A nonlinear incremental adaptive dynamic optimization control method for helicopters

Abstract

The present invention discloses a helicopter nonlinear incremental adaptive dynamic optimization control method, including establishing a helicopter maneuvering flight dynamic mathematical model; establishing an incremental control law model of a helicopter angular rate loop; establishing a control law model of a helicopter attitude loop; establishing an optimal incremental control law model of a helicopter speed loop, and completing the design of a helicopter three-loop control model; based on the helicopter three-loop control model, using the maneuvering flight dynamic mathematical model as a tracking signal, realizing the helicopter nonlinear incremental adaptive dynamic optimization control, and verifying the helicopter trajectory tracking performance. The present invention provides a general mathematical description establishment method for the maneuvering flight trajectory, designs the helicopter overall control law, and when a trajectory signal is given, the maneuvering trajectory is tracked and controlled while meeting the helicopter flight characteristics, achieving a satisfactory control effect.

Description

Technical Field

[0001] The invention belongs to the technical field of aircraft control, and in particular relates to a nonlinear incremental adaptive dynamic optimization control method for a helicopter. Background Art

[0002] Compared to fixed-wing aircraft, helicopters have a clear advantage in maneuverability: helicopters can hover for long periods of time, cover flight paths such as vertical takeoff and landing. Helicopters are able to fly backwards, sideways and perform extremely agile maneuvers at high and low airspeeds. These characteristics allow helicopters to perform missions that other aircraft cannot accomplish, including military missions, search and rescue, firefighting and transportation, which are usually performed in urban environments.

[0003] However, helicopters are highly nonlinear and complex systems that are inherently unstable. This is mainly due to the extremely coupled rotor-fuselage interaction, which creates various inter-axis couplings in its response. This behavior makes helicopter flying a very difficult job with an incredible workload for the pilot, especially in fast combat, strong crosswinds or low light conditions. Therefore, the implementation of stability augmentation systems is crucial to ensure the safety and effectiveness of helicopter operations. These current situations clearly demonstrate the necessity of developing control strategies for these highly complex systems.

[0004] The flight control system is crucial to the maneuverability of the aircraft. For this purpose, experts from Europe and the United States, led by the United States, have specially customized the ADS-33E-PRF helicopter flight quality specification, which stipulates 23 types of maneuvering flight subjects, covering all flight subjects from limited maneuverability to rapid maneuverability, and each maneuvering subject stipulates different levels of performance index requirements. The increase in performance requirements has obviously prompted the aerospace industry to develop better flight control laws. They must not only track the reference information input by the pilot, but also ensure the stability of the helicopter and the effectiveness of the flight. In addition, inappropriate control laws may lead to a reduction in its flight envelope due to problems related to actuator saturation during aggressive maneuvers.

[0005] Flight control systems have evolved dramatically over the past few decades, starting with limited-authority analog systems that provide a little stability enhancement up to full-authority digital systems that are essential to guarantee full-envelope performance. Linear controllers represent the simplest form of control systems. Formal analysis of these techniques dates back to the late nineteenth century, and since then, linear controllers have been used in many different types of applications, and several powerful tools have been developed to design them. However, as the name implies, linear controllers are derived based on the feedback of a linear system or the linearization of a nonlinear system with respect to some solution, with the main advantage being that the desired behavior of a linear control system can be systematically specified in the time or frequency domain. This linearization serves only as a good representation of the true nonlinear system in the vicinity of a reference solution, and as the conditions of the system deviate from it, the accuracy of the linear approximation decreases, and the performance of the controller degrades. If the task of the control system involves large ranges or high speeds of motion, nonlinear effects will become significant in the dynamics, and the closed-loop system may become unstable. Helicopters and other modern military aircraft are notable examples of highly nonlinear systems, which are inherently unstable. However, no universal method exists for designing nonlinear controllers, but several different approaches can be taken. For nonlinear systems, concepts such as impulse response or transfer function do not exist. Instead, some qualitative indicators such as accuracy and speed of response are sought in the target operating area.

[0006] To overcome the shortcomings associated with the limited effectiveness of a single linear controller for a nonlinear system, a technique called gain scheduling was intuitively developed. It consists of selecting multiple operating (equilibrium) points covering the entire operating range of the system and for each operating (equilibrium) point, a linear approximation of the nonlinear system is performed and a linear feedback control law is designed. Each of these laws is valid for a neighborhood of a specific point. Between the operating points, the parameters of different controllers are interpolated (scheduled) resulting in a global control system. The main limitations associated with this technique are the complexity of deriving formal stability proofs for such control and the fact that its design is fixed and inflexible. Any mismatch between the model and the real system results in a degradation in performance. Apart from this, the selection of operating points and the individual controller design is a tedious and time-consuming process. Moreover, the final controller still needs to be validated through extensive nonlinear simulations to ensure that the global control law has the desired local properties introduced for its operating point. Gain scheduling is a conceptually simple and well-established approach that has been successfully applied to many complex systems. It remains the mainstream strategy for controlling most of the aircraft. However, the desire for enhanced agility in modern aircraft requires them to operate in a wider range of operating conditions, even at the expense of their own static stability, an expansion that involves not only fundamental changes in their configuration but also the replacement of traditional control strategies by more advanced alternatives based on purely nonlinear controllers. Most importantly, these techniques are able to handle a wider range of conditions for intrinsically nonlinear systems.

[0007] The basic idea behind nonlinear dynamic inversion (NDI) is to first transform the nonlinear system into an equivalent linear system and then use well-known classical linear methods such as proportional-integral-derivative (PID) controllers or linear quadratic regulators (LQR) to complete the design. This transformation is obtained through a combination of state feedback and coordinate transformation, which reduces the dynamics of the controlled variable to a simple integrator. Since the system is linearized after this transformation, a single linear controller is sufficient to ensure control over the entire envelope and gain scheduling is not required. As a result, NDI has become one of the most powerful and commonly used techniques in nonlinear control. After many years of using this type of design, control engineers now believe that NDI will eventually replace gain scheduling as a popular flight control technique. NDI is widely used in aerospace systems because it allows the desired flying qualities to be directly added to the closed-loop response. But its main disadvantage is that it relies on the exact elimination of system nonlinearities. However, in complex systems such as aircraft, the exact elimination of nonlinearities becomes impossible and the performance of the controller deteriorates due to the presence of model uncertainties or frequent changes in their parameters. In addition, the NDI method is only applicable to systems that can be transformed into a linearized form. Such systems are called feedback linearizable systems.

