Active-disturbance-rejection control method and system with control input constraint

Abstract

The invention provides an active disturbance rejection control method and system with control input constraint, the system constructs a prediction model of the system based on an ideal closed-loop transfer function of an ADRC system, the ADRC system regards unmodeled dynamics, external disturbance and the like as total disturbance, and the total disturbance is estimated and compensated through an extended state observer and a control law. Therefore, the prediction model of the DMC system established based on the ADRC system is more accurate, and the control performance is better. The ADRC-CIC control method provided by the invention can be designed by considering control input constraints. Through the constraint conversion method, the control input constraint of the ADRC can be successfully converted into the constraint which can be directly processed by the optimization module. Therefore, the ADRC-CIC can be used for solving the control problem with the control input constraint, and has the strong robustness of the ADRC and the constraint processing capability of the DMC.

Description

Technical Field

[0001] The present invention relates to an active disturbance rejection control method and system with control input constraints, which can be used for control with constraint conditions such as quadrotor unmanned aerial vehicles, and belongs to the technical fields of active disturbance rejection control and optimal control. Background Art

[0002] Problems such as inaccurate models, parameter mismatches, as well as the inherent nonlinear and strong coupling characteristics in quadrotor unmanned aerial vehicles pose great challenges to the control of unmanned aerial vehicles. At the same time, quadrotor unmanned aerial vehicles are extremely vulnerable to external disturbances. Active Disturbance Rejection Control (ADRC) is a control method with low dependence on models, which can consider unmodeled dynamics, parameter mismatches, nonlinearities, external disturbances, and coupling effects between multiple variables as part of the total disturbance. By designing an extended state observer and a control law to estimate and compensate for the total disturbance respectively, it not only improves the robustness of the system but also realizes implicit decoupling in multivariable control. ADRC is an effective control method for quadrotor unmanned aerial vehicles.

[0003] Currently, it is possible to achieve flight control of quadrotor unmanned aerial vehicles using an ADRC system. However, various physical, safety, and economic constraints in the flight control of quadrotor unmanned aerial vehicles are inevitable. Although existing ADRC control can achieve basic constraint management through simple output limiting, its core design lacks an explicit processing mechanism for system constraints. Rough direct limiting can temporarily limit the amplitude of the control quantity, but it may damage the dynamic coupling relationship between the ADRC observer and the controller, leading to risks such as observation instability or deterioration of stability. How to effectively introduce constraint conditions into the ADRC control system to broaden its applicable control fields has become a research direction. Summary of the Invention

[0004] To solve the problems existing in the prior art, the present invention proposes an active disturbance rejection control system with control input constraints (Active Disturbance Rejection Control With Control Input Constraints, ADRC-CIC) and a control method. The control system adopts a double-closed-loop control structure, with the outer loop using Dynamic Matrix Control (DMC) and the inner loop using ADRC control.

[0005] The specific technical solution of the present invention is as follows:

[0006] An active disturbance rejection control method with control input constraints, which adopts a double-closed-loop control system, with the outer loop using dynamic matrix control and the inner loop using an ADRC system for control, and includes the following steps:

[0007] S1. Conduct a unit step response test on the ideal closed-loop transfer function of the ADRC system, and obtain the step response coefficient from the output response value. Thus, obtain the dynamic matrix A in the prediction model, where A ∈ R P×M , P is the prediction time domain, and M is the control time domain;

[0008] S2. At the current moment k, construct a prediction model according to the dynamic matrix A, the initial prediction output vector y M0 (k), and the optimal control input increment vector Δu 1 (k). Its output is the prediction output vector y M (k); the initial values of the initial prediction output vector y M0 (k) and the optimal control input increment vector Δu 1 (k) are both set to zero vectors;

[0009] S3. Obtain the prediction error vector e(k + 1) based on the system output y(k) and the prediction output vector y M (k) at the current moment. Correct the prediction output vector y M (k) through the prediction error vector e(k + 1) to obtain the corrected prediction output vector y c (k + 1). Shift the corrected prediction output vector y c (k + 1) to obtain the initial prediction output vector y M0 (k + 1) at the k + 1 moment, which is used to update the prediction output vector y M (k + 1);

[0010] S4. Update the reference trajectory vector W(k) according to the system output y(k) and the reference input r at the current moment. Construct an objective function from the reference trajectory vector W(k) and the prediction output vector y M (k), and find the optimal solution of the objective function and take as the optimal control input increment vector Δu 1 (k + 1) at the k + 1 moment, which is used to update the prediction output vector y M (k + 1);

[0011] S5. One way of the optimal control input increment vector is output to the prediction model to update the prediction output vector with the initial prediction output vector y M0 (k + 1);

[0012] The optimal control input increment vector Another output takes its first element as the control input, and after differential transformation, the control signal u 1 (k) is obtained, and it is converted into a continuous control signal u 1 through a zero-order hold. As the input of the ADRC system, the system output y is converted into a discrete system output y(k) through a zero-order hold and is respectively fed back to the reference trajectory vector W(k) and the prediction model.

[0013] The further design lies in that

[0014] In S1, the expression of the ideal closed-loop transfer function of the ADRC system is as follows:

[0015]

[0016] where G(s) represents the ideal closed-loop transfer function of the ADRC system, y(s) represents the Laplace transform of the output, r(s) represents the Laplace transform of the input, s represents the Laplace operator, K p and K d are the PD controller gains;

[0017] The dynamic matrix A is expressed as:

[0018]

[0019] where respectively represent the step response coefficients at each sampling moment.

