error of the actual value of the first state variable of the i-th subsystem, η represents the design parameter in the virtual control signal, T d Indicates the time it takes for the preset system to stabilize.

[0104] It should be noted that when i=1, 2 in formula (14), formula (14) can be transformed into formula (14-1) and formula (14-2).

[0105] In step 103, based on the error in the actual value of the first state variable of the subsystem, the error in the estimated value of the second state variable of the subsystem, the estimated vector of the first unknown parameter vector related to the state variable of the subsystem, the estimated vector of the second unknown parameter vector related to the subsystem, and the fuzzy basis function of the state variable, the adaptive law of the state variable of the subsystem is obtained and the estimated value of the state variable of the subsystem is updated.

[0106] Specifically, the adaptive law of the state variable of the subsystem includes a first adaptive law of the state variable of the subsystem and a second adaptive law of the state variable of the subsystem. The adaptive law of the state variable of the subsystem and the second adaptive law of the state variable of the subsystem are obtained by the following formula:

[0107]

[0108] in, represents the first adaptive law of the first state variable of the i-th subsystem, represents the first adaptive law for the second state variable of the i-th subsystem, represents the error of the actual value of the first state variable of the ith subsystem after quantization, represents the error of the estimated value of the second state variable of the ith subsystem after quantization, represents the fuzzy basis function of the actual value of the first state variable of the i-th subsystem after quantization, represents the fuzzy basis function of the estimated value of the second state variable of the i-th subsystem after quantization, express The estimated vector of express The estimated vector of represents the first unknown parameter vector associated with the actual value of the first state variable of the i-th subsystem, represents the first unknown parameter vector associated with the estimated value of the second state variable of the i-th subsystem, ψ、ω、 represents the design parameters in the adaptive law, represents the second adaptation rate of the i-th subsystem, express The estimated vector of represents the second unknown parameter vector associated with the i-th subsystem, i = 1, 2, s = 1, 2, η represents the design parameters in the virtual control signal, T d Indicates the time it takes for the preset system to stabilize.

[0109] It should be noted that when i=1,2 in formula (13-1), formula (13-1) can be transformed into formula (13).

[0110] The estimated values of the first state variable and the second state variable of the subsystem shown in formula (7) are updated by the following formula:

[0111]

[0112] in, represents the rate of change of the estimated value of the first state variable of the i-th subsystem, represents the rate of change of the estimated value of the second state variable of the i-th subsystem, represents the estimated value of the second state variable of the i-th subsystem, express The transpose of the estimated vector, express The transpose of the estimated vector, represents the first unknown parameter vector associated with the first state variable of the i-th subsystem, represents the first unknown parameter vector associated with the second state variable of the i-th subsystem, represents the fuzzy basis function of the state variables of the double inverted pendulum system, g i,1 represents the gain parameter of the observer of the first state variable of the i-th subsystem, g i,2 represents the gain parameter of the observer of the second state variable of the i-th subsystem, y i represents the output of the i-th subsystem, represents the estimated value of the output of the ith subsystem,

[0113] It should be noted that when i=1,2 in formula (7-1), formula (7-1) can be transformed into formula (7).

[0114] Furthermore, the method provided by an embodiment of the present invention further includes: constructing a Lyapunov function as shown below based on the error in the actual value of the first state variable of the subsystem, the error in the estimated value of the second state variable of the subsystem, the first unknown parameter vector, and the second unknown parameter vector, and determining the stability of the double inverted pendulum system based on the Lyapunov function;

[0115]

[0116] Among them, V0 represents the basic error energy index, V1 represents the related variable index, V2 represents the comprehensive state index, P1, P2 and represents a positive definite matrix, e i represents the error between the state variable of the ith subsystem and the estimated value of the state variable of the ith subsystem, z i,1 represents the error in the actual value of the first state variable of the i-th subsystem, express and The error between the estimated vectors, represents the second unknown parameter vector associated with the i-th subsystem, express The transpose of the estimated vector, express The estimated vector of express The transpose of the estimated vector, express The estimated vector of represents the first unknown parameter vector associated with the actual value of the first state variable of the i-th subsystem, represents the first unknown parameter vector associated with the actual value of the second state variable of the second subsystem, represents the filtering error of the i-th subsystem, represents the error between the filtered signal and the virtual control signal, Represents the rate of change of the filtered signal, T represents transpose, and i=1,2.