[0008] In response to the model uncertainty problem that often exists in flight systems, the NDI controller has evolved into its incremental form. The main advantage of incremental nonlinear dynamic inversion (INDI) is that since it replaces the control input with incremental instructions, the controller does not need any model data that is completely dependent on the system state, which significantly enhances the robustness of the control law to uncertainty or disturbance modeling. This incremental control law converts the NDI model dependency into a dependency on the system state, thereby improving the measurement accuracy requirements of the sensor. At the same time, the noise interference caused by the acceleration sensor should be minimized. Therefore, the INDI controller is also called a controller based on a measurement sensor.

[0009] In recent years, adaptive optimal control of nonlinear systems has been studied by scholars at home and abroad, represented by Lewis, Zhang Huaguang, Liu Derong, etc., because it combines the advantages of optimal control and adaptive control, overcomes the shortcomings of adaptive control that cannot quantitatively analyze system performance and optimal control parameters cannot be designed online. The core problem of optimal control of nonlinear systems is to solve the sufficient conditions for optimal control, namely the solution of the HJB equation. The HJB equation is the Riccati equation for linear systems, and an analytical solution can be obtained. However, for nonlinear systems or cost functions that are not quadratic forms of states and control inputs, it is necessary to solve the HJB equation to obtain the optimal control strategy, but solving partial differential equations such as HJB is a very difficult task. In addition, as the dimensions of state quantities and input quantities increase, the dynamic programming method will encounter the "curse of dimensionality" problem. Therefore, in order to solve the HJB equation and the need for online design of control parameters and overcome the "curse of dimensionality" problem, scholars at home and abroad have proposed many different adaptive optimal control methods. Werbos first proposed the framework of the adaptive dynamic programming (ADP) method. Its main idea is to use a function approximation structure, such as a neural network, to estimate the cost function for solving dynamic programming problems. The basic structure of ADP technology is the actuator-evaluator structure. The actuator module makes decisions or controls by interacting with the environment, and the evaluator module adjusts the control strategy by judging the performance of the system through the evaluation function. ADP theory integrates methods such as reinforcement learning, dynamic programming and function approximation. It uses the function approximation structure to estimate the cost function and adopts offline or online update methods to approximate the optimal solution of the system, thereby effectively solving the optimal control problem of nonlinear systems. The unique structure of ADP technology makes it show great potential and advantages in solving the control problems of complex nonlinear systems. In recent years, ADP technology has been successfully applied to the fields of electronic systems, intelligent traffic control and industrial control. However, how to combine ADP technology with aerospace applications to solve the control problems of aircraft with strong coupling, complex nonlinearity and high dynamic characteristics has always been a more difficult problem.

[0010] In view of the current research status, the incremental adaptive dynamic optimization method obtained by combining the incremental method with the ADP algorithm can be independent of the current system model information. By online identification of the incremental model of the system, relevant research can be carried out based on the local linear incremental model of the original nonlinear system, which is called heuristic dynamic programming (IHDP) based on the incremental model. Although some scholars have begun to study IHDP, the system control problems that have been considered and studied are still very limited, and there are still many control problems that have not been considered waiting to be studied. Summary of the invention

[0011] The technical problem to be solved by the present invention is to provide a helicopter nonlinear incremental adaptive dynamic optimization control method in view of the shortcomings of the above-mentioned prior art, and to provide a control method based on sensor state feedback in view of the limitations of the existing model-based helicopter nonlinear control system, so that the control system can still quickly and accurately complete the tracking of reference instructions when facing aerodynamic parameter changes and disturbances; according to the time scale separation principle, on the basis of grouping state quantities according to the speed of change over time, the helicopter control law is constructed in a ring-by-ring manner; a general construction method for the mathematical description of the helicopter maneuvering flight trajectory is given, and the speed and yaw angle instructions required for the trajectory can be obtained by giving boundary conditions; when the established maneuvering flight trajectory is given to the control system, the helicopter can achieve a satisfactory tracking effect.

[0012] In order to achieve the above technical objectives, the technical solution adopted by the present invention is:

[0013] A helicopter nonlinear incremental adaptive dynamic optimization control method, comprising:

[0014] Step 1: According to the requirements of the typical maneuvering subjects of ADS-33E-PRF, a mathematical model of the helicopter maneuvering flight trajectory is established as the input signal of the helicopter overall controller. Based on the time scale separation principle, a helicopter three-loop control model is constructed through steps 2-4;

[0015] Step 2: Using the incremental dynamic inversion method to establish the incremental control law model of the helicopter angular rate loop;

[0016] Step 3: Use the dynamic inverse method to establish the control law model of the helicopter attitude loop;

[0017] Step 4: After converting the system state increment equation into the error increment dynamic equation, the optimal increment control law model of the helicopter speed loop is established by using the incremental adaptive dynamic programming method to complete the design of the helicopter overall control law model;

[0018] Step 5: Based on the helicopter three-loop control model, the mathematical model of the maneuvering flight trajectory established in step 1 is used as the tracking signal to implement the helicopter nonlinear incremental adaptive dynamic optimization control and verify the helicopter trajectory tracking performance.

[0019] To optimize the above technical solutions, the specific measures taken also include:

[0020] In the above step 1, according to the time scale separation principle, the helicopter state quantities are divided into angular rate loop, attitude loop and speed loop according to the speed of change;

[0021] The angular rate loop has aerodynamic parameter changes and disturbances, and the attitude loop and the velocity loop have no model uncertainty.

[0022] The optimal incremental control law model of the speed loop is used to track the speed, and the attitude command signal is input to the control law model of the attitude loop to track the attitude angle. The control law model of the attitude loop outputs an angular rate command signal to track the angular rate.