[0020] The further design lies in that

[0021] In S2, the prediction model is constructed according to the dynamic matrix A, the initial prediction output vector y M0 (k) and the optimal control input increment vector Δu 1 (k), and its output is the prediction output vector y M (k) at the current moment. The expression of the prediction model is:

[0022] y M (k) = AΔu 1 (k) + y M0 (k).

[0023] The further design lies in that

[0024] In S3, the prediction error vector e(k + 1) is obtained according to the system output y(k) and the prediction output vector y M (k) at the current moment. The prediction output vector y M (k) is corrected through the prediction error vector e(k + 1) to obtain the corrected prediction output vector y c(k + 1), the corrected predicted output vector y c (k + 1) is shifted to obtain the initial predicted output vector y at time k + 1 M0 (k + 1), specifically:

[0025] S31, according to the system output y(k) at the current time and the predicted output vector y M (k), the prediction error vector e(k + 1) is obtained, and the corrected predicted output vector y is obtained through the prediction error vector e(k + 1) c (k + 1) has the following expression:

[0026] y c (k + 1) = y M (k) + h 1 e(k + 1)

[0027] Where,

[0028]

[0029] e(k + i) = y(k) - y M (k) (i = 1, … P)

[0030] In the formula, h 1 is the correction vector, h 1 is the correction coefficient, and i represents the time variable in the prediction domain;

[0031] S32, at time k + 1, the corrected predicted output vector y is shifted using the shift matrix c (k + 1) to obtain the initial predicted output vector y at time k + 1 M0 (k + 1), the initial predicted output vector y at time k + 1 M0 (k + 1) and the corrected predicted output vector y c (k + 1) have the following relationship:

[0032] y M0 (k + 1) = S · y c (k + 1)

[0033] Where, the shift matrix S is expressed as follows:

[0034]

[0035] In the formula, S ∈ R P×P .

[0036] Furthermore, the design is as follows,

[0037] In S4, according to the reference trajectory vector W(k) and the predicted output vector y M(k) Construct the objective function and solve the optimal solution of the objective function Specifically:

[0038] Under unconstrained conditions, the objective function is as follows:

[0039]

[0040] In the formula, Q and R are weight matrices, and their expressions with W(k) are as follows:

[0041]

[0042] w(k + i) = (1 - α i )r + α i y(k) (i = 1, 2, …, P)

[0043] Q = q·I P×P

[0044]

[0045] Among them, α is the softening coefficient, q, is the weight value, and I is the identity matrix.

[0046] The optimal solution of the objective function is:

[0047]

[0048] In the formula, Δu 1 (k) is the optimal control input increment vector at time k.

[0049] Furthermore, the design is as follows.

[0050] In S4, construct the objective function according to the reference trajectory vector W(k) and the predicted output vector y M (k) and solve the optimal solution of the objective function Specifically:

[0051] Under the control input constraint conditions, the objective function is as follows:

[0052]

[0053] s.t.: u min ≤ u(k) ≤ u max

[0054] In the formula, u(k) is the control input directly entering the controlled object at each sampling time, and u max and u min respectively represent the upper and lower bounds of u(k) (i.e., the limit of the driving torque provided by the motor);

[0055] To solve the optimal solution of the objective function, it is necessary to first perform a transformation of the control input constraint, and equivalently transform the constraint on u into the constraint on u 1 The expression of the constraint transformation is as follows:

[0056]

[0057] In the formula, b 0 is the controller gain; are the estimates of the system output y, the estimate of the derivative of the system output y, and the estimate of the total disturbance by the extended state observer respectively, u 1max and u 1min respectively represent the upper and lower bounds of u 1 (k) after transformation.

[0058] Then, combined with the prediction model, the objective function is transformed into:

[0059]

[0060] s.t.: u 1min ≤u 1 (k) ≤ u 1max

[0061] In the formula, E = W(k) - y M0 (k) is an intermediate variable;

[0062] The objective function is transformed into a quadratic programming problem as:

[0063]

[0064] s.t.: A q Δu 1 ≤ b q

[0065] where,

[0066]

[0067]

[0068] The optimal solution of the objective function is obtained as:

[0069] Furthermore, the design is that the controlled object is a quadrotor UAV.

[0070] An active disturbance rejection control system with control input constraints includes the following modules:

[0071] Dynamic matrix establishment module: Perform a unit step response test on the ideal closed-loop transfer function of the ADRC system, and obtain the step response coefficient from the output response value Thus, the dynamic matrix A in the prediction model is obtained, where A ∈ R P×M , P is the prediction horizon, and M is the control horizon;

[0072] Prediction model construction module: At the current moment k, according to the dynamic matrix A, the initial prediction output vector y M0 (k) and the optimal control input increment vector Δu 1 (k), a prediction model is constructed, and its output is the prediction output vector y M (k) at the current moment. The initial values of the initial prediction output vector y M0 (k) and the optimal control input increment vector Δu 1 (k) are both set to zero vectors;

[0073] Correction module: Based on the system output y(k) and the prediction output vector y M (k) at the current moment, the prediction error vector e(k + 1) is obtained. The prediction output vector y M (k) is corrected through the prediction error vector e(k + 1) to obtain the corrected prediction output vector y c (k + 1). The corrected prediction output vector y c (k + 1) is shifted to obtain the initial prediction output vector y M0 (k + 1) at the moment k + 1, which is used to update the prediction output vector y M (k + 1);