[0117] The embodiment of the present invention provides a set of simulation schematic diagrams for verifying the effectiveness of the preset time output feedback control method of the inverted pendulum system with a state quantization mechanism, such as Figure 3A-Figure 7 shown.

[0118] Specifically, Figure 3A and Figure 3B The trajectory tracking performance of the preset time output feedback quantization control method for the double inverted pendulum system provided by the embodiment of the present invention is shown in FIG. 1 , where the blue solid line represents the actual output y of the system. i The red dotted line represents the expected output y of the system i,r The horizontal axis represents time (seconds) and the vertical axis represents the actual output y of the i-th subsystem i and the expected output y i,r The reference trajectory is in the form of a sine wave and is used to test the tracking capability of the system. Figure 3A and Figure 3B As can be seen from the figure, the actual output curve closely follows the reference trajectory, with no significant overshoot or steady-state error, demonstrating that the system can achieve high-precision state quantization control within the preset time. The preset time control strategy and output feedback quantization mechanism further enhance the system's anti-interference capability, enabling the output to accurately track the reference signal without being affected by noise and uncertainty, maintaining stability throughout the control process.

[0119] Figure 4A and Figure 4B The tracking error trajectories of the double inverted pendulum system provided by the embodiment of the present invention under different design parameters are respectively shown, with the horizontal axis representing time (seconds) and the vertical axis representing the tracking error between the system output and the reference trajectory. Figure 4A In, T d Indicates the time it takes for the preset system to achieve stability. The curves represent T d =8 (blue curve), T d= 10 (red curve) and T d =12 (green curve), according to the control design principle, the smaller T d The value can make the system achieve stability within the predefined time earlier, so it can be seen in the figure that as T d As the error decreases, the system converges faster and the tracking error decreases accordingly. The rectangular magnified area further shows the error changes of the system in a specific time period, indicating that the control strategy can converge quickly and remain stable in a short time. Figure 4B In the figure, η represents the design parameter in the control design process, and the curves correspond to (blue curve), (red curve) and (Green curve). According to the control design principle, a smaller η value can lead to a smaller tracking error. Therefore, it can be observed from the figure that as η decreases, the tracking accuracy of the system is significantly improved. The rectangular magnified area further shows the detailed changes in the tracking error and the error dynamic characteristics under different parameter configurations. Overall, by reasonably selecting T d The embodiment of the present invention provides a double inverted pendulum system preset time output feedback quantization control method that can achieve fast response while ensuring high-precision tracking, and has significant advantages.

[0120] Figure 5A and 5B The embodiment of the present invention provides the state variables of the two subsystems in the double inverted pendulum system and their corresponding quantization process, reflecting the impact of the state quantization mechanism on the operation of the system. The blue solid line represents the actual or estimated value of the state variable, while the red dotted line represents the value of the state variable after quantization. The horizontal axis represents time (seconds) and the vertical axis represents the value of the state variable. Figure 5A In the middle, the red dotted line x 1,1 The blue solid line represents the actual value of the first state variable of the first subsystem represents the actual value of the first state variable of the first subsystem after quantization, Figure 5B Middle, red dotted line Represents the estimated value of the second state variable of the first subsystem, the blue solid line The second state variable estimation value of the first subsystem after quantization processing is shown in FIG. The horizontal axis represents time (seconds) and the vertical axis represents the value of the state variable. Figure 5A and Figure 5BAs can be seen in the figure, the actual state variable appears as a continuous sinusoidal curve, while the quantized curve exhibits step-like fluctuations. This quantization process is one of the key technologies in the control method of the present invention. By segmenting the continuous state variable into a finite number of discrete levels within a preset time, the system can achieve precise control of the state with limited computing resources, significantly reducing the noise caused by fluctuations and improving the stability and robustness of the system. The rectangular magnified area in the figure clearly shows the quantization details of the state variable in each time period, verifying the accuracy of the quantization process.