[0023] In the above step 1, the performance indicators of typical maneuvering subjects in the ADS-33E-PRF helicopter flight quality specifications are analyzed, and a dynamic mathematical model of helicopter maneuvering flight is established based on its boundary conditions, including:

[0024] Step 1.1: Divide the maneuver trajectory into several time periods according to the maneuver description, and determine the conditions that need to be achieved in each time period, such as the upper and lower limits of the flight speed, the upper and lower limits of the displacement in each direction, and the upper and lower limits of the attitude angle.

[0025] Step 1.2: Determine a high-order nonlinear function for the displacement in each direction of the ground coordinate system as follows:

[0026] x(t)=a1t 5 +b1t 4 +c1t 3 +d1t 2 +e1t+f1

[0027] Among them, x represents the displacement in the ground coordinate system, a1, b1, c1, d1, e1, f1 are unknown parameters, and t represents time.

[0028] Step 1.3: Substitute the determined boundary conditions into the high-order nonlinear function, solve the unknown coefficients through the method of undetermined coefficients, and obtain the relationship between the displacement of the helicopter in each direction and time in each time period. The relationship between the helicopter speed and time can be obtained by differentiating it with respect to time. At this point, the dynamic mathematical model of helicopter maneuvering flight is established.

[0029] The specific process of step 2 above is:

[0030] Step 2.1: Consider the following angular rate loop model:

[0031]

[0032] Where, ω = [pqr] is the helicopter angular velocity, m is the helicopter moment and J is the helicopter inertia matrix;

[0033] Step 2.2: Combined with the helicopter model information, depending on whether there is a control variable in the model, the above angular rate loop model is written as:

[0034]

[0035] Where f(x) = J -1[m(x)-ω×Jω], g(x,u)=J -1 m(x,u);

[0036] m(x) and m(x,u) represent the torque generated by the component that does not require the manipulated variable input and the torque generated by the component that requires the manipulated variable input, respectively;

[0037] Step 2.3: Carrying out Taylor expansion near x0,u0, we have

[0038]

[0039] Step 2.4: Under the high sampling frequency of the control system, assume that x = x0 and select the virtual control law model Thus the above Taylor expansion is simplified to:

[0040]

[0041] Step 2.5: Solve the partial derivative of g(x,u) with respect to the input information by the central finite difference method;

[0042] Step 2.6: Establish the moment equation for the lateral and longitudinal cyclic pitch and tail rotor collective pitch:

[0043]

[0044] Among them, u'=[θ 1s θ 1c θ 0tr ] are the three control variables of the helicopter except the total distance;

[0045] Step 2.7: The incremental control law model of the angular rate loop is obtained as follows:

[0046]

[0047] The specific process of step 3 above is:

[0048] Step 3.1: Consider the following posture loop model:

[0049]

[0050] Where θ = [φ θ ψ] T is the helicopter Euler angle, and the Ω matrix is:

[0051]

[0052] Step 3.2: Take the virtual control law model of the attitude loop as:

[0053]

[0054] Step 3.3: The control law model of the attitude loop is obtained as follows:

[0055]

[0056] The specific process of step 4 above is:

[0057] Step 4.1: According to the flight characteristics of the helicopter, the yaw angle ψ is obtained and input into the speed controller in the form of a command signal for generating a command signal, and is also input into the control law model of the attitude loop for tracking the attitude angle;

[0058] And the input command signal of the speed controller is three speed commands V xcom ,V ycom ,V zcom and the yaw angle command ψ com ;

[0059] The yaw angle command ψ com It is used to generate control signals that meet the yaw angle. Command tracking will be implemented in the attitude loop.

[0060] The output control signal is the pitch angle θ ref , Roll Angle and the total distance θ 0ref ;

[0061] Wherein the subscripts com and ref both represent reference signals, com represents the required command solved by the speed controller, and ref represents the reference signal generated by the controller and fed into the inner loop;

[0062] Step 4.2: The helicopter trajectory loop model is as follows:

[0063]

[0064] Where x = [V x V y V z ] T ,

[0065] f(·) and g(·) are nonlinear functions;

[0066] Step 4.3: Taylor expand the helicopter trajectory loop model around x0,u0, while ignoring x-x0, and obtain

[0067]

[0068] in

[0069] Step 4.4: Assume the desired state x d Satisfy the following form:

[0070]

[0071] Among them, u d It is the control law model when the system state reaches the expected value;

[0072] The error system is:

[0073]

[0074] Where, e = xx d , Δu e =Δu-Δu d ;

[0075] Where Δu d From the following formula we get

[0076]

[0077] Among them, G -1 represents the generalized inverse of the G matrix;

[0078] Δu d Used to keep the tracking error close to 0;

[0079] Step 4.5: Discretize the error state equation at a high sampling frequency, and we have

[0080] Δe k+1 =G k-1 Δu e,k

[0081] For the optimal control problem in infinite time domain, the control goal is to find the optimal control for the error tracking system so as to minimize the following performance index:

[0082]

[0083] Where Q ≥ 0 and R ≥ 0, the utility function is

[0084]

[0085] The Hamiltonian function is:

[0086]

[0087] Among them, e k+1 =e k +G k-1 Δu e,k ,thereby Using the Bellman optimality principle, The following HJB equation needs to be satisfied:

[0088]

[0089] According to the optimality principle Solve the corresponding single-step optimal incremental control law model in the above formula

[0090]

[0091] Substituting the above formula into the HJB equation, we get

[0092]

[0093] in, In order to solve the above HJB equation, a neural network optimal control algorithm is used to solve it.

