Control device

Abstract

To provide a control device of a linear motor which can prevent leakage of control information to the outside and alteration of a control parameter, etc.SOLUTION: A control device 10 of a linear motor comprises an encryption unit 80 which encrypts a parameter and a communication signal concerning control of the linear motor and controls the linear motor by using the encrypted parameter and the communication signal.SELECTED DRAWING: Figure 5

Description

[Technical Field]

[0001] The present disclosure relates to a control device for a linear motor. [Background technology]

[0002] A motor has a stator and a mover, and is configured to move the mover relative to the stator by magnetically generating a thrust between the stator and the mover. A typical example of a motor is a linear motor, which has a mover in which multiple permanent magnets are arranged so that their magnetism alternates, and a stator in which a coil is wound around each of multiple magnetic pole teeth, and is configured to be spaced apart by a predetermined distance, and which generates a thrust by the attraction / repulsion force between the permanent magnets and the stator coils when an AC current is passed through the stator coils, thereby linearly moving the mover relative to the stator.

[0003] It is known that cogging generally occurs in motors, including linear motors. Cogging is a periodic fluctuation in thrust force that accompanies periodic fluctuations in magnetic attractive force that depend on the position of the mover relative to the stator. The occurrence of cogging adversely affects the operation of the motor, and may prevent desired operating characteristics from being obtained. For example, in the case of a linear motor, stable constant speed control becomes impossible. Because such cogging is an unavoidable phenomenon for motors, various methods have been proposed to correct the cogging that occurs so that desired operating characteristics can be obtained (see Patent Documents 1 and 2).

[0004] It is also disclosed that the linear motor for driving the stage is equipped with a disturbance compensator that uses a disturbance observer to compensate for disturbance factors such as fluctuations in the guiding friction of the linear guide mechanism that fluctuate depending on the position of the stage (see Patent Document 3). [Prior art documents] [Patent documents]

[0005] [Patent Document 1] Japanese Patent Application Laid-Open No. 2004-120861 [Patent Document 2] Japanese Patent Application Publication No. 2019-221032 [Patent Document 3] Japanese Patent Application Laid-Open No. 2001-218497 Summary of the Invention [Problem to be solved by the invention]

[0006] However, although the above-mentioned linear motors are capable of correcting cogging and compensating for disturbances, the programs (control signals) and control parameters related to the linear motor's operation are accessible to third parties. This means that the technology (control elements) of such linear motors may be stolen or parameters may be changed maliciously from the outside. These problems are not addressed in Patent Documents 1-3, and cannot be resolved.

[0007] The present disclosure has been made in view of the above circumstances, and aims to provide a linear motor control device that can prevent control information from being leaked to the outside and control parameters and the like from being tampered with. [Means for solving the problem]

[0008] The control device according to the present disclosure is a control device for a linear motor, and includes an encryption unit that encrypts parameters and communication signals related to the control of the linear motor, and controls the linear motor using the encrypted parameters and communication signals.

[0009] In the present disclosure, the linear motor is controlled using encrypted parameters and communication signals, so that leakage of control information to the outside and tampering with control parameters and the like can be prevented.

[0010] In the control device according to the present disclosure, the objects to be encrypted by the encryption unit include the target position of the mover and the detected position and moving speed of the mover.

[0011] In the present disclosure, parameters and communication signals, including the target position of the mover and the detected position and movement speed of the mover, are encrypted, and the linear motor is controlled using the encrypted parameters and communication signals, thereby preventing leakage of control information to the outside and tampering with control parameters, etc.

[0012] The control device according to the present disclosure includes a damping processing unit that damps nonlinearity of the dynamics of the linear motor before encryption by the encryption unit.

[0013] In the present disclosure, prior to encryption, the damping processing unit performs nonlinear damping of the dynamics of the linear motor, which is nonlinear and cannot be encrypted, and makes the dynamics of the linear motor linear, thereby enabling encryption.

[0014] In the control device according to the present disclosure, the encryption unit performs encryption using homomorphic encryption.

