Controller, control method, and program

Abstract

To provide a method for controlling an airframe while changing a control gain in accordance with a state of the airframe.SOLUTION: A controller controls posture of an airframe that flies, through rotation of a rotor and includes means for constructing a linear parameter-varying (LPV) system where a rotation speed of the rotor, a pitch angular speed of the airframe, and a roll angular speed of the airframe are scheduling variables κ in a state equation where x is a state of the airframe and u is a command value of a posture angle inputted to the airframe, and then solving a minimization problem that minimizes an evaluation function formed by a state of the LPV system and a secondary format of input to calculate the K(κ) in state feedback control by u=-K(κ)u where the gain is K(κ).SELECTED DRAWING: Figure 1

Description

[Technical Field]

[0001] The present disclosure relates to a control device, a control method, and a program. [Background technology]

[0002] Patent Document 1 discloses a control system design method in which vehicle specifications, disturbance conditions, parameter variation ranges, and target responses are set, a dynamic model of the vehicle is created, LPV modeling is performed based on the dynamic model, the set conditions are formulated as an inverse LMI problem, a controller is derived using an LMI design method, and a control system design algorithm with a step response, which is a standard for the target response, as a constraint condition is created using an LMI step-constrained servo system configuration. The design method in Patent Document 1 tends to result in conservative control because the control gains are fixed. For example, when considering airframe control of a mobile object flying with a rotor (rotating wing), a change in the rotor rotation speed changes the magnitude of the gyro moment based on the rotor's angular momentum. However, if the control gains are fixed, it is not possible to adequately respond to changes in the airframe's state, such as changes in the gyro moment. [Prior art documents] [Patent documents]

[0003] [Patent Document 1] Japanese Patent Application Publication No. 11-110003 Summary of the Invention [Problem to be solved by the invention]

[0004] To provide a method for controlling an aircraft while changing a control gain in response to a change in the state of the aircraft.

[0005] The present disclosure provides a control device, a control method, and a program that can solve the above problems. [Means for solving the problem]

[0006] A control device according to the present disclosure is a control device for controlling the attitude of an airframe flying by rotor rotation, the control device comprising: an LPV system constructed by using a state equation in which x is a state of the airframe and u is an attitude angle command value input to the airframe, with the rotor rotation speed, the airframe pitch angular velocity, and the airframe roll angular velocity as scheduling variables κ; and means for calculating K(κ) in state feedback control of the LPV system by u=-K(κ)u where K(κ) is a gain by solving a minimization problem that minimizes an evaluation function formed by a quadratic form of the state and input of the LPV system. The control device according to the present disclosure may also comprise means for calculating K(κ) by solving a minimization problem that includes both a pole placement condition and an LQR condition, instead of the means for calculating K(κ) by solving a minimization problem that includes both a pole placement condition and an LQR condition, that is, by minimizing an evaluation function formed by a quadratic form of the state and input while satisfying an LMI that ensures that the poles of a closed-loop system of the airframe system are located within a specified region.

[0007] A control method according to the present disclosure is a control method executed by a control device, in which an LPV system is constructed using a state equation in which x represents the state of an airframe moving due to rotor rotation and u represents a command value of an attitude angle input to the airframe, with the rotor rotation speed, the airframe pitch angular velocity, and the airframe roll angular velocity being scheduling variables κ, and the LPV system is controlled by state feedback control using u = -K(κ)u where K(κ) is a gain, by solving a minimization problem that minimizes an evaluation function formed by a quadratic form of the state and input of the LPV system. The control method according to the present disclosure may also calculate K(κ) by solving a minimization problem that minimizes an evaluation function formed by a quadratic form of the state and input while satisfying an LMI that ensures that the poles of a closed-loop system of the airframe system are located within a specified region.

[0008] A program according to the present disclosure causes a computer to execute a process of constructing an LPV system using a state equation in which x represents a state of an airframe moving due to rotor rotation and u represents a command value of an attitude angle input to the airframe, with the rotor rotation speed, the airframe pitch angular velocity, and the airframe roll angular velocity being scheduling variables κ, and calculating K(κ) in state feedback control of the LPV system by u=-K(κ)u where K(κ) is a gain by solving a minimization problem that minimizes an evaluation function formed by a quadratic form of the state and input of the LPV system. The program according to the present disclosure may also calculate K(κ) by solving a minimization problem that minimizes an evaluation function formed by a quadratic form of the state and input while satisfying an LMI that ensures that the poles of a closed-loop system of the airframe system are located within a specified region. [Effects of the Invention]

[0009] According to the control device, control method, and program of the present disclosure, it is possible to control the aircraft while changing the control gain in response to changes in the state of the aircraft. [Brief explanation of the drawings]