[0074] Optimization module: Based on the system output y(k) and the reference input r at the current moment, the reference trajectory vector W(k) is updated. The objective function is constructed from the reference trajectory vector W(k) and the prediction output vector y M (k), and the optimal solution of the objective function is obtained and is used as the optimal control input increment vector Δu 1 (k + 1) at the moment k + 1, which is used to update the prediction output vector y M (k + 1);

[0075] Update and control module: The optimal control input increment vector is output to the prediction model to update the prediction output vector with the initial prediction output vector y M0 (k + 1) at the moment k + 1;

[0076] The optimal control input increment vector is output in another path. Its first element is taken as the control input, and after differential conversion, the control signal u 1 (k) is obtained, and it is converted into a continuous control signal u 1As the input of the ADRC system, the system output y is converted into a discrete system output y(k) by a zero-order holder and fed back to the reference trajectory vector W(k) and the prediction model respectively.

[0077] An electronic device comprises a memory and a processor, wherein the memory stores a computer program, and the processor is used to call and run the computer program stored in the memory to execute the method as claimed in any one of claims 1 to 7.

[0078] A computer-readable storage medium stores a computer program, wherein the computer program, when executed by a processor, implements the steps of any of the above methods.

[0079] Compared with the prior art, the present invention has the following beneficial effects:

[0080] The present invention provides an anti-disturbance control system and method with control input constraints, and constructs a prediction model of the system based on the ideal closed-loop transfer function of the ADRC system. Since the ADRC system regards unmodeled dynamics and external disturbances as total disturbances, and estimates and compensates for the total disturbances through an extended state observer and control law, the prediction model of the DMC system established based on the ADRC system is more accurate and has better control performance.

[0081] The present invention introduces the DMC system based on the fact that the ADRC system cannot handle constraints, so that the entire system has a good ability to handle input constraints. At the same time, ADRC overcomes the deficiency that the DMC system can only control asymptotically stable objects. The combination of the ADRC system and the DMC system can realize the control of any object, such as a drone itself is not asymptotically stable object, or other control situations that require constraints.

[0082] The ADRC-CIC control method proposed in the present invention can be designed by considering the control input constraints. Through the constraint conversion method, the control input constraints of ADRC can be successfully converted into constraints that can be directly processed by the optimization module. Therefore, ADRC-CIC can be used to solve control problems with control input constraints, which combines the strong robustness of ADRC and the ability of DMC to handle constraints. BRIEF DESCRIPTION OF THE DRAWINGS

[0083] Figure 1 It is a control structure diagram of ADRC-CIC in the embodiment;

[0084] Figure 2 This is a comparison chart of the tracking effect under nominal conditions and with disturbance added in the test example;

[0085] Figure 3 It is a comparison chart of control effects under control input constraints in the test instance;

[0086] Figure 4 It is a comparison diagram of control signals under control input constraints in the test example;

[0087] Figure 5 It is the effect diagram of the control signal with the addition of constraints of ADRC-CIC under control input constraints in the test example;

[0088] Figure 6 It is a comparison diagram of the control effect of control amplitude limiting and control constraint conversion in the test example;

[0089] Figure 7 It is one of the comparison diagrams of the control effect of ADRC control amplitude limiting and ADRC-CIC control constraint conversion in the test example;

[0090] Figure 8 It is the second comparison diagram of the control effect of ADRC control amplitude limiting and ADRC-CIC control constraint conversion in the test example; Specific implementation manner

[0091] Example 1:

[0092] The active disturbance rejection control method with control input constraints of the present invention adopts a double-closed-loop control system, with dynamic matrix control in the outer loop and ADRC system control in the inner loop, and includes the following steps:

[0093] S1. Conduct a unit step response test on the ideal closed-loop transfer function of the ADRC system, and obtain the step response coefficient from the output response value Thus, the dynamic matrix A in the prediction model is obtained, where A ∈ R P×M , P is the prediction time domain, and M is the control time domain;

[0094] S2. At the current moment k, construct a prediction model according to the dynamic matrix A, the initial prediction output vector y M0 (k) and the optimal control input increment vector Δu 1 (k), and its output is the prediction output vector y M (k) at the current moment; the initial values of the initial prediction output vector y M0 (k) and the optimal control input increment vector Δu 1 (k) are both set to zero vectors;

[0095] S3. Obtain the prediction error vector e(k + 1) according to the system output y(k) and the prediction output vector y M (k) at the current moment, and correct the prediction output vector y M (k) through the prediction error vector e(k + 1) to obtain the corrected prediction output vector y c (k + 1), and use the corrected prediction output vector yc The initial predicted output vector y at time (k + 1) is obtained by shifting (k + 1) M0 (k + 1), which is used to update the predicted output vector y at time (k + 1) M (k + 1);

[0096] S4. According to the system output y(k) and the reference input r at the current time, update the reference trajectory vector W(k). Construct an objective function from the reference trajectory vector W(k) and the predicted output vector y M (k), and find the optimal solution of the objective function And use as the optimal control input increment vector Δu at time (k + 1) 1 (k + 1), which is used to update the predicted output vector y at time (k + 1) M (k + 1);

[0097] S5. The optimal control input increment vector One way is output to the prediction model and update the predicted output vector with the initial predicted output vector y at time (k + 1) M0 (k + 1);

[0098] The optimal control input increment vector The other way is to output and take its first element as the control input, and perform differential transformation to obtain the control signal u 1 (k), and convert it into a continuous control signal u through a zero-order hold 1 As the input of the ADRC system, the system output y is converted into a discrete system output y(k) through a zero-order hold and respectively fed back to the reference trajectory vector W(k) and the prediction model.