[0121] Figure 6A and Figure 6B The comparison curves of the state variables and their estimated values of the two subsystems in the double inverted pendulum system provided by the embodiment of the present invention are respectively shown. The blue solid line represents the actual value of the state variable, while the red solid line represents the state variable value estimated by the fuzzy state observer. The horizontal axis represents time (seconds) and the vertical axis represents the value of the state variable. Figure 6A In the middle, the blue curve x 1,2 The red curve represents the actual value of the second state variable of the first subsystem. Represents the estimated value of the second state variable of the first subsystem. Figure 6B In the middle, the blue curve x 2,2 The red curve represents the actual value of the second state variable of the second subsystem. represents the estimated value of the second state variable of the second subsystem. Figure 6A and Figure 6B As can be seen in the figure, the estimated value and the actual value maintain a high degree of consistency in overall trend and fluctuation amplitude. Even in the presence of a small amount of high-frequency oscillation and slight deviation, the estimated value can still closely track the changes in the actual state. In particular, in the high-frequency fluctuation range, the estimated value can quickly respond to state changes and avoid significant lag or deviation. This result shows that the fuzzy state observer in this invention can effectively estimate the unmeasurable states of each subsystem in the double inverted pendulum system, accurately capture the dynamic changes in the system state, ensure the integrity and accuracy of the system state information, and improve the overall control performance of the system.

[0122] Figure 7 The control input response curves of the two subsystems in the double inverted pendulum system provided by the embodiment of the present invention are shown, wherein the red curve u1 represents the time quantization control of the first subsystem (the control input of the first subsystem), and the blue curve u2 represents the time quantization controller of the second subsystem (the control input of the second subsystem). The horizontal axis represents time (seconds) and the vertical axis represents the amplitude of the control input. These two curves reflect the changes in the control input of each subsystem in the dynamic process of the control system. Figure 7It can be observed that the control inputs u1 and u2 fluctuate essentially synchronously within each time period, indicating that the two subsystems in the double inverted pendulum system exhibit high cooperative control characteristics. This characteristic ensures that the two subsystems can coordinate their responses during dynamic processes, avoiding instability caused by inconsistent control strategies. Furthermore, the amplitude variation of the control input reflects the control strength of the system under different states. Regions with higher amplitudes indicate that the system requires stronger control force to cope with dynamic changes, while regions with lower amplitudes indicate that the system has reached a relatively stable state and the control strength is gradually decreasing. Overall, the control input signal exhibits high-frequency fluctuations, and the amplitude of the fluctuations varies slightly within each time period. This high-frequency fluctuation is due to the discrete characteristics introduced by the quantitative control strategy of the present invention. Under this control strategy, the system flexibly adapts to changes in the system state by periodically adjusting the control input, enabling the double inverted pendulum system to remain stable under complex dynamic conditions.

[0123] From the above simulation result diagram, it can be seen that the preset time output feedback quantization control method of the double inverted pendulum system provided by the embodiment of the present invention can ensure that the inverted pendulum system achieves preset time stability and the output state converges to the desired accuracy range within the preset time.

[0124] The preset time output feedback quantitative control method for a double inverted pendulum system provided by the embodiment of the present invention has wide applications in the fields of robot balance control, aerospace attitude adjustment, unmanned driving, and industrial automation control.

[0125] For example, bipedal robots and wheeled mobile robots need to maintain balance in real time when walking and moving. This method can use the state quantization mechanism to reduce the amount of data transmitted from the robot's sensors (such as accelerometers, gyroscopes, etc.) to the controller, alleviating communication pressure. By presetting time control, it can ensure that the robot quickly adjusts its posture when encountering external interference (such as road bumps and collisions), restores balance within a preset time, maintains a stable motion state, and improves the robot's motion stability and adaptability in complex environments. When a spacecraft is flying in space, it is affected by various interferences (such as micro-meteoroid impacts and space environment forces), and its posture is prone to change. The implementation of the present invention can ensure that the spacecraft accurately completes the posture adjustment task within the specified time. For example, when a satellite is performing orbital maneuvers or ground observation, its posture is stable to meet the mission requirements. When a car is driving, it faces complex road conditions and traffic environments and requires precise control to ensure safety and stability. The state quantization of the method provided by the implementation of the present invention can reduce the amount of data transmitted by on-board sensors (such as radars and cameras) and improve data processing efficiency. The preset time control enables the vehicle to respond accurately within the preset time when encountering emergencies (such as emergency braking, avoiding obstacles), adjust the vehicle speed, steering, etc., and at the same time use the fuzzy logic system and state observer to handle the uncertainty of the vehicle dynamics model, thereby improving the safety and stability of unmanned vehicles; on some high-precision industrial production lines, precise control of the robotic arm is crucial. The method provided by the present invention can reduce the amount of data transmission of the robotic arm joint sensor through state quantization, and the preset time control can ensure that the robotic arm completes operations such as material grabbing, handling, and assembly within the specified time, thereby improving production efficiency. The fuzzy logic system and state observer can compensate for nonlinear factors and unknown interference in the movement of the robotic arm, ensure the movement accuracy of the robotic arm, and meet the needs of industrial production for high-precision control.