[0010] [Figure 1] FIG. 1 is a diagram illustrating an example of a control system according to an embodiment. [Figure 2] FIG. 1 is a diagram illustrating an example of a single-rotor machine according to an embodiment. [Figure 3] FIG. 10 is a diagram illustrating an example of a symbol according to the embodiment. [Figure 4A] FIG. 1 is a first diagram showing an example of an LMI domain on a complex plane according to an embodiment. [Figure 4B] FIG. 2 is a second diagram showing an example of an LMI domain on a complex plane according to the embodiment. [Figure 4C] FIG. 3 is a third diagram showing an example of an LMI domain on a complex plane according to the embodiment. [Figure 4D] FIG. 4 is a fourth diagram showing an example of an LMI region on a complex plane according to the embodiment. [Figure 4E]FIG. 5 is a diagram showing an example of an LMI region on a complex plane according to the embodiment. [Figure 5A] FIG. 10 is a diagram illustrating an example of a parameter variation range according to the embodiment. [Figure 5B] FIG. 10 is a diagram illustrating an example of a correspondence relationship between scheduling variables and parameter endpoint numbers according to the embodiment. [Figure 5C] FIG. 2 is a diagram showing an example of required specifications (design parameters) according to the embodiment. [Figure 6A] FIG. 1 is a first diagram showing an example of pole placement according to an embodiment. [Figure 6B] FIG. 2 is a second diagram showing an example of pole placement according to the embodiment. [Figure 6C] FIG. 3 is a third diagram showing an example of pole placement according to the embodiment. [Figure 6D] FIG. 4 is a fourth diagram showing an example of pole placement according to the embodiment. [Figure 6E] FIG. 5 is a diagram showing an example of pole placement according to the embodiment. [Figure 6F] FIG. 6 is a diagram showing an example of pole placement according to the embodiment. [Figure 6G] FIG. 7 is a diagram showing an example of pole placement according to the embodiment. [Figure 6H] FIG. 8 is an eighth diagram showing an example of pole placement according to the embodiment. [Figure 6I] FIG. 9 is a diagram showing an example of pole placement according to the embodiment. [Figure 7] FIG. 2 is a configuration diagram of a control system according to the embodiment. [Figure 8] FIG. 2 illustrates an example of a hardware configuration of a control system according to an embodiment. DETAILED DESCRIPTION OF THE INVENTION

[0011] <Embodiment> The control method of the present disclosure will be described below with reference to FIGS. (composition) FIG. 1 is a diagram illustrating an example of a control system according to an embodiment. The control system 1 is a control system for an eVTOL (Electric Vertical Take-off and Landing) 6. The eVTOL 6 has one rotor 6a and flies by rotating the rotor 6a. The rotor 6a is provided with, for example, four flaps (wings), not shown, and the flight direction and attitude of the eVTOL 6 are controlled by controlling the angle of the flaps. A target thrust / attitude calculator 2 receives as input sensor values, which are values obtained by observing the state of the eVTOL 6 using various sensors, a target position (x, y, z), and accelerations in the x, y, and z directions for compensating for disturbances, calculated by a compensator 5, to calculate a target thrust F, a target pitch angle θ, and a target roll angle φ of the eVTOL 6. The target pitch angle θ and target roll angle φ calculated by the target thrust / attitude calculator 2 are input to an attitude controller 3, and the target yaw angle ψ and rotor rotation speed n (sensor values) are also separately input to the attitude controller 3. The attitude controller 3 calculates the flap control angle δ (roll control angle δ) of the eVTOL 6 from these values. roll , pitch steering angle δ pitch , yaw steering angle δ yaw ) is calculated. The target thrust F calculated by the target thrust / attitude calculator 2 and the flap steering angle calculated by the attitude controller 3 are input to the converter 4, which converts the target thrust F into the rotation speed of the rotor equipped to the eVTOL 6 and commands it to the eVTOL 6. The converter 4 also converts the flap steering angle δ into a flap steering angle command and commands it to the eVTOL 6. The compensator 5 receives as input the rotation speed command and steering angle command issued to the eVTOL 6 by the converter 4 and the sensor values observed for the eVTOL 6, and calculates a compensation amount to compensate for disturbances applied to the eVTOL 6. The compensation amount related to thrust calculated by the compensator 5 is input to the target thrust / attitude calculator 2. The flap steering angle calculated by the attitude controller 3 is corrected by the compensation amount related to the attitude of the eVTOL 6 calculated by the compensator 5 and input to the converter 4.

[0012] This embodiment focuses on the function and configuration of calculating the flap steering angle δ using the attitude controller 3. The attitude controller 3 according to this embodiment constructs an LPV (Linear Parameter-Varing) system with the rotor rotation speed, roll angular velocity, and pitch angular velocity as scheduling variables for the equation of motion of the attitude of the eVTOL 6, and constructs a gain-scheduled controller. It is characterized by determining and scheduling gains that satisfy pole placement conditions and LQR (Linear-Quadratic Regulator) conditions. Below, we will explain the procedure for formulating the problem of calculating the flap steering angle δ while deriving such gains.

[0013] An LPV system is a linear system in which the coefficient matrix of the system depends on a time-varying parameter k(t), as shown in the following equation (1), where x is the state and u is the input to the system.