[0094] It is approximated by the following neural network function:

[0095]

[0096] in is the activation function, is the ideal weight parameter, is the approximate error of building the neural network;

[0097] Since the target weights are unknown, the cost function It can be estimated by the following formula:

[0098]

[0099] Among them, W k W c The estimated value of (k)||, yes An estimated value of

[0100] So as to evaluate the network error ε k Expressed as

[0101]

[0102] in,

[0103] The target error function is:

[0104]

[0105] The update law of weights is expressed as:

[0106]

[0107] Thus, the optimal incremental control law model is obtained:

[0108]

[0109] The specific process of step 5 above is:

[0110] Step 5.1: Based on the helicopter overall control law model, input the maneuvering flight reference signal and the instructions to be tracked into the controller, including Vx, Vy, Vz and yaw angle ψ;

[0111] Step 5.2: Take the dynamic mathematical model of maneuvering flight established in step 1 as the reference trajectory and obtain the reference signal that satisfies the centripetal rotation trajectory. The desired inner loop instruction is obtained by solving the state of the reference signal,

[0112]

[0113] This results in the error system:

[0114]

[0115] The helicopter trajectory tracking problem is transformed into the adjustment problem of the above error system, the nonlinear incremental adaptive dynamic optimization control of the helicopter is realized, and the helicopter trajectory tracking performance is verified.

[0116] The present invention has the following beneficial effects:

[0117] The invention is based on the mathematical description of helicopter maneuvering flight trajectory that meets the ADS-33E-PRF specification, combined with the analysis of helicopter maneuvering flight characteristics and control problems, and based on the time scale separation principle, the helicopter incremental controller is divided into loops for control according to the speed of state quantity change; based on the full nonlinear model of the helicopter, the controller of the angular rate loop is firstly designed, and considering the uncertainty and interference of aerodynamic parameters in the loop, the incremental dynamic inversion method is adopted to obtain the control law model of the loop, thereby reducing the influence of model uncertainty on the tracking effect; secondly, the attitude loop control law model is constructed, and the dynamic inversion method is adopted to convert the input attitude command into an angular rate command and transmit it to the angular rate loop controller; finally, the trajectory loop controller is designed, and the system state equation is converted into an error dynamic equation, and the helicopter system tracks the speed through the incremental adaptive dynamic programming method, and the trajectory is tracked after integration.

[0118] The present invention designs a helicopter incremental control law model, comprehensively considering the flight control problem when there is model uncertainty; at the same time, a mathematical model of the helicopter maneuvering flight trajectory is established, and the maneuvering trajectory is tracked and controlled while meeting the helicopter flight characteristics, achieving a satisfactory control effect. Specifically:

[0119] 1. The present invention provides a general mathematical description establishment method for maneuvering flight trajectory and designs the overall control law of the helicopter. When the trajectory signal is given, the helicopter system can achieve a satisfactory trajectory tracking effect.

[0120] 1. Different from the control method that requires accurate model information, the control method of the present invention mainly uses the state measured by the sensor as the main basis for designing the control law, and still has good control effect in the presence of model uncertainty and disturbance;

[0121] 2. Different from the traditional incremental dynamic inversion, due to the complex dynamic model of the helicopter, an approximate method is adopted in the speed loop to deal with the relationship between the total pitch and the longitudinal speed. In the present invention, the IADP method is used to design the speed loop control law, optimize the control system, and achieve satisfactory control effect. BRIEF DESCRIPTION OF THE DRAWINGS

[0122] Figure 1 is the reference trajectory for the centripetal rotation maneuver;

[0123] Figure 2 is the angular rate loop tracking curve;

[0124] Figure 3 Tracking curve for attitude loop;

[0125] Figure 4 It is the speed loop tracking curve;

[0126] Figure 5 It is the overall trajectory tracking curve of the helicopter;

[0127] Figure 6 The control principle diagram of the method of the present invention is as follows;

[0128] Figure 7 The diagram of the evaluation network. DETAILED DESCRIPTION

[0129] The embodiments of the present invention are further described in detail below in conjunction with the accompanying drawings.

[0130] See also Figure 6 The present invention provides a helicopter nonlinear incremental adaptive dynamic optimization control method, comprising:

[0131] Step 1: According to the requirements of the typical maneuvering subjects of ADS-33E-PRF, a mathematical model of the helicopter maneuvering flight trajectory is established as the input signal of the helicopter overall controller. After completing the mathematical model of the maneuvering flight trajectory, the helicopter overall control model, i.e. the helicopter three-loop control model, is built through steps 2-4 based on the principle of time scale separation;

[0132] Step 2: Using the incremental dynamic inversion method to establish the incremental control law model of the helicopter angular rate loop;

[0133] Step 3: Use the dynamic inverse method to establish the control law model of the helicopter attitude loop;

[0134] Step 4: After converting the system state increment equation into the error increment dynamic equation, the optimal increment control law model of the helicopter speed loop is established by using the incremental adaptive dynamic programming method to complete the design of the helicopter overall control law model;

[0135] Step 5: Based on the helicopter three-loop control model, the mathematical model of the maneuvering flight trajectory established in step 1 is used as the tracking signal to implement the helicopter nonlinear incremental adaptive dynamic optimization control and verify the helicopter trajectory tracking performance.

[0136] In the embodiment, according to the time scale separation principle, the helicopter state quantities are divided into three groups: angular rate loop, attitude loop and speed loop according to the speed of change;

[0137] The angular rate loop has aerodynamic parameter changes and disturbances, and the attitude loop and the velocity loop have no model uncertainty.

[0138] In the embodiment, the optimal increment control law model of the speed loop is used to track the speed, and the attitude command signal is input to the control law model of the attitude loop to track the attitude angle, and the control law model of the attitude loop outputs the angular rate command signal to track the angular rate;

[0139] In the embodiment, in step 1, the typical maneuvering subject performance indicators in the ADS-33E-PRF helicopter flight quality specification are analyzed, and a helicopter maneuvering flight dynamic mathematical model is established according to its boundary conditions, specifically including:

[0140] Step 1.1: Divide the maneuver trajectory into several time periods according to the maneuver description, and determine the conditions that need to be achieved in each time period, such as the upper and lower limits of the flight speed, the upper and lower limits of the displacement in each direction, and the upper and lower limits of the attitude angle.