[0015] In the present disclosure, homomorphic encryption is used to encrypt parameters and communication signals, so that calculations can be performed using the encrypted parameters and communication signals without using a secret key, and therefore the linear motor can be controlled using the encrypted parameters and communication signals.

[0016] In the control device according to the present disclosure, the encryption unit performs encryption using a homomorphic encryption method in which the key used is updatable.

[0017] In the present disclosure, homomorphic encryption, which allows updating keys, is used to encrypt parameters and communication signals, so attacks on the control system can be quickly detected and responded to.

[0018] In the control device according to the present disclosure, the damping processing unit performs the nonlinear damping using an estimated cogging force function, and the estimated cogging force function (^f cog ) is defined by the following formula:

[0019]

number

[0020] In the present disclosure, encryption is performed using the estimated cogging force function, and therefore, by generating an appropriate thrust force related to cogging, the influence of the cogging force on the mover of the linear motor can be suppressed.

[0021] The control device according to the present disclosure includes an output processing unit that outputs a cogging force when position information of the mover of the linear motor is input.

[0022] In accordance with the present disclosure, the dynamics of a linear motor can be represented as an interconnection between the linear dynamics of the mover and an output processing section that outputs a cogging force depending on the position of the mover. [Effects of the Invention]

[0023] According to the present disclosure, it is possible to provide a linear motor control device that can prevent control information from being leaked to the outside and control parameters and the like from being tampered with. [Brief explanation of the drawings]

[0024] [Figure 1] FIG. 2 is a perspective view showing the configuration of a linear motor. [Figure 2] FIG. 2 is a side view showing the configuration of a linear motor. [Figure 3] 1 is a block diagram showing the configuration of an embodiment of a linear motor control device according to the present invention; [Figure 4] FIG. 10 is an explanatory diagram illustrating parameters related to an estimated cogging force function ^fcog. [Figure 5] FIG. 1 is a diagram conceptually illustrating an encrypted control system (control device). [Figure 6]1 is a graph illustrating the investigation and evaluation process using Equation (2) to determine the parameter α of the cogging force model according to Equation (1); [Figure 7] 10 is a graph showing experimental results when ^fcog compensation is performed in the control device (linear motor) according to the present embodiment. [Figure 8] 10 is a graph showing experimental results using a linear motor with nonlinear compensation and a disturbance observer. [Figure 9] 10 is a graph showing the results of comparing the tracking control performance of an encrypted control system in a control device with a non-encrypted control system. [Figure 10] 10 is a graph showing the results of an experiment on detecting cyber attacks against a control system. DETAILED DESCRIPTION OF THE INVENTION

[0025] DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENTS The present invention will be described in detail with reference to the drawings showing embodiments thereof. In the following, a case will be described in which the present invention is applied to a positioning stage that employs a linear motor as an example of a motor.

[0026] 1 and 2 are a perspective view and a side view showing the configuration of a linear motor 1. The linear motor 1 has a mover 2 and a stator 3 that face each other with a predetermined distance between them.

[0027] The mover 2 is configured by supporting and fixing, at equal intervals, for example, 14 rectangular permanent magnets 21 to a thin plate-like back yoke 22 and arranging them side by side in the direction of movement (left and right direction in FIG. 2). Each permanent magnet 21 is magnetized in the thickness direction (up and down direction in FIG. 2), and the magnetization directions of adjacent permanent magnets 21, 21 are opposite to each other. In other words, permanent magnets 21 magnetized in the direction from the mover 2 side toward the stator 3 side (top to bottom direction in FIG. 2) and permanent magnets 21 magnetized in the direction from the stator 3 side toward the mover 2 side (bottom to top direction in FIG. 2) are arranged alternately.

[0028] On the other hand, the stator 3 is configured by integrally providing, for example, 30 rectangular magnetic pole teeth 32 at equal intervals in the moving direction on a thin plate-like stator 31, and by winding a coil 33 around each magnetic pole tooth 32. U, V, and W in Fig. 2 respectively represent the U-phase, V-phase, and W-phase of a three-phase AC power supply, and three pairs of forward and reverse two-slot are formed as one set to perform three-phase parallel current conduction. The linear motor 1 has a basic unit of a seven-pole, six-slot configuration having seven permanent magnets 21, six magnetic pole teeth 32, and coils 33.