[0099] Embodiment 2:

[0100] The active disturbance rejection control method with control input constraints of the present invention adopts a double closed-loop control system. The outer loop adopts dynamic matrix DMC control, and the inner loop adopts ADRC system control. The controlled object can be a quadrotor UAV, and includes the following steps:

[0101] S1. The structure of the ADRC-CIC of the present invention is as Figure 1 shown. Under the ADRC-CIC framework, the controlled object of DMC is replaced by a second-order closed-loop ADRC system. The prediction model of ADRC-CIC adopts the ideal closed-loop transfer function of the closed-loop ADRC system as follows:

[0102]

[0103] Wherein, G(s) represents the ideal closed-loop transfer function of the ADRC system, y(s) represents the Laplace transform of the output, r(s) represents the Laplace transform of the input, s represents the Laplace operator, and K p and K d are the PD controller gains.

[0104] Figure 1 In, r is the reference value, W(k) is the reference trajectory vector, and u 1 (k) is the optimal control input vector, and u 1 is the continuous optimal control input of u 1 (k), Δu 1 (k) is the optimal control input increment vector, and y M is the predicted output vector.

[0105] Let P be the prediction horizon, M be the control horizon, k be the current time, and the control increment be Δu 1 (k) = [Δu 1 (k|k), Δu 1 (k + 1|k), …, Δu 1 (k + M - 1|k)] T , at the time of (k + M), Δu 1 (k + M|k) = Δu 1 (k + M + 1|k) = … = 0. Let be the step response coefficient of the prediction model, then the prediction model (1) is expressed as

[0106]

[0107] Wherein, i represents the time variable in the prediction domain;

[0108] Perform a unit step response test on the ideal closed-loop transfer function of the ADRC system, and obtain the step response coefficient from the output response value Thereby obtaining the dynamic matrix A in the prediction model, where A ∈ R P×M ;

[0109]

[0110] Wherein, respectively represent the step response coefficients at each sampling time;

[0111] S2. Construct a prediction model based on the dynamic matrix A, the initial predicted output vector y M0 (k), and the optimal control input increment vector Δu 1 (k), and its output is the predicted output vector y M (k) (the initial predicted output vector y M0(k) and the initial value of the optimal control input increment vector Δu 1 (k) are both set to the zero vector); Let y M (k) = [y M (k + 1|k), y M (k + 2|k), …, y M (k + P|k)] T be the predicted output vector, then the prediction model (2) can be rewritten as

[0112] y M (k) = AΔu 1 (k) + y M0 (k) (4)

[0113] where y M0 (k) = [y M0 (k + 1|k), y M0 (k + 2|k), …, y M0 (k + P|k)] T is the initial predicted output vector, and Δu 1 (k) = [Δu 1 (k|k), Δu 1 (k + 1|k), …, Δu 1 (k + M - 1|k)] T is the control increment vector.

[0114] S3. Obtain the prediction error vector e(k + 1) based on the current system output y(k) and the predicted output vector y M (k), and correct the predicted output vector y M (k) through the prediction error vector e(k + 1) to obtain the corrected predicted output vector y c (k + 1). Shift the corrected predicted output vector y c (k + 1) to obtain the initial predicted output vector y M0 (k + 1) at time k + 1, which is used to update the predicted output vector y M (k + 1) at time k + 1;

[0115] S31. For the model mismatch caused by interference, the predicted output should be corrected through the prediction error. The corrected predicted output vector can be expressed as:

[0116] y c (k + 1) = y M (k) + h 1 e(k + 1) (5)

[0117] Specifically,

[0118]

[0119] where h 1 is the correction vector, h 1 is the correction coefficient, and i represents the time variable in the prediction domain;

[0120] S32. At time k + 1, the adopted shift matrix shifts the corrected predicted output vector y c (k + 1) to obtain the initial predicted output vector y M0 (k + 1) at time k + 1. The relationship between the initial predicted output vector y M0 (k + 1) at time k + 1 and the corrected predicted output vector y c (k + 1) is as follows:

[0121] y M0 (k + 1) = S · y c (k + 1) (7)

[0122] where the shift matrix S is

[0123]

[0124] where S ∈ R P×P .

[0125] S4. Update the reference trajectory vector W(k) according to the system output y(k) and the reference input r at the current time. Construct an objective function from the reference trajectory vector W(k) and the predicted output vector y M (k), and find the optimal solution of the objective function and take as the optimal control input increment vector Δu 1 (k + 1) at time k + 1, which is used to update the predicted output vector y M (k + 1) at time k + 1 in Equation (4);

[0126] S41. Since the desired predicted output should be as close as possible to the desired value and the control increment Δu 1 (k) cannot change suddenly, at time k, an objective function can be constructed under unconstrained conditions as follows:

[0127]

[0128] where Q and R are weight matrices, and their expressions with W(k) are as follows:

[0129]

[0130] where α is the softening coefficient, q, is the weight value, and I is the identity matrix.

[0131] Based on Equation (9), the optimal solution of the objective function without constraints is as follows:

[0132]

[0133] where Δu 1 (k) is the optimal control input increment vector at time k.