[0014]

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[0015] u=-Kx (2) When stabilizing an LPV system using the state feedback of equation (2) above, if the state feedback gain K is also changed in the same way, K = K(k(t)), in accordance with changes in the dynamic characteristics of the controlled object (changes in k(t)), a control law that matches the dynamic characteristics of the controlled object at that time will be applied in real time as needed, and improvement in control performance can be expected. This is GS (Gain-Scheduled) control, and from this perspective, the time-varying parameter k(t) is called a scheduling variable.

[0016] Figure 2 shows an eVTOL6 with a suspended load (payload7). Figure 3 shows a list of symbols used below. Let us consider the equation of motion for the rotation of an eVTOL6 with a suspended load. The suspended load is suspended from the center of gravity (h p = 0), the rotational motion equation of the eVTOL6 is given by the following equation (3).

[0017]

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[0018] Furthermore, the kinematics of the rotational motion is given by the following equation (4).

[0019]

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[0020] Here, for simplicity, the following is assumed: The roll angle and pitch angle are assumed to be sufficiently small (φ=0, θ=0 [rad]). ·Z-axis symmetric rigid body (I x =I y ). - Roll steering angle δ as a virtual control variable roll , pitch steering angle δ pitch , yaw steering angle δ yaw Introduce. Based on these assumptions, equations (1) and (2) can be rearranged as shown in equation (3) below.

[0021]

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[0022] Here, the scheduling variables are κ=[κ1, κ2, κ3]=[p, q, n]. T If we take this, equation (3) can be expressed as the following equation (4), and the rotational motion equation of eVTOL6 is the state equation (x · This can be expressed in the LPV system using the output equation (y = ~) and the output equation (y = ~), where p is the pitch angular velocity, q is the roll angular velocity, and n is the rotor speed.

[0023]

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[0024] where x, u, A(k), B, and C are as follows:

[0025]

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[0026] In x, φ is the roll angle of the aircraft, θ is the pitch angle, ψ is the yaw angle, p is the pitch angular velocity, q is the roll angular velocity, r is the yaw angular velocity, k ff is a given coefficient, δ roll is the roll angle of the flap, δ pitch is the flap pitch angle, δ yaw is the flap yaw angle.

[0027] (Matrix polytope representation of LPV systems) Here, we consider the polytope representation (convex combination representation) of the LPV system using the system of the above equation (7) as an example. If the variation range of the scheduling variables is ki(t)∈[κ i _, κ i ￣], the coefficient matrix A(x) can be expressed as a convex combination of eight endpoint matrices Ai (equation (6)). i _ is κ i The minimum value of κ i ￣ is κ i indicates the maximum value of

[0028]

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[0029] The endpoint matrix Ai is given by: A1=A(κ1_, κ2_, κ3_), A2=A(κ1_, κ2_, κ3￣), A3=A(κ1_, κ2￣, κ3_), A4=A(κ1_, κ2￣, κ3￣), A5=A(κ1￣, κ2_, κ3_), A6=A(κ1￣, κ2_, κ3_), A7=A(κ1￣, κ2￣, κ3_), A8=A(κ1￣, κ2￣, κ3￣).

[0030] In addition, the convex coupling coefficient λi can be expressed in real time in accordance with the change in the scheduling variable κ as follows: λ1=η0 1 η0 2 η0 3 , λ2=η0 1 η0 2 η1 3 , λ3=η0 1 η1 2 η0 3 , λ4=η0 1 η1 2 η1 3 , λ5=η1 1 η1 2 η0 3 , λ6=η1 1 η1 2 η1 3 , η0 i =(κi￣-κ(t))÷(κi￣-κi_), η1 i =1-η0 i , i=1~8.

[0031] In the GS (Gain Schedule) control design of the LPV system, the control gain K(t) in equation (2) is given as follows using the convex coupling coefficient λi:

[0032]

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[0033] Here, Ki is an end point controller designed for the end point model Ai of the controlled object, and can be designed using LMI (Linear Matrix Inequality).

[0034] (GS controller design using LMI) (1) State feedback controller design based on quadratic stability The quadratic stability of an LPV system is used as an example to demonstrate that GS control design for an LPV system reduces to the LMI condition. Here, we consider an LPV system in which only the coefficient matrix A depends on the scheduling parameter κ. Here, we consider the quadratic stabilization problem of "finding the control gain K(κ) that stabilizes the LPV system of the following equation (10) using the state feedback control of the following equation (11)."

[0035]

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[0036] u=-K(κ)x (11) In this case, the closed loop system can be expressed by the following equation (12).

[0037]

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[0038] The fact that the system of equation (12) is quadratically stable is equivalent to the existence of a positive definite symmetric matrix P>0 that satisfies the following inequality according to the Lyapunov stability condition. (A(κ)-BK(κ)) T P+P(A(κ)-BK(κ))<0 (13) Here, if the state feedback gain K(κ) is expressed as a convex combination of the scheduling parameter endpoints (total of N), similar to the matrix polytope expression of the coefficient matrix A(κ), then equation (14) is obtained. Substituting equation (14) into equation (13) yields equation (15).