[0126] Based on the same inventive concept, an embodiment of the present invention provides a double inverted pendulum system preset time output feedback quantization control device. Since the principle of solving the technical problem of the device is similar to the double inverted pendulum system preset time output feedback quantization control method, the implementation of the device can refer to the implementation of the method, and the repeated parts will not be repeated.

[0127] like Figure 8 As shown, the device includes an obtaining unit 801, a determining unit 802 and an updating unit 803. In each control cycle:

[0128] an obtaining unit 801 for obtaining an error in the actual value of the first state variable of the subsystem and an error in the estimated value of the second state variable of the subsystem according to an actual value of the first state variable of the subsystem, an estimated value of the second state variable of the subsystem, an expected output value of the subsystem, and a second-order low-pass filter dynamic equation;

[0129] A determining unit 802 is configured to determine a preset time quantized controller for the subsystem based on a preset time quantized controller equation according to an error in an actual value of the quantized first state variable of the subsystem, an error in an estimated value of the quantized second state variable of the subsystem, and a rate of change of the quantized filtered signal;

[0130] An updating unit 803 is configured to obtain an adaptive law of the state variables of the subsystem and update the estimated values of the state variables of the subsystem based on an error in the actual value of the first state variable of the quantized subsystem, an error in the estimated value of the second state variable of the quantized subsystem, an estimated vector of a first unknown parameter vector related to the state variables of the subsystem, an estimated vector of a second unknown parameter vector related to the subsystem, and a fuzzy basis function of the state variables.

[0131] It should be understood that the units included in the above-described double inverted pendulum system preset time output feedback quantitative control device are merely logical divisions based on the functions implemented by the device. In actual applications, the above-described units can be superimposed or separated. Furthermore, the functions implemented by the double inverted pendulum system preset time output feedback quantitative control device provided in this embodiment correspond one-to-one with the double inverted pendulum system preset time output feedback quantitative control method provided in the above-described embodiment. A more detailed processing flow implemented by this device has been described in detail in the above-described method embodiment 1 and will not be described in detail here.

[0132] Another embodiment of the present invention also provides a computer device, which includes: a processor and a scene database; the scene database is used to store computer program code, and the computer program code includes computer instructions; when the processor executes the computer instructions, the electronic device executes each step of the preset time output feedback quantitative control method of the double inverted pendulum system shown in the above method embodiment.

[0133] Another embodiment of the present invention further provides a computer-readable storage medium, which stores computer instructions. When the computer instructions are executed on a computer device, the computer device executes each step of the preset time output feedback quantitative control method for the double inverted pendulum system shown in the above method embodiment.

[0134] Obviously, those skilled in the art may make various changes and modifications to the present invention without departing from the spirit and scope of the present invention. Thus, if such changes and modifications fall within the scope of the claims and their equivalents, the present invention is intended to include such changes and modifications.