[0029] When a three-phase alternating current is passed through the coil 33 of the stator 3 to generate a magnetic field in the magnetic pole teeth 32, the permanent magnets 21 of the mover 2 are sequentially magnetically attracted and repelled by this magnetic field, generating a thrust in the mover 2, causing the mover 2 to move linearly relative to the stator 3.

[0030] The present invention relates to a control device 10 for a linear motor 1. The control device 10 according to this embodiment performs nonlinear compensation control to suppress periodic disturbances, and disturbance observer control to suppress other non-periodic disturbances. The nonlinear compensation control suppresses periodic disturbances, such as cogging, in the constant velocity range. The disturbance observer control utilizes a steady-state Kalman filter to suppress disturbances (friction, vibration, etc.) that cannot be fully suppressed by the nonlinear compensation control in the constant velocity range.

[0031] Furthermore, the control device 10 of the linear motor 1 according to this embodiment controls the linear motor 1 by encrypting control signals and control parameters related to the driving of the linear motor 1, in addition to the nonlinear compensation control and disturbance observer control described above.

[0032] 3 is a block diagram showing the configuration of one embodiment of a control device 10 for a linear motor 1 according to the present invention. The control device 10 includes a motion controller 100, a controlled object 40, an estimated cogging function unit 51 (attenuation processing unit), an encoder 44, and a differentiator 62. The controlled object 40 includes the linear motor 1, a cogging function unit 41 (output processing unit), and an adder 42. The motion controller 100 includes a disturbance observer 61, a first subtractor 72, and a second subtractor 71.

[0033] A nonlinear compensation control system 50 is configured with the estimated cogging function unit 51, and a disturbance observer control system 60 is configured with the disturbance observer 61 and the differentiator 62.

[0034] Furthermore, the motion controller 100 has a speed control unit 111, a third subtractor 112, a position control unit 121, and a fourth subtractor 122. The speed control unit 111 and the third subtractor 112 constitute a speed control unit 110, and the position control unit 121 and the fourth subtractor 122 constitute a position control unit 120.

[0035] The input terminal of the linear motor 1 related to the controlled object 40 is connected to the output terminal of the adder 42, and the output terminal of the linear motor 1 is connected to the input terminal of the encoder 44. The encoder 44 outputs the measured position y p The output terminal of the cogging function unit 41 is connected to one of the addition input terminals of an adder 42, and the other addition input terminal of the adder 42 is connected to the output terminal of an amplifier (not shown).

[0036] The output terminal of the encoder 44 is connected to the input terminal of the estimated cogging function unit 51 and the input terminal of the differentiator 62. The output terminal of the estimated cogging function unit 51 is connected to the subtraction input terminal of the first subtractor 72. The output terminal of the first subtractor 72 is connected to the input terminal of the amplifier, and the output terminal of the second subtractor 71 is connected to the addition input terminal of the first subtractor 72 and one input terminal of the disturbance observer 61.

[0037] The output terminal of the differentiator 62 is connected to the other input terminal of the disturbance observer 61 and the subtraction input terminal of the third subtractor 112. In addition, the output terminal of the disturbance observer 61 is connected to the subtraction input terminal of the second subtractor 71.

[0038] The output terminal of speed control unit 111 is connected to the addition input terminal of second subtractor 71, and the input terminal of speed control unit 111 is connected to the output terminal of third subtractor 112. As described above, the subtraction input terminal of third subtractor 112 is connected to the output terminal of differentiator 62, and the addition input terminal of third subtractor 112 is connected to the output terminal of position control unit 121. The input terminal of position control unit 121 is connected to the output terminal of fourth subtractor 122, and the subtraction input terminal of fourth subtractor 122 is connected to the output terminal of encoder 44.

[0039] The fourth subtractor 122 receives the reference value r of the position of the linear motor 1 (the mover 2 of the linear motor 1). p , that is, the target position is input from the outside, and the measured position y p is input, and the fourth subtractor 122 calculates the difference between them (r p -y p ) is the position command e p The position control unit 121 outputs the speed command (reference value r v ) is calculated and output.