[0141] Step 1.2: Determine a high-order nonlinear function (usually the highest power is five, and the rest are undetermined coefficients) for the displacement in each direction of the ground coordinate system as follows:

[0142] x(t)=a1t 5 +b1t 4 +c1t 3 +d1t 2 +e1t+f1

[0143] Among them, x represents the displacement in the ground coordinate system, a1, b1, c1, d1, e1, f1 are unknown parameters, and t represents time.

[0144] Step 1.3: Substitute certain boundary conditions into the high-order nonlinear function, usually displacement, velocity and acceleration. For example, the displacement of the helicopter at the initial moment is 0, the flight speed is V, and the acceleration is 0. The unknown coefficients are obtained by the method of undetermined coefficients.

[0145]

[0146] Similarly, by substituting the boundary conditions at other times in the corresponding period, the relationship between the displacement of the helicopter in this direction and time can be solved. The relationship between the helicopter speed and time can be obtained by differentiating it with respect to time. At this point, the dynamic mathematical model of helicopter maneuvering flight is completed.

[0147] In the embodiment, in step 2, on the basis of time scale separation, the controller design is carried out for the angular rate loop with the fastest changing rate. Due to the characteristics of the helicopter, there are a large number of aerodynamic derivative changes in this loop when the state changes, and incremental dynamic inversion is used for control;

[0148] The specific process is:

[0149] Step 2.1: Consider the following angular rate loop model:

[0150]

[0151] Where, ω = [pqr] is the helicopter angular velocity, m is the helicopter moment and J is the helicopter inertia matrix;

[0152] Step 2.2: Combined with the helicopter model information, depending on whether there is a control variable in the model, the above angular rate loop model is written as:

[0153]

[0154] Where f(x) = J -1 [m(x)-ω×Jω], g(x,u)=J -1 m(x,u);

[0155] m(x) and m(x,u) represent the torque generated by the component that does not require the manipulated variable input and the torque generated by the component that requires the manipulated variable input, respectively;

[0156] Step 2.3: Carrying out Taylor expansion near x0,u0, we have

[0157]

[0158] Step 2.4: Under the high sampling frequency (100Hz) of the control system, x=x0 can be considered, and the virtual control law model is selected Thus the above Taylor expansion is simplified to:

[0159]

[0160] Step 2.5: Since the helicopter model contains a large number of nonlinear relationships, it is difficult to solve the partial derivatives of g(x,u) with respect to the input information by analytical methods. Here, the central finite difference method is used for solution.

[0161] Step 2.6: Since the change of collective pitch often causes the vertical speed change of the helicopter, it can be considered that the control variable is more inclined to change the magnitude of the longitudinal force, so the control variable is moved to the speed loop to control the longitudinal speed.

[0162] The torque equation for the lateral and longitudinal periodic pitch change and the tail rotor collective pitch is established as:

[0163]

[0164] Among them, u'=[θ 1s θ 1c θ 0tr ] are the three control variables of the helicopter except the total distance;

[0165] Step 2.7: The incremental control law model of the angular rate loop is obtained as follows:

[0166]

[0167] In the embodiment, the specific process of step 3 is:

[0168] Since the attitude loop does not have the problem of model uncertainty, the control law model of the loop can be directly obtained by dynamic inversion.

[0169] Step 3.1: Consider the following posture loop model:

[0170]

[0171] Where θ = [φ θ ψ] T is the helicopter Euler angle, and the Ω matrix is:

[0172]

[0173] Step 3.2: Take the virtual control law model of the attitude loop as:

[0174]

[0175] Step 3.3: The control law model of the attitude loop is obtained as follows:

[0176]

[0177] In the embodiment, the specific process of step 4 is:

[0178] Step 4.1: According to the flight characteristics of the helicopter, the yaw angle ψ is input into the speed controller in the form of a command signal to generate a command signal, and is also input into the control law model of the attitude loop to track the attitude angle;

[0179] Combined with the analysis in step 2, it can be clearly seen that the input command signal of the speed controller is three speed commands V xcom ,V ycom ,V zcom and the yaw angle command ψ com ;

[0180] The yaw angle command ψ com It is used to generate control signals that meet the yaw angle. Command tracking will be implemented in the attitude loop.

[0181] The output control signal is the pitch angle θ ref , Roll Angle and the total distance θ 0ref ;

[0182] Wherein the subscripts com and ref both represent reference signals, com represents the required command solved by the speed controller, and ref represents the reference signal generated by the controller and fed into the inner loop;

[0183] Step 4.2: The helicopter trajectory loop model is as follows:

[0184]

[0185] Where x = [V x V y V z ] T ,

[0186] f(·) and g(·) are nonlinear functions;

[0187] Step 4.3: Similarly, perform Taylor expansion on the helicopter trajectory loop model around x0,u0, while ignoring x-x0, and obtain

[0188]

[0189] in

[0190] Step 4.4: Assume the desired state x d Satisfy the following form:

[0191]

[0192] Among them, u d It is the control law model when the system state reaches the expected value;

[0193] The error system is:

[0194]

[0195] Where, e = xx d , Δu e =Δu-Δu d ;

[0196] Through the above transformation, the original tracking problem can be transformed into the adjustment problem of the error system.

[0197] From this step, it can be seen that the incremental control law model consists of two parts. One part is the incremental control law Δu under the desired state. d , and the other part is the feedback increment control law Δu e .

[0198] Where Δu d From the following formula we get

[0199]

[0200] Among them, G -1 represents the generalized inverse of the G matrix;

[0201] Δu d Used to keep the tracking error close to 0;

[0202] Step 4.5: Discretize the error state equation at a high sampling frequency, and we have

[0203] Δe k+1 =G k-1 Δu e,k

[0204] In the present invention, for the optimal control problem in infinite time domain, the main control goal is to find the optimal control for the error tracking system so as to minimize the performance index of the following formula:

[0205]

[0206] Where Q ≥ 0 and R ≥ 0, the utility function is

[0207]

[0208] The Hamiltonian function is:

[0209]

[0210] Among them, e k+1 =e k +G k-1 Δu e,k ,thereby Using the Bellman optimality principle, The following HJB (Hamilton-Jacobi-Bellman) equation needs to be satisfied:

[0211]

[0212] According to the optimality principle The corresponding single-step optimal incremental control law model in the above formula can be solved

[0213]

[0214] Substituting the above formula into the HJB equation, we get

[0215]

[0216] in, In order to solve the above HJB equation, a neural network optimal control algorithm is used to solve it.