[0039]

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[0040]

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[0041] A sufficient condition for satisfying equation (15) is that there exists a common positive definite matrix P>0 for the following N simultaneous inequalities: (A i -BK i ) T P+P(A i -BK i )<0, i=1~N (16) where Y=P -1 Then, by multiplying the left and right matrices of the above equation, the dual expression of equation (16) is (A i -BK i )Y+Y(A i -BK i ) T <0, i = 1 to N (17) The above equation is the product of variables YK i , Y.K. i T It is not an LMI because it includes the variable transformation W i =K i By introducing Y, equation (17) can be reduced to the LMI as follows: (A i Y-BW i )+(A i Y-BW i ) T <0, i = 1 to N (18)

[0042] In other words, the quadratic stabilization problem of the LPV system is reduced to the LMI problem of the existence of a common positive definite matrix Y>0 that satisfies the simultaneous LMI of equation (18). The control gain in this case is equation (19), and K i =W i Y -1 This becomes:

[0043]

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[0044] In practical control design, it is necessary to satisfy the design requirements (response), and the stabilization requirements shown above alone are insufficient. Below we show the correspondence between typical control design problems and LMI conditions. For ease of explanation, we will show an LMI for a time-invariant system, but by performing a similar equation expansion as above, it can also be applied to gain-scheduled control design for LPV systems.

[0045] (2) Pole placement using LMI We show that the pole placement design of a closed-loop linear system with state feedback reduces to an LMI. First, we define a representation of a convex region on the complex plane as the pole placement region. D (z)=α+zβ+z￣β T The domain D={z∈C:f D (z)<0} is called the LMI domain, and f D (z) is called the characteristic function. Note that C is a complex number, and z￣ is the contracted complex number of z.

[0046] Next, consider a closed loop system (equation (21)) after state feedback is applied to a system that can be described by the state equation of the following equation (20).

[0047]

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[0048]

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[0049] A necessary and sufficient condition for all poles (eigenvalues) of this closed-loop system to exist in the LMI domain D is the existence of a real symmetric positive definite matrix P>0 that satisfies the following equation (22).

[0050]

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[0051] The above equation is not an LMI because it contains a product of variables, Y=P-1 Then, considering the dual expression of the above equation, we obtain equation (23).

[0052]

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[0053] Furthermore, by introducing the variable transformation W=KY, we obtain equation (24), and the song placement problem is reduced to an LMI. In other words, the closed loop system of equation (21) is D (z)=α+zβ+z￣β T <0, the LMI domain D={z∈C:f D The necessary and sufficient condition for having a pole within {(z)<0} is the existence of a positive definite matrix Y that satisfies the LMI condition of the following equation (24). In this case, the feedback gain is K=WY -1 This becomes:

[0054]

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[0055] Possible methods for specifying the range of pole placement that are meaningful for improving system response include (a) specifying the maximum value of the real part of the pole (specifying the minimum value of damping), (b) specifying the minimum value of the real part of the pole (specifying the maximum value of damping), (c) specifying the ratio of the pole to the real part and imaginary part, and (d) placing within a radius of a certain size.

[0056] (a) LMI condition that specifies the maximum real part of the poles Figure 4A shows the LMI domain on the complex plane that defines the maximum value of the real part of the pole. The point z = x + j on the left side of the line x = -σ is expressed as follows using z and ẑ. (Note that x here represents the real part and is different from the x of the state. The same applies below.) x<-σ⇔2σ+z+z￣<0 The above f D Comparing with the matrix inequality of (z), since α = 2 and β = 1, a necessary and sufficient condition for the existence of a feedback gain K that places the poles of the closed-loop system of equation (21) in this region is the existence of a positive definite matrix Y>0 that satisfies the following LMI condition. (AY-BW)+(AY-BW)T+2σY<0 In this case, the feedback gain is K=WY -1 This becomes:

[0057] (b) LMI condition that specifies the minimum real part of the pole Figure 4B shows the LMI region on the complex plane that defines the minimum value of the real part of the pole. The point z = x + j on the right side of the line x = -σ can be expressed as follows using z and ẑ. x<-σ⇔-2σ-zz￣<0 The above f D Comparing with the matrix inequality of (z), since α = -2 and β = -1, a necessary and sufficient condition for the existence of a feedback gain K that places the poles of the closed loop system of equation (21) in this region is the existence of a positive definite matrix Y>0 that satisfies the following LMI condition. -(AY-BW)-(AY-BW)T-2σY<0 In this case, the feedback gain is K=WY -1 This becomes:

[0058] (c) LMI condition that specifies the ratio of the real and imaginary parts of the poles Figure 4C shows the LMI domain on the complex plane that defines the ratio of the real and imaginary parts of the poles. The point z = x + jy in the sector |argz-π|<θ on the left half plane is expressed as follows using z and ẑ.

[0059]

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[0060] The above f D Comparing with the matrix inequality of (z), we get the following.

[0061]

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[0062]

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[0063] (d) LMI condition for placement within a certain radius Figure 4D shows an LMI domain on the complex plane placed within a radius of a certain size. The point z = x + jy that exists within a circle with center (-c, 0) and radius r is expressed as follows using z and ẑ.