[0040] The third subtractor 112 receives the reference value r of the velocity, which is an output from the position control unit 121. v is input, and the velocity output y v is input, and the third subtractor 112 calculates the difference between them (r v -y v ) is the speed command e v to the speed control unit 111. The speed control unit 111 calculates the speed error amount based on the difference from the third subtractor 112, and outputs the current command ( ~ u) is calculated and output.

[0041] The addition input terminal of the second subtractor 71 receives a current command from the speed control unit 111. ~ The second subtractor 71 receives the current command u as an input, and receives the control output ^d (estimated value of the disturbance) from the disturbance observer 61 as an input to its subtraction input terminal. ~The control output ^d is subtracted from u to output the current command u'. The current command u' output from the second subtractor 71 is input to the disturbance observer 61 and the first subtractor 72. The estimated cogging force (an estimated value of the periodic correction of cogging) is output from the estimated cogging function unit 51 and input to the subtraction input terminal of the first subtractor 72. The symbol "^" represents an estimated value.

[0042] The first subtractor 72 subtracts the estimated cogging force from the current command u' to calculate and output the current command u. The current command u output from the first subtractor 72 is input to the amplifier. The amplifier is, for example, a PWM amplifier, and outputs a control signal (current command) to the controlled object 40 based on the current command u.

[0043] The controlled object 40 is modeled by the linear motor 1 and a cogging function part 41. The cogging function part 41 calculates the measured position y p The cogging force output from the cogging function unit 41 is added to the thrust force output from the amplifier by an adder 42 and input to the linear motor 1.

[0044] Also, the measured position y p is output to the differentiator 62 and the fourth subtractor 122.

[0045] The control device 10 according to this embodiment having the above-described configuration takes into consideration the dynamics of the mover 2 (hereinafter, for ease of explanation, may be simply referred to as "the mover 2") of the linear motor 1. Such dynamics are determined by the linear dynamics of the mover 2 and the cogging function unit 41 (cogging force function f cog ) (see Figure 3).

[0046] Further, the estimated cogging function unit 51 calculates the estimated cogging force function ^f cogis used to damp the nonlinearity of the dynamics of the linear motor 1, which is nonlinear. In addition, a disturbance observer 61 is provided to nominalize the damped system into a linear model. In other words, the estimated cogging function unit 51 and the disturbance observer 61 make it possible to treat the nonlinear dynamics of the linear motor 1 as a linear system with unknown input disturbances.

[0047] On the other hand, the dynamics of the linear motor 1 are nonlinear and therefore cannot be encrypted as is. In contrast, in the control device 10 of this embodiment, as described above, the estimated cogging function unit 51 is used to attenuate the nonlinearity of the dynamics of the linear motor 1 and make it linear. That is, in the control device 10 of this embodiment, the dynamics of the linear motor 1 are made linear prior to encryption processing. Specifically, such nonlinear compensation can only be achieved by the estimated cogging function unit 51 using Equation (1), which will be described later. The control parameters and communication signals related to the dynamics of the linear motor 1, which have been made linear in this way, are encrypted by the encryption unit 80.

[0048] Figure 4 shows the estimated cogging force function ^f cog 4 is an explanatory diagram illustrating parameters relating to the above. In the graph of Fig. 4, the vertical axis represents the amplitude of the cogging force, and the horizontal axis represents the position.

[0049] As described above, the estimated cogging function unit 51 calculates the estimated cogging force function ^f cog The nonlinearity of the dynamics of the mover 2 of the linear motor 1 is damped using the estimated cogging force function ^f cog to generate the appropriate thrust.

[0050]

number

[0051] If the estimation is close to the ideal function, the mover 2 is not affected by the cogging force. In other words, in the above case 1, the current command u′ is pThe dynamics from the current command u′ to the measurement position y p The dynamics up to can be considered as a specific (nominalized) linear system with nonlinear disturbances. The estimated cogging force function ^f cog is formulated as follows:

[0052]

number

[0053] where k∈Z ≧0 is the step, θ(y p ):=2πy p / β+δ, and y p is the displacement of the mover 2, α is the amplitude of the cogging force, β is the length of one cycle of the cogging force, and δ is the initial phase of the cogging force (see Figure 4).