[0217] It can be approximated by the following neural network function:

[0218]

[0219] in is the activation function, is the ideal weight parameter, is the approximate error in constructing the neural network.

[0220] Since the target weights are unknown, the cost function It can be estimated by the following formula:

[0221]

[0222] Among them, W k W c The estimated value of (k)||, yes An estimated value of

[0223] So as to evaluate the network error ε k It can be expressed as

[0224]

[0225] in,

[0226] The target error function is:

[0227]

[0228] The update law of weights is expressed as:

[0229]

[0230] Thus, the optimal incremental control law model is obtained:

[0231]

[0232] In the embodiment, the specific process of step 5 is:

[0233] Step 5.1: Based on the helicopter overall control law model, input the maneuvering flight reference signal and the instructions to be tracked into the controller, including Vx, Vy, Vz and yaw angle ψ;

[0234] Step 5.2: Take the dynamic mathematical model of maneuvering flight established in step 1 as the reference trajectory and obtain the reference signal that satisfies the centripetal rotation trajectory. The desired inner loop instruction is obtained by solving the state of the reference signal,

[0235]

[0236] This results in the error system:

[0237]

[0238] The helicopter trajectory tracking problem is transformed into the adjustment problem of the above error system, the nonlinear incremental adaptive dynamic optimization control of the helicopter is realized, and the helicopter trajectory tracking performance is verified.

[0239] Example 1

[0240] The helicopter nonlinear incremental adaptive dynamic optimization control method of the present invention is further described in detail below in conjunction with Bo-105 helicopter centripetal rotation maneuver tracking control embodiment 1:

[0241] The method specifically comprises:

[0242] Step 1: Establish the dynamic mathematical model of helicopter maneuver flight for the medium maneuver subject “centripetal rotation” in ADS-33E-PRF, specifically:

[0243] Establishment of mathematical model of centripetal maneuver flight trajectory

[0244] Through the study of the performance indicators of the centripetal rotation maneuver subject in the ADS-33E-PRF helicopter flight quality specification, mathematical models were established according to their boundary conditions. The satisfactory performance of the centripetal rotation subject requires that the body should rotate one circle within 45 seconds. Taking the counterclockwise rotation as an example, the helicopter starts to move laterally around a circle with a radius R of 30.5m from a stable hovering position 20m away from the origin on the z axis. It is assumed that the body reaches the desired lateral speed after hovering for 3s, continues to rotate at a basically constant speed for 37s, and then begins to decelerate. After another 3s, the body returns to the starting point and maintains a stable hover. Since the nose should be aligned with the center of the circle during the rotation process, the relationship between the desired lateral speed and the yaw angular rate is:

[0245] v com =-rR

[0246] Assuming that the starting maneuvering time is zero, combining the consistency of boundary conditions and the continuity of motion state, the yaw rate r (rad / s) that meets the requirements can be obtained as follows:

[0247]

[0248] Thus, the expected lateral velocity in the body coordinate system can be obtained. On this basis, the coordinate transformation matrix T is introduced to transform the velocity in the body coordinate system into the velocity in the ground coordinate system.

[0249]

[0250] The centripetal rotation reference trajectory is obtained as Figure 1 shown.

[0251] Step 2: Combined with the analysis of the maneuvering flight characteristics and control problems of the Bo-105 helicopter, based on the principle of time scale separation, the helicopter incremental controller is divided into loops according to the speed of state quantity change.

[0252] Based on the full nonlinear model of the helicopter, the control law model of the angular rate loop is first designed. Taking into account the uncertainty and interference of the aerodynamic parameters of the loop, the incremental dynamic inversion method is used to obtain the control law model of the loop, thereby reducing the influence of model uncertainty on the tracking effect.

[0253] Specifically:

[0254] Model design of helicopter angular rate loop control law

[0255] On the basis of time scale separation, the controller design of the angular rate loop with the fastest changing rate is carried out. Due to the characteristics of the helicopter, this loop has a large number of aerodynamic derivative changes when the state changes, and the incremental dynamic inversion is used for control. Consider the angular rate loop model of the Bo-105 helicopter

[0256]

[0257] The inertia matrix

[0258] Combined with the helicopter model information, depending on whether there is a control variable in the model, the above formula can be written as

[0259]

[0260] According to the Bo-105 model information, f(x) = J -1 [m fus (x)+m ht (x)+m vt (x)-ω×Jω], g(x,u)=J -1 [m mr (x,u)+m tr (x,u)]. fus ,m ht ,m vt ,m mr ,m tr are the moments generated by the helicopter fuselage, horizontal tail, vertical tail, main rotor and tail rotor respectively. Taylor expansion of the above equation around x0,u0 gives

[0261]

[0262] Under the high sampling frequency (100Hz) of the control system, x=x0 can be considered, and the virtual control law model is selected So the above formula can be simplified to

[0263]

[0264] Since the helicopter model contains a lot of nonlinear relationships, it is difficult to solve the partial derivative of g(x,u) with respect to the input information by analytical method. Here, the central finite difference method is used for solution. Since the change of collective pitch often causes the vertical speed change of the helicopter, it can be considered that the control amount is more inclined to change the magnitude of the longitudinal force, so the control amount is moved to the speed loop to control the longitudinal speed. The torque equation for the lateral and longitudinal periodic pitch change and the tail rotor collective pitch can be obtained by the following expression:

[0265]

[0266] Among them, u'=[θ 1s θ 1c θ 0tr ] are the three control variables of the helicopter except the total distance. Therefore, the incremental control law model of this loop can be expressed as

[0267]

[0268] Given the angular rate command obtained by solving the centripetal rotation trajectory, the tracking status of the ring is obtained as follows Figure 2 shown.