[0134] At time (k + 1), the control increment vector in Equation (4) can be replaced by That is

[0135]

[0136] Take The first element is the current control increment

[0137]

[0138] Then the current optimal control input is

[0139]

[0140] Or adopt S42. For the constrained optimization problem:

[0141] Under the control input constraint conditions, the objective function is as follows:

[0142]

[0143] where u(k) is the control input directly entering the controlled object at each sampling time, u max and u min respectively represent the upper and lower bounds of u(k) (i.e., the limits of the driving torque provided by the motor);

[0144] Figure 1 The optimization module in 1 can solve the constrained optimization problem. Since DMC cannot directly solve the optimization problem with u constraints, the constraints of u should be equivalently transformed into the constraints of u Figure 1 1 The relationship between u and u

[0145]

[0146] where u 1 (k) is the control signal obtained by differential transformation, u 1 is the continuous control signal input to the ADRC system obtained by transformation, and u is the control signal output by the ADRC system;

[0147] Substituting the bound in (16) into (15) gives an equivalent transformation of the constraint on u into the constraint on u 1 , and the expression for the constraint transformation is as follows:

[0148]

[0149] where b 0 is the controller gain; are the estimates of the system output y, the derivative of the system output y, and the total disturbance by the extended state observer respectively, and u 1max and u 1min represent the upper and lower bounds of u 1 (k) after transformation respectively.

[0150] From (17), it can be seen that if u 1min ≤u 1 (k)≤u 1max holds, then u min ≤u(k)≤u max also holds. Therefore, an equivalent optimization problem for (15) can be established as:

[0151]

[0152] Substituting (4) into (18) gives

[0153]

[0154] where E = W(k) - y M0 (k) is an intermediate variable; E T QE is a constant and has no effect on the optimal solution of J(Δu 1 ), so it is discarded.

[0155] The objective function is transformed into a quadratic programming problem, and according to (19), it can be derived as:

[0156]

[0157] where

[0158]

[0159] Then the optimal solution of (20) is:

[0160]

[0161] For (21), the current optimal control increment can be obtained from (13); then, the current optimal control input can be obtained through (14). Finally, replace u 1 in (16) with It can satisfy the constraint on the control signal u in (15).

[0162] S5. The optimal control input increment vector One way is to output it to the prediction model and update the prediction output vector y M0 (k + 1) of the (k + 1)-th moment for the update of the prediction output vector;

[0163] The optimal control input increment vector The other way is to take its first element as the control input, perform differential transformation to obtain the control signal u 1 (k), and convert it into a continuous control signal u through a zero-order hold 1 As the input of the ADRC system, the system output y is converted into a discrete system output y(k) through a zero-order hold and fed back to the reference trajectory vector W(k) and the prediction model respectively.

[0164] Embodiment 3:

[0165] This example provides an active disturbance rejection control system with control input constraints, including the following modules:

[0166] Dynamic matrix establishment module: Conduct a unit step response test on the ideal closed-loop transfer function of the ADRC system, and obtain the step response coefficient from the output response value Thereby obtaining the dynamic matrix A in the prediction model, where A ∈ R P×M , P is the prediction time domain, and M is the control time domain;

[0167] Prediction model construction module: At the current moment k, according to the dynamic matrix A, the initial prediction output vector y M0 (k) and the optimal control input increment vector Δu 1 (k) to construct a prediction model, and its output is the prediction output vector y M (k) at the current moment;

[0168] Correction module: Obtain the prediction error vector e(k + 1) according to the system output y(k) and the prediction output vector y M (k) at the current moment, and correct the prediction output vector y M (k) through the prediction error vector e(k + 1) to obtain the corrected prediction output vector y c (k + 1), and shift the corrected prediction output vector y c (k + 1) to obtain the initial prediction output vector y M0 (k + 1) at the (k + 1)-th moment;

[0169] Optimization module: According to the system output y(k) and the reference input r at the current moment, update the reference trajectory vector W(k), and construct an objective function from the reference trajectory vector W(k) and the predicted output vector y M (k), and find the optimal solution of the objective function And use As the optimal control input increment vector Δu 1 (k + 1) at the (k + 1)-th moment;

[0170] Update and control module: The optimal control input increment vector One way outputs to update the predicted output vector with the initial predicted output vector y M0 (k + 1) at the (k + 1)-th moment;

[0171] Optimal control input increment vector The other way outputs, takes its first element as the control input, performs differential conversion to obtain the control signal u 1 (k), and converts it into a continuous control signal u 1 As the input of the ADRC system, the system output y is converted into a discrete system output y(k) and fed back to the reference trajectory vector W(k) and the prediction model respectively.

[0172] Example 4:

[0173] This example provides an electronic device, which includes a memory and a processor. The memory stores a computer program, and the processor is used to call and run the computer program stored in the memory to execute the method of the above example.

[0174] Example 5:

[0175] This example provides a computer-readable storage medium, which stores a computer program. When the computer program is executed by a processor, it realizes the steps of the method of the above example.

[0176] Test example:

[0177] The effectiveness of the active disturbance rejection control system with control input constraints ADRC-CIC of the present invention will be verified from hardware-in-the-loop (HIL) experiments. All HIL experiments are carried out under natural wind disturbances. Since the control of the three attitudes is similar, and it is easier to achieve the desired closed-loop performance in the yaw channel than in the roll and pitch channels, only the closed-loop responses of the roll and pitch angles are shown. In addition, ADRC-CIC is also discussed. The controller parameters are shown in Table 1. To quantitatively compare the results, two metrics are calculated. The metric values and improvements are listed in Tables 2 and 3 respectively.