[0054] This function follows a squared sine wave form, since it is inversely proportional to the square of the relative position of the stator 31 and the permanent magnet 21. The estimated cogging force function ^f cog The period and initial phase of are determined by the stator pitch and the distance between the end position and the mover position, respectively. The cogging force model is determined by physical characteristics except for amplitude. A reasonable selection ensures that the dynamics of the linear motor 1 approaches the linear dynamics of the mover 2. To experimentally evaluate the effectiveness of each, we use Esum(α) from a step response experiment, as described below.

[0055]

number

[0056] where y v is the velocity of the mover 2, for example, the velocity output y v and ^y v Yes vrepresents the step response of the estimated linear model derived from ( ). An appropriate α is chosen to minimize the cost function Esum(α). Once the value of α is determined, an estimated model ŝP(s) can be obtained, which is used to design the motion controller 100. The modeling error is estimated by introducing a disturbance observer 61, as described below.

[0057] The disturbance observer 61 is designed to mitigate the modeling error of the cogging force, which is treated as a disturbance. The dynamics of this modeling error are assumed to be similar to a step disturbance. A nominal model of the linear motor 1, defined as the estimated model ŝP(s), is obtained, for example, from the above-mentioned controlled object 40. Such a model has current as an input and velocity as an output. An extended system including the dynamics of the estimated model ŝP(s) and the disturbance model can be formulated as follows:

[0058]

number

[0059]

number

[0060] where x∈R are the states of the obtained nominal model s^P(s) and its realizations (A, B, C), and η∈R are the states of the disturbance model and its realizations (A d , C d ), d∈R is the disturbance, and u′∈R is the control input of the compensated plant. The Luenberger observer is used as the disturbance observer 61 of the augmented system as follows:

number

[0061]

number

[0062] where ^x∈R and ^η∈R are the estimates of x and η, respectively, and L T =T[L x L d ] is the observer gain. The estimated disturbance ^d from the disturbance observer 61 is fed back to the input of the linear motor 1 via the second subtractor 71, as described above. That is, as explained in FIG. 3, u'= ~ u-^d, and normalization is performed as a result.

[0063] The speed control section 111 and the position control section 121 are designed for a nominal linear model ^P. The speed control section 111 is a proportional-integral (PI) compensator.

[0064]

number

[0065]

number

[0066] Here, as mentioned above, r p and r v is the position and velocity reference, e p :=r p -y p and e v :=r v -y v represents the feedback error. v and x p are the state vectors of the PI controller (speed control section 111) and the P controller (position control section 121), respectively, and (A v , B v , C v , D v ) and (A p , B p , C p , D p ) is a realization of PI and P compensators in discrete-time state-space representation.

[0067] Below we describe a secure position control system for a linear motor 1 that allows operation with encrypted time-varying control parameters and encrypted communication signals in the controller 10. This is achieved by using a combination of controller encryption techniques and updatable homomorphic encryption.

[0068] The control device 10 uses a well-known, updatable ElGamal encryption scheme (see K. Teranishi, N. Shimada, and K. Kogiso, “Stability-guaranteed dynamic ElGamal cryptosystem for encrypted control systems,” IET Control Theory & Applications, vol. 14, no. 16, pp. 2242-2252, 2020.) The use of the ElGamal encryption scheme not only strengthens the control system through encryption using a key update mechanism, but also enables the detection of cyberattacks such as parameter tampering and replay attacks.