[0064]

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[0065]

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[0066] The necessary and sufficient condition for the existence of the feedback gain K that places the poles of the closed loop system of equation (21) in this region is the existence of a positive definite matrix Y>0 that satisfies the LMI condition of equation (30) below. In this case, the feedback gain is K=WY -1 This becomes:

[0067]

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[0068] (3) LQR controller design using LMI Next, we show that the gain design of LQR reduces to a minimization problem with an LMI constraint. LQR is a state feedback control that minimizes the performance index of the following equation (31) for the system of the above equation (20). The first term on the right-hand side of equation (31) becomes larger as the system state deviates from the target, and the second term becomes larger as the input to the system increases.

[0069]

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[0070] The gain K is given by the Riccati equation, P0A+A T P0-P0BR -1 B T From the stable solution of P0+Q=0, K=R -1 B T P0. Substituting this K into the above Riccati equation gives the following equation (32). P0(A-BK)+(A-BK) T P0+K T RK+Q=0 (32) To treat equation (32) as an inequality, P = P T Defining >P0 gives the following equation (33). P(A-BK)+(A-BK) T P+K T RK+Q<0 (33) Y=P -1 >0, the dual expression of the above equation (33) is as follows: (A-BK)Y+Y(A-BK) T +YK T RKY+YQY<0 (34) Furthermore, by introducing a variable transformation W=KY, it can be transformed into the following equation (35). AY-BW+YA T -W T B T- W T B T +YQY<(W) T (-R -1 ) -1 (W T ) T ···(35) By Schur Complement, equation (35) is equivalent to the following equation (36).

[0071]

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[0072] Further transformation gives equation (37), and applying Schur Complement again gives equation (38).

[0073]

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[0074]

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[0075] Equation (38) is an LMI for Y and W. When the positive definite matrix Y and matrix W that satisfy the LMI of equation (38) are found, the control gain is K = WY -1 So P=P T >P0, the evaluation function at that time is given by the following equation (39). J=x T (0)P0x(0) <x T (0)Px(0) ···(39) When solving the optimal regulator using an LMI, a new variable S(>P) is introduced to restrict the upper bound of the performance index, and the gain that minimizes the performance index is found by minimizing trace(S). Note that trace(S) represents the sum of the diagonal elements of S. S>P=IY -1 I therefore by Schur Complement

[0076]

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[0077] It becomes. Therefore, the LQR controller design problem using LMI is as follows. For the system of Equation (20), the state feedback gain that minimizes the quadratic evaluation function represented by Equation (31) can be calculated by solving the following minimization problem. At this time, the feedback gain is K = WY -1 It becomes.

[0078] [Number]

[0079] (4) Multi-objective control problem using LMI As an advantage of expressing control requirements using LMI instead of equations, it can be cited that it is easy to derive a control law that satisfies multiple specifications. For example, as shown in Figure 4E, -σ max < x < -σ min、 While placing the poles within the range of |y| < xsinθeig, the problem of obtaining the state feedback gain that minimizes the evaluation function of Equation (31) becomes as follows by the above (2) Pole region placement using LMI and (3) LQR controller design using LMI.

[0080] For the system of Equation (20), while minimizing the quadratic evaluation function represented by Equation (31), the poles are -σ max < x < -σ min、 The state feedback gain specified by |y| < xsinθeig can be obtained by solving the following minimization problem. At this time, the feedback gain is K = WY -1 It becomes.

[0081] [Number]

[0082] (Design of LPV controller for eVTOL) Based on the content summarized above, for the rotational motion system of eVTOL6 expressed by the above formula (5), it is confirmed that the gain scheduling control design corresponding to parameter variations satisfies the specified pole placement. Here, consider the following control problem.

[0083] <eVTOL Attitude Control Problem> Let the scheduling variables be κ = [κ1, κ2, κ3] = [p, q, n] T (where p is the pitch angular velocity, q is the roll angular velocity, and n is the rotor speed). For the system of equation (20), while minimizing the quadratic evaluation function expressed by equation (31), the poles are set to -σ max <x < -σ min、 |y| < xsinθeig (x in this formula represents the real part of the complex plane, not the x of the state quantity. y represents the imaginary part). The state feedback control law u = -K(κ)u is obtained by solving the following minimization problem (Equation (43)) under the LMI condition constraint. The feedback gain at the endpoints is K i = W i Y -1 That is. However, A, B, x, and u in equation (20) are as shown in equation (7). (Solving equation (43) is to solve a minimization problem that minimizes the evaluation function composed of the quadratic form of the state and input while satisfying the LMI that guarantees that the poles of the closed-loop system of the eVTOL6 airframe system are arranged within the specified region. "Minimizing the evaluation function composed of the quadratic form of the state and input" includes satisfying the LMI constraint of the LQR condition.