[0178] In the experiment, the following conditions are as follows:

[0179] 1. ADRC-CIC (standard), representing the control system of the present invention, includes a second-order ADRC system, a controlled object, and a dynamic matrix control module. The second-order ADRC system includes an extended state observer (ESO) and a PD controller. The controlled object is a quadrotor UAV; the dynamic matrix control module includes a prediction model, an optimization unit, a feedback, and a correction unit. Specifically, as shown in Figure 1 where the dynamic matrix control module has no constraints.

[0180] 2. ADRC-CIC (with constraints), which means that on the basis of ADRC-CIC (standard), the dynamic matrix module adds control input constraints and performs constraint conversion, and then re-seeks the optimal solution. The constraint condition is: ±0.001 N-m.

[0181] 3. ADRC-CIC (with disturbance), which means that on the basis of ADRC-CIC (standard), at 42.5 seconds, a constant disturbance with an amplitude of 0.03 N-m is added to the roll channel of the controlled object.

[0182] 4. ADRC-CIC (clipping) means that on the basis of ADRC-CIC (standard), the control signal u is clipped, and the clipping range is (0.001 < u < +0.001).

[0183] 5. ADRC (standard) includes an extended state observer (ESO) and a PD controller.

[0184] 6. ADRC (with disturbance), which means that on the basis of ADRC (standard), at 42.5 seconds, a constant disturbance with an amplitude of 0.03 N-m is added to the roll channel of the controlled object.

[0185] 7. ADRC (clipping) means that on the basis of ADRC (standard), the control signal u is clipped, and the clipping range is (0.001 < u < +0.001).

[0186] In Table 1, ω o is the observer bandwidth; ω c is the controller bandwidth; b 0 is the controller gain; P is the prediction horizon; M is the control horizon; q is a weight; r is a weight; h 1 is the correction coefficient; α is the softening coefficient.

[0187] Table 1 Controller Parameters

[0188]

[0189] Table 2 Performance Indicators

[0190]

[0191]

[0192] Table 3 Performance Index Improvement

[0193]

[0194] There are the following indexes, and their calculation methods are given

[0195]

[0196] Among them, e 1 = r - y represents the attitude tracking error, r represents the desired attitude, y represents the actual attitude, u is the control signal, ITAE represents the integral of time multiplied by the absolute error, and E represents the integral of the square of the control signal.

[0197] Experiments 1 to 3 were all carried out on a hardware-in-the-loop (HIL) platform with a sampling period of 4 ms.

[0198] Experiment 1: Under nominal conditions, ADRC and ADRC-CIC were compared;

[0199] Experiment 2: In order to demonstrate the control performance of ADRC-CIC (with constraints), a control input constraint conversion was added in Experiment 2.

[0200] Experiment 3: The control signal clipping strategy and the control constraint conversion method were compared.

[0201] Experiment 1: Tracking Performance and Disturbance Rejection Test under Nominal Conditions

[0202] Let the target values of the roll angle and pitch angle be 12°, and the test time be 70 seconds. The step response was given to compare ADRC-CIC and ADRC under nominal conditions.

[0203] First, from 0 seconds to 40 seconds, ADRC-CIC (standard) and ADRC (standard) were tested, that is, the tracking performance under nominal conditions.

[0204] Then, at 42.5 seconds, a constant disturbance with an amplitude of 0.03 N-m was added to the roll channel of both systems to test the disturbance rejection ability of ADRC-CIC (with disturbance) and ADRC (with disturbance).

[0205] At the same time, the same disturbance was added to the pitch channel at 49.5 s. The index values of the roll angle were calculated from 37.5 seconds to 53 seconds, and the values of the pitch angle were calculated from 44.5 seconds to 60 seconds.

[0206] As Figure 2As shown in (a) and (b), under nominal conditions, both ADRC (standard) and ADRC-CIC (standard) can track the target roll angle and pitch angle. During the rising stage, the response speed of ADRC is slightly faster than that of ADRC-CIC. After that, the response of ADRC fluctuates around the reference point with a large error. However, finally, both reach the reference point almost simultaneously. Due to the slower response of ADRC-CIC during the rising stage, its ITAE value is slightly larger than that of ADRC. It can be seen from the E index in Experiment 1 of Table 2 that ADRC-CIC consumes slightly more energy. This is due to the slow response of the outer-loop DMC. Generally speaking, the performance of ADRC-CIC and ADRC is similar under nominal conditions.

[0207] After adding disturbances, as Figure 2 shown in (a) and (b), the responses of ADRC (with disturbances) and ADRC-CIC (with disturbances) deviate from the reference values. In contrast, the fluctuation amplitude of ADRC-CIC is slightly smaller than that of ADRC, and it is more obvious in the pitch channel. However, during the recovery stage, ADRC returns to the reference faster. It can be known from the E index in Experiment 1 of Table 2 that after adding disturbances, the control energies consumed by ADRC-CIC and ADRC are similar.

[0208] Therefore, for the double-closed-loop structure, ADRC-CIC has better anti-interference ability than ADRC. However, due to the slow response of the outer loop, the speed of ADRC-CIC returning to the reference value is slower than that of ADRC, resulting in the tracking error of ADRC-CIC may be larger than that of ADRC.

[0209] Figure 2 ADRC (standard / with disturbances) and ADRC-CIC (standard / with disturbances) in respectively represent controlling under nominal conditions first and then adding disturbance control.

[0210] Experiment 2: Tracking performance test under control input constraints

[0211] Based on the above results under nominal conditions, the next step is to test the performance of ADRC-CIC after the control input constraint conversion. In this case, the reference is set to 0°. The control input constraint is ±0.001 N-m.