[0069] The definition of the updateable encryption scheme is as follows: <Definition 1> The updateable ElGamal encryption scheme has three algorithms, Gen, Enc, and Dec, and two update rules, Tk and Tc. The algorithms are defined as follows: Gen:λ→(pk,sk)=((G,q,g,h),s) Enc:(m,pk)→(c1,c2)=(g r mod p,mh r mod p) Dec:((c1,c2),sk)→m=c2c1 -s mod p

[0070] where Gen is the key generation algorithm, Enc is the encryption algorithm, Dec is the decryption algorithm, λ is the key length, pk = (G, q, g, h) is the public key, sk = s is the secret key randomly selected from Z, q is a k-bit Sophie-Germain prime satisfying p = 2q + 1, g is the generator of the plaintext space G, and r is Z. q Here, G={g i mod p|i∈Z p}(=:M), g q mod p=1, h=g s mod p. Furthermore, the update rules for the keys h and s and the ciphertexts c1 and c2 are defined as follows:

[0071]

number

[0072] where G, q, and g are time-invariant, and w(k) is the Z q The initial key is pk(0) = ((G, q, g, h(0)) and sk(0) = s(0), which is given by the Gen algorithm.

[0073] The updateable ElGamal encryption scheme according to the present invention has the following two properties.

[0074]

number

[0075] Real numbers cannot be directly addressed through the encryption scheme of Definition 1. Therefore, to implement the designed control device 10 securely, the encoder Ecd γ :R→M and decoder Dcd γ :M → R, must be used. These are Ecd γ (a):="γa+p1 R<0 (a)” M, Dcd γ (b):=1 / γ{b-q1Z>0 (b)}, where γ>0 is a scaling parameter and '·'M rounds the argument to the nearest element in the set M. Also, for a given set X, if a∈X, then 1 X (a)=1.

[0076] The controller encryption uses a multiplicative homomorphic encryption scheme (see K. Kogiso and T. Fujita, “Cyber-security enhancement of networked control systems using homomorphic encryption,” in IEEE Conference on Decision and Control, pp. 6836-6843, 2015.), and forms the encrypted controller as follows (see K. Teranishi, M. Kusaka, N. Shimada, J. Ueda, and K. Kogiso, “Secure observer-based motion control based on controller encryption,” in American Control Conference, pp. 2978-2983, 2019.) <Definition 2>.

[0077]

number

[0078] Here, Φ(k):=Enc(Ecd γΦ (Φ),pk(k)) and ξ￣(k):=Enc(Ecd γξ (ξ(k)),pk(k)) represents the encrypted coefficients of the designed controller and the encrypted input to the encrypted controller, where pk(k)=(G,q,g,h(k)).

[0079] Scaling parameter γ Φ >0 and γ ξ >0 is Φ∈R 5×8 and ξ∈R 8Φ∈R 5×8 and ξ∈R 8 satisfies the following equation:

[0080]

number

[0081] This equation represents the global formula for all (unencrypted) controllers associated with the control device 10. Here, the matrix Φ and vectors ξ and Ψ are defined as follows:

[0082]

number

[0083]

number

[0084] This comprehensive formula is derived from equations (1), (4a, 4b)-(6), e p , e v ,^d,u′, ~ Remove u and u= ~ u-^d-^f cog (y p ) can be obtained using

[0085] 5 is a diagram conceptually showing an encrypted control system (control device 10). For convenience, the disturbance observer 61 and the encoder 44 are omitted from the illustration in FIG. The encryption unit 80 configured as above is included in the motion controller 100, and p , x v , ^x, ^η, r p , y p , y v The control signals and control parameters relating to the driving of the linear motor 1 are encrypted.

[0086] The relationship between the encrypted output ̂Ψ in (8) and the unencrypted output ψ in (9) can lead to quantization errors in the encrypted control system. × ε The explicit form of is given as follows:

[0087]

number

[0088] And the corresponding plaintext V ψ is obtained as where sk(k)=s(k).

[0089]

number

[0090] The configuration of the control device 10 according to this embodiment will be described below using a specific example. The control device 10 (motion controller 100) is configured using, for example, a computer.

[0091] FIG. 6 is a graph illustrating the investigation and evaluation process using Equation (2) to determine the parameter α of the cogging force model according to Equation (1). FIG. 6A is a graph showing the step response of the estimated linear model when u′(k)=1.0A. In FIG. 6A, the solid line is the estimated linear model and the dashed line is the measured value. Also in FIG. 6A, the vertical axis is speed and the horizontal axis is time. Furthermore, FIG. 6B is a graph showing the evaluation of Esum(α) for α values ​​between 0.7 and 1.6. In FIG. 6B, the vertical axis is Esum(α) and the horizontal axis is α.