[0269] Step 3: Construct the attitude loop control law model, use the dynamic inversion method to convert the input attitude command into an angular rate command and transmit it to the angular rate loop controller, specifically:

[0270] Design of helicopter attitude control law model

[0271] Since the attitude loop does not have the problem of model uncertainty, the control law model of the loop can be directly obtained by dynamic inversion. Consider the attitude loop model of the Bo-105 helicopter

[0272]

[0273] The Ω matrix is

[0274]

[0275] The virtual control law model of the loop is taken as

[0276]

[0277] The control law model of the loop can be obtained as

[0278]

[0279] Given the attitude angle command obtained by solving the centripetal rotation trajectory, the tracking status of the loop is obtained as follows Figure 3 shown.

[0280] Step 4: Design the speed loop control law model, transform the system state equation into the error dynamic equation, and use the incremental adaptive dynamic programming method to complete the helicopter system's speed tracking, and realize the trajectory tracking after integration, specifically:

[0281] Model Design of Helicopter Speed ​​Loop Control Law

[0282] Due to the flight characteristics of helicopters, the yaw angle ψ is often input into the speed controller in the form of a command signal to generate a command signal, and is also input into the attitude controller for attitude angle tracking. Combined with the analysis in step 2, it can be clearly seen that the input command signals of the speed controller are three speed commands V xcom ,V ycom ,V zcom and the yaw angle command ψ com , where the yaw angle command ψ com It is used to generate the control signal that meets the yaw angle. The command tracking will be realized in the attitude loop. The output control signal is the pitch angle θ ref , Roll Angle and the total distance θ0ref , where the subscripts com and ref both represent reference signals, com represents the required instruction obtained by trajectory solution, and represents the reference signal generated by the controller and fed into the inner loop. The trajectory loop model of the Bo-105 helicopter is as follows

[0283]

[0284] Taylor expansion of the above equation around x0,u0, while ignoring x-x0, yields

[0285]

[0286] Assume that the desired state x d Satisfy the following form

[0287]

[0288] The error system can be expressed as

[0289]

[0290] Through the above transformation, the original tracking problem can be transformed into the regulation problem of the error system. From this step, it can be seen that the incremental control law model consists of two parts. One part is the incremental control law model Δu under the desired state. d , and the other part is the feedback increment control law model Δu e . Where Δu d It can be obtained by the following formula

[0291]

[0292] Among them, G -1 Denotes the generalized inverse of the G matrix. Discretizing the error state equation at a high sampling frequency, we have

[0293] Δe k+1 =G k-1 Δu e,k

[0294] For the optimal control problem in infinite time domain, the main control goal is to find the optimal control for the error tracking system so as to minimize the following performance index:

[0295]

[0296] Pick and The utility function is

[0297]

[0298] The Hamiltonian function is:

[0299]

[0300] Among them, e k+1 =e k +G k-1 Δu e,k ,thereby Using the Bellman optimality principle, The following HJB (Hamilton-Jacobi-Bellman) equation needs to be satisfied:

[0301]

[0302] According to the optimality principle The corresponding single-step optimal incremental control law model in the above formula can be solved

[0303]

[0304] Substituting the above formula into the HJB equation, we get

[0305]

[0306] in, In order to solve the above HJB equation, a neural network optimal control algorithm is used to solve it.

[0307] It can be approximated by the following neural network function:

[0308]

[0309] in is the activation function, is the ideal weight parameter, is the approximate error of building the neural network.

[0310] See also Figure 7 , since the target weight is unknown, the cost function It can be estimated by the following formula:

[0311]

[0312] Among them, W k W c The estimated value of (k)||, yes The estimated value of . Thus, the error ε of the network is evaluated k It can be expressed as

[0313]

[0314] in, The target error function is

[0315]

[0316] The update law of weights can be expressed as

[0317]

[0318] Take the learning rate μ c =0.5, thus obtaining the optimal incremental control law model

[0319]

[0320] Given the speed command obtained by solving the centripetal rotation trajectory, the tracking status of the loop is obtained as follows Figure 4 shown.

[0321] Step 5: Finally, the centripetal maneuver flight trajectory command signal is given to verify the tracking control effect of the control method on the maneuver flight trajectory. Specifically, on the basis of completing the design of the helicopter overall control law model, the centripetal maneuver flight reference signal is given. The commands that need to be tracked are Vx, Vy, Vz and yaw angle ψ. The helicopter position tracking situation is as follows Figure 5 shown.

[0322] The above are only preferred embodiments of the present invention, and the protection scope of the present invention is not limited to the above embodiments. All technical solutions under the concept of the present invention belong to the protection scope of the present invention. It should be pointed out that for ordinary technicians in this technical field, some improvements and modifications without departing from the principle of the present invention should be regarded as the protection scope of the present invention.