[0084]

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[0085] The variation range of the scheduling variable was set as shown in the table of Fig. 5A, and the numbers of the endpoints of the scheduling variable were set as shown in Fig. 5B. The required specifications (design parameters) of the attitude controller 3 were specified as shown in the table of Fig. 5C. Based on the above settings and the LMI conditions, the control gains at each parameter endpoint were obtained. Figs. 6A to 6H show the poles of the closed-loop system at each endpoint. It can be confirmed that at any endpoint, the closed-loop poles are designed within the specified pole region and the control gains of the endpoints are correctly obtained by the LMI.

[0086] Also, as shown in "Design of State Feedback Controller Based on Second-Order Stability (1)", by convexly combining the control gains of the endpoints according to the scheduling variable, the control requirements are satisfied at any point within the parameter variation. Here, as a representative, the poles of the closed-loop system in the case of the center of the parameter variation are shown in Fig. 6I. It can be confirmed that even at the center of the variable parameter, by performing gain-scheduled control, the poles of the closed-loop system can be specified as required by the design.

[0087] (Operation) The attitude controller 3 acquires the target pitch angle θ, target roll angle φ, target yaw angle ψ, and rotor rotation speed n (sensor value) (step 1). Next, the attitude controller 3 solves the above <Attitude Control Problem of eVTOL> (step 2). Next, the attitude controller 3 commands the converter 4 with u calculated by the <Attitude Control Problem of eVTOL>, that is, the flap rudder angle δ (roll rudder angle δroll, pitch rudder angle δpitch, yaw rudder angle δyaw) (step 3).

[0088] (Effect) As described above, according to this embodiment, the motion equation of the attitude of the eVTOL6 is regarded as an LPV system with the rotor rotation speed, pitch angular velocity, and roll angular velocity as scheduling variables, and the input u (flap rudder angle σ) that approaches the target pitch angle, roll angle, and yaw angle is calculated. More specifically, the scheduling variable is κ = [κ1, κ2, κ3] = [p, q, n] Tand calculates u = -K(κ)u that minimizes the evaluation function (equation (31)) of the state equation (equation (20) above). This makes it possible to control the aircraft while changing the control gain in response to changes in the mass of the eVTOL6 (for example, changes in the suspended load, that is, changes in the rotor rotation speed). For example, in a single-rotor aircraft such as the eVTOL6, changes in mass cause changes in the rotor rotation speed, which changes the magnitude of the gyro moment based on the angular momentum of the rotor, but the control amount (rudder angle) corresponding to this can be calculated.

[0089] Furthermore, for the target LPV system, by using the pole placement LMI condition, the poles of the closed loop system can be placed in the specified pole region. Furthermore, by adding the LMI of the LQR condition, the evaluation function related to the control performance is minimized within the specified pole region. This makes it possible to explicitly specify the response requirements of the control system, and enables a design that balances the state quantity and input within the specified pole placement. Specifically, the LMI of the LQR condition is the following equation from equation (43).

[0090]

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[0091] The pole placement LMI condition is the following equation in equation (43):

[0092]

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[0093] Second Embodiment In the second embodiment, the state equation (Equation (20)) in the first embodiment is considered as an expanded system in which the integral value of the tracking error is added to the target system, and a design that also takes integral compensation into consideration is performed. The tracking error e a =r a -C a x a The integral value of w a is defined by the following equation (50): ra is the target value, C a is the observation matrix.

[0094]

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[0095] When considering an expanded system in which wa is added to the state x, the following equation (51) is obtained: In the second embodiment, ρa corresponds to κ in the first embodiment.

[0096]

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[0097] The steady state values of state x and input u are a∞ , u a∞ Then, the following is satisfied.

[0098]

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[0099] Therefore, the following equation (53) is obtained.

[0100]

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[0101] deviation x a ~=x a -x a∞ , w a ~=w a -w a∞ , u a ~=u a -u a∞ Then, the error model is expressed as follows:

[0102]

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[0103] Here we put it as follows:

[0104]

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[0105] Then, the following equation (55) is obtained, which is the same as in the first embodiment.

[0106]

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[0107] The state feedback control law for this error model is u=-K(ρ a )x and solving it in the same way as in the first embodiment, the optimal state feedback control law is obtained.

[0108]

number

[0109] Assume that equation (56) showing the optimal state feedback control law for equation (54) can be calculated. a ) is the gain of the pitch angular velocity, K2(ρ a ) is the roll angular velocity gain. In this case, the original input u of the system is

[0110]

number

[0111] than w a∞ Assuming =0,

[0112]

number

[0113] From u a∞ =-B a -1 A aC a -1 , x a∞ =C a -1 r a So, u=-K1(ρ a )x a -K2(ρ a )w a +[C a (B a K1(ρ a )-A a (ρ a )) -1 B a ] -1 r a The configuration of the control system of the second embodiment is shown in FIG.

[0114] (operation) The attitude controller 3 acquires the target pitch angle θ, target roll angle φ, target yaw angle ψ, and rotor rotation speed n (sensor values) (Step 1). Next, the attitude controller 3 solves the minimization problem for the above equation (55) by providing constraints in the same way as in the first embodiment (Step 2). Next, the attitude controller 3 commands the calculated u, that is, the flap angle δ (roll angle δroll, pitch angle δpitch, yaw angle δyaw) to the converter 4 (Step 3).