[0092] Figure 3 shows the u' to y p was modeled as ^P(s) = 1.683 / s(s + 6.051), where the MATLAB function "tfest" was used to measure the model parameters from the step response of u'(k) = 1.0 (see Figure 6A).

[0093] In this case, the estimated cogging force function ^f cog α=1.3, β=1.51×10 ―2 , δ=7.55×10 -3 The parameters β and δ are determined by measuring the pitch of the stator 3 and the initial position of the mover 2, as described above. The parameter α is determined by evaluating each value Esum(α) from 0.7 to 1.6. The results are shown in Figure 6B. The estimated model ŝP(s) is calculated by dividing u′ by y v It corresponds to systems up to

[0094] FIG. 7 shows the control device 10 (linear motor 1) according to this embodiment. cog 7 is a graph showing the experimental results when compensation is applied. In FIG. v ) where the horizontal axis is time. The solid line indicates the estimated cogging force function ^f cog The solid and dashed lines show the case where compensation is performed using the estimated cogging function unit 51, and the dashed lines show the case where the estimated cogging function unit 51 is not used. In addition, control inputs u′(k)=1.1A and 1.2A are used. Both the solid and dashed lines show the step response.

[0095] As can be seen from FIG. 7, the behavior of the linear motor 1 to which the control device 10 has applied the above-described nonlinear compensation has reduced fluctuations and is confirmed to be generally linear. Furthermore, the linear motor 1 to which nonlinear compensation has been applied operates with a control input (current) that is lower than the control input without nonlinear compensation. In this way, nonlinear compensation using the estimated cogging function unit 51 is effective in attenuating the cogging force, and the change from u' to y v The system becomes close to linear up to

[0096] Regarding the disturbance observer 61, when the estimation model s^P(s) is realized, from the formula (3a) and the formula (3b), A = 9.94 × 10 -1 , B=9.77×10 -4 , and C=1.68 is obtained. The disturbance is assumed to follow integral action, and Ad =C d = 1. The design of the observer gains in Equation (4a) and Equation (4b) is reduced to a discrete-time LQR problem of a doubly linear system.

[0097]

number

[0098] The dual linear system can be expressed as follows:

[0099]

number

[0100] where ζ∈R 2 is the state. Q=diag(1,10 5 ) and R=1, L x =6.21×10 -1 and L d =1.27×10 2 This becomes:

[0101] 8A and 8B are graphs showing the results of an experiment using a linear motor 1 with nonlinear compensation and equipped with a disturbance observer 61. FIGS. 8A and 8B show the relationship between the velocity y v The vertical axis in Fig. 8A shows the time response of the velocity y v 8B, the vertical axis is the control input u (current) and the horizontal axis is time. The solid line indicates the case where the disturbance observer 61 is provided, and the dashed line indicates the case where the disturbance observer 61 is not provided. The profile of the control input u is manually adjusted to maintain a steady-state velocity of 0.4 m / s for each case. The dashed-dotted lines in Figures 8A and 8B represent the ~ u to y v We show the linear model s^P(s) up to

[0102] As can be seen from FIG. 8, it can be confirmed that the operation of the linear motor 1 becomes more linear with compensation by the disturbance observer 61 than with nonlinear compensation alone. The difference between the solid line and the dashed line in FIG. 8A is used for damping the cogging force. Therefore, when the disturbance observer 61 is added to the linear motor 1 that has been nonlinearly compensated, ~ u to y v This is effective in making the system approach linear up to

[0103] The position control unit 121 and the speed control unit 111 were designed through trial and error in order to limit the speed overshoot and the current input to within ±5% and ±18 A, respectively. Specifically, the parameters of the position control unit 121 are: p =B p =C p =0, D p The parameter of the speed control unit 111 is set to A v =1, B v =3.2×10 -2 , C v =46.9, D v =30.

[0104] The encryption of control parameters and communication signals in the control device 10 will be described below. The coefficient matrix obtained as a result of the experiment is shown below.