Claims

1. A double inverted pendulum system preset time output feedback quantitative control method, characterized in that: Each control cycle includes: According to the actual value of the first state variable of the subsystem included in the double inverted pendulum system, the estimated value of the second state variable of the subsystem, the expected output value of the subsystem and the dynamic equation of the second-order low-pass filter, an error in the actual value of the first state variable of the subsystem and an error in the estimated value of the second state variable of the subsystem are obtained respectively; Determining a preset time quantized controller for the subsystem based on a preset time quantized controller equation according to an error in an actual value of a quantized first state variable of the subsystem, an error in an estimated value of a quantized second state variable of the subsystem, and a rate of change of a quantized filtered signal; Based on the error in the actual value of the first state variable of the quantized subsystem, the error in the estimated value of the second state variable of the quantized subsystem, the estimated vector of the first unknown parameter vector related to the state variable of the subsystem, the estimated vector of the second unknown parameter vector related to the subsystem, and the fuzzy basis function of the state variable, the adaptive law of the state variable of the subsystem is obtained and the estimated value of the state variable of the subsystem is updated.

2. The control method according to claim 1, wherein: Before obtaining the error of the estimated value of the second state variable of the subsystem, the method further includes: determining a virtual control signal of the first state variable of the subsystem according to the error of the actual value of the first state variable of the subsystem, the actual value of the first state variable of the subsystem, a first unknown parameter vector related to the first subsystem, and an estimated vector of the second unknown parameter vector by the following formula; Among them, α i,1 The virtual control signal z represents the first state variable of the i-th subsystem. i,1 represents the error in the actual value of the first state variable of the i-th subsystem, express The transpose of the estimated vector, represents the first unknown parameter vector associated with the actual value of the first state variable of the i-th subsystem, φ i,1 (x i,1 ) represents the fuzzy basis function of the actual value of the first state variable of the i-th subsystem, represents the rate of change of the expected output of the i-th subsystem, express The estimated vector of represents the second unknown parameter vector associated with the i-th subsystem, represents the 1+η power of the error of the actual value of the first state variable of the i-th subsystem, represents the 1-η power of the error of the actual value of the first state variable of the i-th subsystem, represents the 2-η power of the error of the actual value of the first state variable of the i-th subsystem, η represents the design parameter in the virtual control signal, T d Indicates the time it takes for the preset system to stabilize.

3. The control method according to claim 1, wherein: The error of the actual value of the first state variable of the subsystem is determined by the following formula: z i,1 =x i,1 -y i,r The error in the estimated value of the second state variable of the subsystem is determined by the following formula: Among them, z i,1 represents the error in the actual value of the first state variable of the i-th subsystem, x i,1 represents the actual value of the first state variable of the i-th subsystem, y i,r represents the expected output of the i-th subsystem, i = 1, 2, r represents the reference; z i,2 represents the error of the estimated value of the second state variable of the i-th subsystem, represents the estimated value of the second state variable of the i-th subsystem, Indicates α i,1 The filtered signal obtained by filtering is Indicates the rate of change of the filtered signal.

4. The control method according to claim 1, wherein: The preset time quantization controller equation is as follows: Among them, u i represents the preset time quantization controller of the i-th subsystem, represents the error of the actual value of the first state variable of the ith subsystem after quantization, represents the error of the estimated value of the second state variable of the ith subsystem after quantization, It represents the quantized value obtained after the rate of change of the filtered signal is quantized. Indicates α i,1 The filtered signal obtained by filtering, α i,1 represents the virtual control signal of the first state variable of the i-th subsystem, express The transpose of the estimated vector, represents the first unknown parameter vector associated with the estimated value of the second state variable of the i-th subsystem, represents the quantized fuzzy basis function of the estimated value of the second state variable of the i-th subsystem after quantization processing, represents the 1+η power of the error of the actual value of the first state variable of the i-th subsystem, represents the 1-η power of the error of the actual value of the first state variable of the i-th subsystem, represents the 2-η power of the error of the actual value of the first state variable of the i-th subsystem, η represents the design parameter in the virtual control signal, T d Indicates the time it takes for the preset system to stabilize.