Claims

1. A helicopter nonlinear incremental adaptive dynamic optimization control method, characterized in that: include: Step 1: According to the requirements of the typical maneuvering subjects of ADS-33E-PRF, a mathematical model of the helicopter maneuvering flight trajectory is established as the input signal of the helicopter overall controller. Based on the time scale separation principle, a helicopter three-loop control model is constructed through steps 2-4; Step 2: Using the incremental dynamic inversion method to establish the incremental control law model of the helicopter angular rate loop; Step 3: Use the dynamic inverse method to establish the control law model of the helicopter attitude loop; Step 4: After converting the system state increment equation into the error increment dynamic equation, the optimal increment control law model of the helicopter speed loop is established by using the incremental adaptive dynamic programming method to complete the design of the helicopter three-loop control model; Step 5: Based on the helicopter three-loop control model, the mathematical model of the maneuvering flight trajectory established in step 1 is used as the tracking signal to realize the helicopter nonlinear incremental adaptive dynamic optimization control and verify the helicopter trajectory tracking performance; In step 1, according to the time scale separation principle, the helicopter state quantities are divided into angular rate loop, attitude loop and speed loop according to the speed of change; The angular rate loop has aerodynamic parameter changes and disturbances, and the attitude loop and the velocity loop do not have model uncertainty; The optimal incremental control law model of the speed loop is used to track the speed, and the attitude command signal is input to the control law model of the attitude loop to track the attitude angle. The control law model of the attitude loop outputs the angular rate command signal to track the angular rate. In step 1, the typical maneuvering subject performance indicators in the ADS-33E-PRF helicopter flight quality specification are analyzed, and a helicopter maneuvering flight dynamic mathematical model is established according to its boundary conditions, specifically including: Step 1.1: Divide the maneuver trajectory into several time periods according to the maneuver description, and determine the conditions that need to be achieved in each time period, including the upper and lower limits of the flight speed, the upper and lower limits of the displacement in each direction, and the upper and lower limits of the attitude angle; Step 1.2: Determine a high-order nonlinear function for the displacement in each direction of the ground coordinate system as follows: x(t)=a1t 5 +b1t 4 +c1t 3 +d1t 2 +e1t+f1 Among them, x represents the displacement in the ground coordinate system, a1, b1, c1, d1, e1, f1 are unknown parameters, and t represents time; Step 1.3: Substitute the determined boundary conditions into the high-order nonlinear function, solve the unknown coefficients by the method of undetermined coefficients, and obtain the relationship between the displacement of the helicopter in each direction and time in each time period. The relationship between the helicopter speed and time can be obtained by taking the derivative with respect to time. At this point, the mathematical model of the helicopter maneuvering flight trajectory is established; The specific process of step 2 is: Step 2.1: Consider the following angular rate loop model: Where, ω = [pqr] is the helicopter angular velocity, m is the helicopter moment and J is the helicopter inertia matrix; Step 2.2: Combined with the helicopter model information, depending on whether there is a control variable in the model, the above angular rate loop model is written as: where f(x) = J -1 [m(x) - ω × Jω], g(x, u) = J -1 m(x, u); m(x) and m(x,u) represent the torque generated by the component that does not require the manipulated variable input and the torque generated by the component that requires the manipulated variable input, respectively; Step 2.3: Carrying out Taylor expansion near x0,u0, we have Step 2.4: Under the high sampling frequency of the control system, assume that x = x0 and select the virtual control law model Thus the above Taylor expansion is simplified to: Step 2.5: Solve the partial derivative of g(x,u) with respect to the input information by the central finite difference method; Step 2.6: Establish the moment equation for the lateral and longitudinal cyclic pitch and tail rotor collective pitch: Among them, u'=[θ 1s θ 1c θ 0tr ] are the three control variables of the helicopter except the total distance; Step 2.7: The incremental control law model of the angular rate loop is obtained as follows: The specific process of step 3 is as follows: Step 3.1: Consider the following posture loop model: Where θ = [φ θ ψ] T is the helicopter Euler angle, and the Ω matrix is: Step 3.2: Take the virtual control law model of the attitude loop as: Step 3.3: The control law model of the attitude loop is obtained as follows: The specific process of step 4 is as follows: Step 4.1: According to the flight characteristics of the helicopter, the yaw angle ψ is obtained and input into the speed controller in the form of a command signal for generating a command signal, and is also input into the control law model of the attitude loop for tracking the attitude angle; And the input command signal of the speed controller is three speed commands V xcom ,V ycom ,V zcom and the yaw angle command ψ com ; The yaw angle command ψ com It is used to generate control signals that meet the yaw angle. Command tracking will be implemented in the attitude loop. The output control signal is the pitch angle θ ref , Roll Angle and the total distance θ 0ref ; Wherein the subscripts com and ref both represent reference signals, com represents the required command solved by the speed controller, and ref represents the reference signal generated by the controller and fed into the inner loop; Step 4.2: The helicopter trajectory loop model is as follows: Where x = [V x V y V z ] T , f(·) and g(·) are nonlinear functions; Step 4.3: Taylor expand the helicopter trajectory loop model around x0,u0, while ignoring x-x0, and obtain in Step 4.4: Assume the desired state x d Satisfy the following form: Among them, u d It is the control law model when the system state reaches the expected value; The error system is: Where, e = xx d , Δu e =Δu-Δu d ; Where Δu d From the following formula we get Among them, G -1 represents the generalized inverse of the G matrix; Δu d Used to keep the tracking error close to 0; Step 4.5: Discretize the error state equation at a high sampling frequency, and we have No k+1 =G k-1 Thu e,k For the optimal control problem in infinite time domain, the control goal is to find the optimal control for the error tracking system so as to minimize the following performance index: Where Q ≥ 0 and R ≥ 0, the utility function is The Hamiltonian function is: Among them, e k+1 =e k +G k-1 Δu e,k ,thereby Using the Bellman optimality principle, The following HJB equation needs to be satisfied: According to the optimality principle Solve the corresponding single-step optimal incremental control law model in the above formula Substituting the above formula into the HJB equation, we get in, In order to solve the above HJB equation, the neural network optimal control algorithm is used to solve it; It is approximated by the following neural network function: in is the activation function, is the ideal weight parameter, is the approximate error of building the neural network; Since the target weights are unknown, the cost function It can be estimated by the following formula: Among them, W k W c The estimated value of (k)||, yes An estimated value of So as to evaluate the network error ε k Expressed as in, The objective error function is: The update law of weights is expressed as: Thus, the optimal incremental control law model is obtained:

2. A helicopter nonlinear incremental adaptive dynamic optimization control method according to claim 1, characterized in that: The specific process of step 5 is as follows: Step 5.1: Based on the helicopter overall control law model, input the maneuvering flight reference signal and the instructions to be tracked into the controller, including Vx, Vy, Vz and yaw angle ψ; Step 5.2: Take the dynamic mathematical model of maneuvering flight established in step 1 as the reference trajectory and obtain the reference signal that satisfies the centripetal rotation trajectory. The desired inner loop instruction is obtained by solving the state of the reference signal, This results in the error system: The helicopter trajectory tracking problem is transformed into the adjustment problem of the above error system, the nonlinear incremental adaptive dynamic optimization control of the helicopter is realized, and the helicopter trajectory tracking performance is verified.

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