[0115] (effect) According to this embodiment, the controller with integral compensation can satisfy the control design requirements, and the integral gain (K1(ρ a ), K2(ρ a )) can also be scheduled.

[0116] <Third embodiment> In the third embodiment, compensation for disturbances is performed not by an integral compensator but by a disturbance observer (compensator 5). The control system of compensator 5 will be described below.

[0117] The equation of motion for the rotation of the eVTOL6, taking into account external disturbances, can be written as follows:

[0118]

number

[0119] Disturbance d p , d q , d r The disturbance is estimated by a nonlinear observer using an inverse model of the eVTOL6 nonlinear equation of motion (60), and the disturbance is compensated for, thereby apparently eliminating the disturbance. The disturbance estimated value of each equation of motion is calculated using the following equation (61).

[0120]

number

[0121] Compensate for the estimated disturbance (disturbance d p , d q , d r The steering angle component (setting to 0) is expressed by the following equation (62).

[0122]

number

[0123] (operation) Disturbance d p ^ , d q ^ , d r ^ is a sensor value such as an accelerometer or an angular velocity meter, or a value estimated from the sensor value. p ^ , d q ^ , d r ^ and equation (62), the compensation value of the flap steering angle δ, that is, the roll steering angle compensation value δ roll * , pitch steering angle compensation value δ pitch * , yaw steering angle compensation value δ yaw * The converter 4 calculates the roll steering angle δ calculated by the method of the first embodiment. roll , pitch steering angle δ pitch , yaw steering angle δ yaw, and δ roll * , δ pitch * , δ yaw * The roll, pitch, and yaw steering angles are input after adding or subtracting the above.

[0124] (effect) According to this embodiment, the disturbance can be effectively removed by using a disturbance compensator based on a motion model of the target system.

[0125] FIG. 8 is a diagram illustrating an example of a hardware configuration of a control system according to each embodiment. The computer 900 includes a CPU 901 , a main memory device 902 , an auxiliary memory device 903 , an input / output interface 904 , and a communication interface 905 . Each controller of the control system 1, such as the attitude controller 3 and compensator 5, is implemented in a computer 900. Each of the above-described functions is stored in the form of a program in an auxiliary storage device 903. The CPU 901 reads the program from the auxiliary storage device 903, loads it into the main storage device 902, and executes the above-described processing in accordance with the program. The CPU 901 also allocates a storage area in the main storage device 902 in accordance with the program. The CPU 901 also allocates a storage area in the auxiliary storage device 903 for storing data being processed in accordance with the program.

[0126] Note that a program for implementing all or part of the functions of the attitude controller 3 and the compensator 5 may be recorded on a computer-readable recording medium, and the program may be loaded into a computer system and executed to perform processing by each functional unit. The term "computer system" as used herein includes hardware such as an OS and peripheral devices. Furthermore, if a WWW system is used, the term "computer system" also includes a homepage provision environment (or display environment). Furthermore, the term "computer-readable recording medium" refers to portable media such as CDs, DVDs, and USBs, as well as storage devices such as hard disks built into the computer system. Furthermore, if the program is distributed to the computer 900 via a communication line, the computer 900 that receives the program may load the program into the main storage device 902 and execute the above-described processing. Furthermore, the program may be for implementing part of the above-described functions, or may be capable of implementing the above-described functions in combination with a program already stored in the computer system.

[0127] As described above, several embodiments according to the present disclosure have been described, but all of these embodiments are presented as examples and are not intended to limit the scope of the invention. These embodiments can be implemented in various other forms, and various omissions, substitutions, and modifications can be made without departing from the spirit of the invention. These embodiments and their modifications are included in the scope of the invention and its equivalents as defined in the claims, as well as in the scope and spirit of the invention.

[0128] <Additional Notes> The control device, the control method, and the program described in the embodiments can be understood, for example, as follows.

[0129] (1) A control device according to a first aspect is a control device that controls the attitude of an airframe flying by the rotation of a rotor, and includes a means for constructing an LPV (Linear Parameter-Varing) system using the rotor rotation speed, the airframe pitch angular velocity, and the airframe roll angular velocity as scheduling variables κ in a state equation in which x is the state of the airframe and u is a command value of an attitude angle input to the airframe, and for calculating K(κ) in state feedback control of the LPV system by u=-K(κ)u where K(κ) is a gain, by solving a minimization problem that minimizes an evaluation function composed of a quadratic form of the state and input of the LPV system. This enables control that responds to the state of the aircraft. In particular, in the case of single-rotor aircraft, large gyroscopic effects can occur due to changes in rotor rotation, but by varying the gain K using the scheduling variable κ, control that responds to the state (dynamic characteristics) of the aircraft where gyroscopic effects have occurred becomes possible. Note that the process of minimizing the evaluation function in Appendix 1 includes satisfying the LMI constraints of the LQR (Linear-Quadratic Regulator) conditions. By solving a minimization problem that includes the LMI constraints of the LQR conditions, it is possible to explicitly specify the response requirements of the control system, enabling a design that balances the state and input.