5. The control method according to claim 1, wherein: The adaptive law of the state variable of the subsystem includes a first adaptive law of the state variable of the subsystem and a second adaptive law of the state variable of the subsystem; The first adaptive law of the state variables of the subsystem and the second adaptive law of the state variables of the subsystem are obtained by the following formulas: in, represents the first adaptive law of the first state variable of the i-th subsystem, represents the first adaptive law for the second state variable of the i-th subsystem, represents the error in the actual value of the first state variable of the quantized subsystem, represents the error of the estimated value of the second state variable of the ith subsystem after quantization, represents the fuzzy basis function of the actual value of the first state variable of the i-th subsystem after quantization, represents the fuzzy basis function of the estimated value of the second state variable of the i-th subsystem after quantization, express The estimated vector of express The estimated vector of represents the first unknown parameter vector associated with the actual value of the first state variable of the i-th subsystem, represents the first unknown parameter vector associated with the estimated value of the second state variable of the i-th subsystem, and represents the design parameters in the adaptive law, represents the second adaptation rate of the i-th subsystem, express The estimated vector of represents the second unknown parameter vector associated with the i-th subsystem, i = 1, 2, s = 1, 2, η represents the design parameters in the virtual control signal, T d Indicates the time it takes for the preset system to stabilize.

6. The control method according to claim 1, wherein: The estimated values of the first and second state variables of the subsystem are updated using the following formulas: in, represents the rate of change of the estimated value of the first state variable of the i-th subsystem, represents the rate of change of the estimated value of the second state variable of the i-th subsystem, represents the estimated value of the second state variable of the i-th subsystem, express The transpose of the estimated vector, express The transpose of the estimated vector, represents the first unknown parameter vector associated with the first state variable of the i-th subsystem, represents the first unknown parameter vector associated with the second state variable of the i-th subsystem, Represents the state variables of the double inverted pendulum system The fuzzy basis function, g i,1 represents the gain parameter of the observer of the first state variable of the i-th subsystem, g i,2 represents the gain parameter of the observer of the second state variable of the i-th subsystem, y i represents the output of the i-th subsystem, represents the estimated value of the output of the ith subsystem, 7. The control method according to claim 1, wherein: Also includes: Constructing a Lyapunov function as shown below based on the error of the actual value of the first state variable of the subsystem, the error of the estimated value of the second state variable of the subsystem, the first unknown parameter vector, and the second unknown parameter vector, and determining the stability of the double inverted pendulum system based on the Lyapunov function; Among them, V0 represents the basic error energy index, V1 represents the related variable index, V2 represents the comprehensive state index, P1, P2 and represents a positive definite matrix, e i represents the error between the state variable of the ith subsystem and the estimated value of the state variable of the ith subsystem, z i,1 represents the error in the actual value of the first state variable of the i-th subsystem, express and The error between the estimated vectors, represents the second unknown parameter vector associated with the i-th subsystem, express The transpose of the estimated vector, express The estimated vector of express The transpose of the estimated vector, express The estimated vector of represents the first unknown parameter vector associated with the actual value of the first state variable of the i-th subsystem, represents the parameter vector associated with the estimated value of the second state variable of the i-th subsystem, Represents the filtering error of the i-th subsystem, i=1,2.

8. A double inverted pendulum system preset time output feedback quantization control device, characterized in that: Each control cycle includes: an obtaining unit, configured to obtain an error in the actual value of the first state variable of the subsystem and an error in the estimated value of the second state variable of the subsystem according to the actual value of the first state variable of the subsystem included in the double inverted pendulum system, the estimated value of the second state variable of the subsystem, the expected output value of the subsystem, and a second-order low-pass filter dynamic equation; a determining unit configured to determine a preset time quantized controller for the subsystem based on a preset time quantized controller equation according to an error in an actual value of a quantized first state variable of the subsystem, an error in an estimated value of a quantized second state variable of the subsystem, and a rate of change of a quantized filtered signal; An updating unit is configured to obtain an adaptive law for the state variables of the subsystem and update the estimated values of the state variables of the subsystem based on an error in an actual value of the first state variable of the quantized subsystem, an error in an estimated value of the second state variable of the quantized subsystem, an estimated vector of a first unknown parameter vector related to the state variables of the subsystem, an estimated vector of a second unknown parameter vector related to the subsystem, and a fuzzy basis function of the state variables.

9. A computer device, characterized in that: The computer device includes a memory and a processor, the memory stores a computer program, and when the computer program is executed by the processor, the processor executes the control method of the double inverted pendulum system according to any one of claims 1 to 7.

10. A computer-readable storage medium, characterized in that A computer program is stored, and when the computer program is executed by a processor, the processor executes the control method of the double inverted pendulum system according to any one of claims 1 to 7.

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