[0212] This part of the test compares the performance of ADRC (standard), ADRC-CIC (standard), and ADRC-CIC (with constraints).

[0213] As Figure 3 shown in (a) and (b), the attitude is not controlled by ADRC (standard) (blue solid line) and ADRC-CIC (standard) (green dashed line). On the contrary, as Figure 3As shown in (a) and (b), ADRC-CIC (with constraints) (black dashed line) can keep the attitude response stable near 0°, with the maximum roll angle error being 0.37° and the maximum pitch angle error being 0.43°.

[0214] As Figure 4 shown by the roll angle control signal and pitch angle control signal in (a) and (b), due to not considering constraints, the control inputs of ADRC (standard) and ADRC-CIC (standard) differ greatly, and the attitude is still uncontrollable. However, Figure 5 it can be found from (a) and (b) that the control input of ADRC-CIC (with constraints) is strictly within the range of ±0.001 N m. It can also be seen from the ITAE and E indexes in Experiment 2 of Table 2 that when considering control constraints, smaller control energy results in smaller tracking errors.

[0215] The results show that constraints are crucial for the stability of the quadrotor UAV system. Through the proposed constraint transformation method, ADRC-CIC can effectively handle control input constraints, and the performance of ADRC-CIC (with constraints) is better than that of ADRC-CIC (standard) and ADRC (standard) in terms of both control ability and tracking error.

[0216] Experiment 3: Comparison of control amplitude limiting and control constraint conversion

[0217] A comparative experiment was designed to clarify the difference between the control amplitude limiting strategy and the control constraint conversion method.

[0218] This part tests and compares the performance of ADRC (amplitude limiting), ADRC-CIC (amplitude limiting), and ADRC-CIC (with constraints).

[0219] From Figure 6 (a) and (b), it can be seen that ADRC-CIC (amplitude limiting) (green dashed line) makes the attitude angle uncontrollable. While ADRC (amplitude limiting) (blue solid line) and ADRC-CIC (with constraints) (black dashed line) can keep the attitude response stable around 0°.

[0220] In addition, the results of ADRC (amplitude limiting) and ADRC-CIC (with constraints) were compared, as Figure 7As shown in (a) and (b) in the figure. The results show that the attitude response of ADRC-CIC (with constraints) (blue dashed line) is significantly better than that of ADRC (with amplitude limiting) (green solid line). In addition, from the ITAE index and E index of Experiment 3 in Table 3, it can be seen that under the condition of similar control energy, for the roll angle, compared with ADRC (with amplitude limiting), the ITAE value of ADRC-CIC (with constraints) is reduced by 50.5%. At the same time, the pitch angle is reduced by 48.6%, indicating that the tracking performance of ADRC-CIC (with constraints) is significantly better than that of ADRC (with amplitude limiting). At the same time, as Figure 8 shown in (a) and (b) in the figure, the control inputs of ADRC (with amplitude limiting) and ADRC-CIC (with constraints) are strictly within the range of ±0.001 N-m.

[0221] Therefore, it can be seen from the results that by solving the optimization problem, more reasonable control signals can be obtained, thereby achieving better performance. On the contrary, directly limiting the control input has worse performance than the method of control constraint transformation.

Claims

1. An active disturbance rejection control method with control input constraints, characterized in that: The method adopts a double closed-loop control system, the outer loop adopts dynamic matrix control, and the inner loop adopts ADRC system control, including the following steps: S1. Perform a unit step response test on the ideal closed-loop transfer function of the ADRC system and obtain the step response coefficient from the output response value. Thus, the dynamic matrix A in the prediction model is obtained, where A∈R P×M , P is the prediction time domain, M is the control time domain; S2. The current moment is moment k, according to the dynamic matrix A, the initial prediction output vector y M0 (k) and the optimal control input increment vector Δu1(k) to construct a prediction model, whose output is the predicted output vector y at the current moment M (k) S3. Based on the current system output y(k) and the predicted output vector y M (k) obtains the prediction error vector e(k+1), and uses the prediction error vector e(k+1) to predict the output vector y M (k) Correction is performed to obtain the corrected prediction output vector y c (k+1), the corrected prediction output vector y c (k+1) shifts to get the initial prediction output vector y at time k+1 M0 (k+1); S4. Update the reference trajectory vector W(k) according to the current system output y(k) and the reference input r, and update the reference trajectory vector W(k) with the predicted output vector y M (k) Construct the objective function and find the optimal solution for the objective function and will As the optimal control input increment vector Δu1(k+1) at time k+1 S5. The optimal control input increment vector One output is the initial prediction output vector y at the k+1 time M0 (k+1) Update the predicted output vector; Optimal control input increment vector The first element of the other output is taken as the control input, and the differential transformation is performed to obtain the control signal u1(k), which is converted into a continuous control signal u1 as the input of the ADRC system. The system output y is converted into a discrete system output y(k) and fed back to the reference trajectory vector W(k) and the prediction model respectively.

2. The active disturbance rejection control method with control input constraints according to claim 1, characterized in that: In S1, the expression of the ideal closed-loop transfer function of the ADRC system is as follows: Where G(s) represents the ideal closed-loop transfer function of the ADRC system, y(s) represents the Laplace transform of the output, r(s) represents the Laplace transform of the input, s represents the Laplace operator, and K p , K d is the PD controller gain; The dynamic matrix A is expressed as: In the formula, Represent the step response coefficient at each sampling moment.