[0130] (2) A control device according to a second aspect is the control device of (1), wherein the calculating means specifies that the poles are to be placed within a predetermined range in addition to minimizing the evaluation function in the minimization problem, and further specifies an LMI (Linear Matrix Inequality) condition for the pole placement as a constraint. This allows the response requirements of the control system to be explicitly specified, and enables a design that balances the state quantity and input within the specified pole placement.

[0131] (3) A control device according to a third aspect is a control device according to (1) to (2), wherein the calculating means solves the minimization problem for a state equation of an augmented system in which integral compensation that integrates the difference between the target value of the state and the state is added to the state equation. This allows control to be performed to reduce the deviation between the target and the actual state.

[0132] (4) A control device according to a fourth aspect is a control device according to (1) to (2), further comprising a compensation means for calculating a pitch angular velocity, a roll angular velocity, and a yaw angular velocity of the aircraft that cancel out external disturbances based on an equation of motion that takes into account the external disturbances acting on the aircraft. This enables control that responds to disturbances.

[0133] (5) A control method according to a fifth aspect is a control method executed by a control device, in which an LPV (Linear Parameter-Varing) system is constructed using a state equation in which x is a state of an airframe moving due to rotor rotation and u is a command value of an attitude angle input to the airframe, with the rotor rotation speed, the pitch angular velocity of the airframe, and the roll angular velocity of the airframe being scheduling variables κ, and the LPV system is controlled by state feedback control using u=-K(κ)u where K(κ) is a gain, by solving a minimization problem that minimizes an evaluation function composed of a quadratic form of the state and input of the LPV system.

[0134] (6) A program according to a sixth aspect includes the following steps: a) constructing an LPV (Linear Parameter-Varing) system using a state equation in which x is a state of an aircraft moving due to rotor rotation and u is a command value of an attitude angle input to the aircraft, with the rotation speed of the rotor, the pitch angular velocity of the aircraft, and the roll angular velocity of the aircraft as scheduling variables κ; and b) calculating K(κ) in state feedback control of the LPV system by u=-K(κ)u where K(κ) is a gain by solving a minimization problem that minimizes an evaluation function formed of a quadratic form of the state and input of the LPV system; Execute the following. [Explanation of symbols]

[0135] 1. Control System 2...Target thrust / attitude calculator 3. Attitude Controller 4. Converter 5...compensator 6. eVTOL 900···Computer 901 CPU 902...Main memory 903...Auxiliary storage device 904 Input / Output Interface 905···Communication Interface

Claims

1. A control device that controls the attitude of a flying aircraft by rotating a rotor, a means for constructing an LPV (Linear Parameter-Varing) system using the rotation speed of the rotor, the pitch angular velocity of the airframe, and the roll angular velocity of the airframe as scheduling variables κ in a state equation in which x is the state of the airframe and u is a command value of an attitude angle to be input to the airframe, and calculating K(κ) in state feedback control of the LPV system by u=-K(κ)u where K(κ) is a gain, by solving a minimization problem that minimizes an evaluation function formed of a quadratic form of the state and input of the LPV system; A control device comprising:

2. the calculating means specifies that the poles are to be placed within a predetermined range in addition to minimizing the evaluation function in the minimization problem, and further specifies an LMI (Linear Matrix Inequality) condition for the pole placement as a constraint condition. The control device according to claim 1 .

3. the calculating means solves the minimization problem for a state equation of an augmented system obtained by adding integral compensation, which integrates a difference between the target value of the state and the state, to the state equation; The control device according to claim 1 or 2.

4. a compensation means for calculating a pitch angular velocity, a roll angular velocity, and a yaw angular velocity of the airframe that cancel out the disturbance based on an equation of motion that takes into account the disturbance acting on the airframe; The control device according to claim 1 or 2, further comprising:

5. A control method executed by a control device, In a state equation in which x represents the state of an airframe moving due to rotor rotation and u represents a command value of an attitude angle input to the airframe, an LPV (Linear Parameter-Varing) system is constructed with the rotation speed of the rotor, the pitch angular velocity of the airframe, and the roll angular velocity of the airframe as scheduling variables κ, and the LPV system is subjected to state feedback control by u=-K(κ)u, where K(κ) is a gain, by solving a minimization problem that minimizes an evaluation function formed of a quadratic form of the state and input of the LPV system. Control method.

6. On the computer, a process of constructing an LPV (Linear Parameter-Varing) system using the rotation speed of the rotor, the pitch angular velocity of the aircraft, and the roll angular velocity of the aircraft as scheduling variables κ in a state equation in which x is the state of the aircraft moving due to the rotation of the rotor and u is a command value of the attitude angle input to the aircraft, and calculating K(κ) in state feedback control of the LPV system by u=-K(κ)u where K(κ) is a gain, by solving a minimization problem that minimizes an evaluation function composed of a quadratic form of the state and input of the LPV system; A program that executes the following.

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