3. The active disturbance rejection control method with control input constraints according to claim 2, characterized in that: In S2, the dynamic matrix A and the initial prediction output vector y are M0 (k) and the optimal control input increment vector Δu1(k) to construct a prediction model, whose output is the predicted output vector y at the current moment M (k), the expression of the prediction model is: y M (k)=AΔu1(k)+y M0 (k)。 4. The active disturbance rejection control method with control input constraints according to claim 3, characterized in that: In S3, the system output y(k) at the current moment and the predicted output vector y M (k) obtains the prediction error vector e(k+1), and uses the prediction error vector e(k+1) to predict the output vector y M (k) Correction is performed to obtain the corrected prediction output vector y c (k+1), the corrected prediction output vector y c (k+1) shifts to get the initial prediction output vector y at time k+1 M0 (k+1), specifically: S31, based on the current system output y(k) and the predicted output vector y M (k) obtains the prediction error vector e(k+1), and obtains the corrected prediction output vector y through the prediction error vector e(k+1) c The expression for (k+1) is as follows: y c (k+1)=y M (k)+h1e(k+1) in, e(k+i)=y(k)-y M (k)(i=1,…P) In the formula, h1 is the correction vector, h2 is the correction coefficient, and i represents the moment variable in the prediction domain; S32, at time k+1, the shift matrix used converts the corrected prediction output vector y c (k+1) shift, get the initial prediction output vector y at time k+1 M0 (k+1), the initial prediction output vector y at time k+1 M0 (k+1) and the corrected predicted output vector y c The (k+1) relationship is as follows: and M0 (k+1)=S·y c (k+1) The shift matrix S is expressed as follows: Where S∈R P×P .

5. The active disturbance rejection control method with control input constraints according to claim 4, characterized in that: In S4, according to the reference trajectory vector W(k) and the predicted output vector y M (k) Construct the objective function and find the optimal solution of the objective function Specifically: Under unconstrained conditions, the objective function is as follows: Where Q and R are weight matrices, which are expressed as follows with W(k): w(k+i)=(1-a i )r+a i y(k)(i=1,2,…,P) Q=q·I P×P Among them, α is the softening coefficient, q, is the weight, and I is the unit matrix. The optimal solution of the objective function is: Where Δu1(k) is the optimal control input increment vector at time k.

6. The active disturbance rejection control method with control input constraints according to claim 4, characterized in that: In S4, according to the reference trajectory vector W(k) and the predicted output vector y M (k) Construct the objective function and find the optimal solution of the objective function Specifically: Under the control input constraints, the objective function is as follows: s.t.:u min ≤u(k)≤u max Where u(k) is the control input that directly enters the controlled object at each sampling moment, u max and u min They represent the upper and lower bounds of u(k) respectively; To solve the optimal solution of the objective function, the control input constraint transformation must be performed first, and the constraint on u must be equivalently transformed into the constraint on u1. The constraint transformation expression is as follows: Where b0 is the controller gain; They are respectively the estimation of the system output y by the extended state observer, the estimation of the differential of the system output y, and the estimation of the total disturbance, u 1max and u 1min They represent the upper and lower bounds of u1(k) after transformation respectively. Combined with the prediction model, the objective function is transformed into: s.t.:u 1min ≤u1(k)≤u 1max Where, E = W(k)-y M0 (k) is an intermediate variable; The objective function is converted into a quadratic programming problem: s.t.:A q Δu1≤b q in, The optimal solution of the objective function is obtained as:

7. The active disturbance rejection control method with control input constraints according to claim 5 or 6, characterized in that: The controlled object is a quad-rotor drone.

8. An active disturbance rejection control system with control input constraints, characterized in that: Includes the following modules: Dynamic matrix building module: Perform unit step response test on the ideal closed-loop transfer function of the ADRC system and obtain the step response coefficient from the output response value Thus, the dynamic matrix A in the prediction model is obtained, where A∈R P×M , P is the prediction time domain, M is the control time domain; Prediction model construction module: The current moment is k, according to the dynamic matrix A, the initial prediction output vector y M0 (k) and the optimal control input increment vector Δu1(k) to construct a prediction model, whose output is the predicted output vector y at the current moment M (k); Correction module: Based on the current system output y(k) and the predicted output vector y M (k) obtains the prediction error vector e(k+1), and uses the prediction error vector e(k+1) to predict the output vector y M (k) Correction is performed to obtain the corrected prediction output vector y c (k+1), the corrected prediction output vector y c (k+1) shifts to get the initial prediction output vector y at time k+1 M0 (k+1); Optimization module: According to the current system output y(k) and reference input r, update the reference trajectory vector W(k), which is obtained by combining the reference trajectory vector W(k) with the predicted output vector y M (k) Construct the objective function and find the optimal solution for the objective function and will As the optimal control input increment vector Δu1(k+1) at time k+1; Update and control module: The optimal control input increment vector One output is the initial prediction output vector y at the k+1 time M0 (k+1) Update the predicted output vector; Optimal control input increment vector The first element of the other output is taken as the control input, and the differential transformation is performed to obtain the control signal u1(k), which is converted into a continuous control signal u1 as the input of the ADRC system. The system output y is converted into a discrete system output y(k) and fed back to the reference trajectory vector W(k) and the prediction model respectively.

9. An electronic device, characterized in that: The electronic device comprises a memory and a processor, wherein the memory stores a computer program, and the processor is configured to call and run the computer program stored in the memory to execute the method according to any one of claims 1 to 7.

10. A computer-readable storage medium storing a computer program, characterized in that: When the computer program is executed by a processor, the steps of the method as claimed in any one of claims 1 to 7 are implemented.

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