[0105]

number

[0106] The encrypted coefficients are given by the following equation (13): The key length of the renewable ElGamal encryption was set to 62 bits to ensure that the control process is completed within the sampling period. The encrypted controller f x ε and γ ζ =10 8 The safe configuration consisting of the remaining processes such as Ecd and Dcd is implemented in the computer associated with the control device 10.

[0107]

number

[0108] The tracking control performance of an encrypted control system in the control device 10, which uses encryption of control parameters and communication signals, is evaluated in comparison with a non-encrypted control system. FIG. 9 is a graph showing the results of comparing the tracking control performance of the encrypted control system in the control device 10 with that of a non-encrypted control system.

[0109] In Figure 9A, the position command r p (reference position value) and control position y p 9A, the vertical axis represents the position, the horizontal axis represents the time, and the dashed line represents the position command r p 9B shows the actual control input u. In FIG. 9B, the vertical axis is the control input (current) and the horizontal axis is time. FIG. 9C and FIG. 9D show the actual control input u(k)- V 9C shows the position tracking error and quantization error for the actual control input calculated using ψ5(k). In Fig. 9C, the vertical axis represents the position tracking error, and the horizontal axis represents time. In Fig. 9D, the vertical axis represents the quantization error, and the horizontal axis represents time. 9B, 9C, and 9D, the gray lines represent the encrypted control system related to the control device 10, and the black lines represent the unencrypted control system.

[0110] As can be seen in FIG. 9A, the control position y of the encryption control system p is consistent with the unencrypted control system. Also, as can be seen in Figure 9B, the control input u of the encrypted control system is roughly consistent with the unencrypted control system.

[0111] FIG. 9C confirms that the control using encryption of the control parameters and communication signals can achieve similar tracking performance in the steady state, since both tracking errors are within the range of ±1 μm, which is the central minimum resolution.

[0112] On the other hand, due to the rounding operation during encoding, V ψ is not always equal to ψ. This mismatch may cause quantization errors during encoding and decoding, which may affect control performance. Furthermore, it is generally difficult to theoretically analyze such performance degradation. In contrast, in the control system related to the control device 10, as can be seen from Figure 9D, it was confirmed that the quantization error occurring in the encrypted control system is on the order of microamperes and is negligible because it does not affect the position tracking performance.

[0113] In this way, experimental verification confirmed that by encrypting control parameters and communication signals in the control device 10, a safe position control system for the linear motor 1 can be realized without degrading control performance.

[0114] We then confirmed that the control system of the control device 10 can detect cyber-attacks. We compared the encrypted control system of the control device 10, which uses the updatable homomorphic encryption method, with an encrypted control system that uses the static key homomorphic encryption method (hereinafter referred to as the comparison encrypted control system).

[0115] In detail, the encrypted control parameter Φ 1 41 We performed a tampering attack by adding 1 to and overwriting the current encrypted feedback signal Φ̂ by 7 seconds, and a replay attack by continuously replacing the current encrypted feedback signal Φ̂ with the one recorded in advance at 7 seconds. In the tampering attack, Φ̂ = (Φ̂ 1 ,Φ￣ 2 )

[0116] Figure 10 is a graph showing the experimental results of detecting cyber attacks on control systems. Fig. 10A shows the experimental results of a tampering attack on a control system, and Fig. 10B shows the experimental results of a replay attack on a control system. In Fig. 10, the solid black line represents the control system of the control device 10 according to this embodiment, the solid gray line represents a comparative encrypted control system, and the light gray dashed line represents the case where there is no attack.

[0117] The tampering and replay cyber attacks began 7 seconds after the control started. The cyber attack detector was set to a threshold of 8A and monitored the decoded control input. If the control input exceeded the threshold, the control operation was stopped by setting the control input to zero.

[0118] As can be seen from Figure 10A, it was confirmed that both the control system of the control device 10 and the comparative encrypted control system can detect tampering attacks in real time. This is because the homomorphic encryption used in both control systems cannot preserve the addition of the encrypted data, and therefore the tampering parameter Φ 1 41 This is because when the signal related to +1 is decrypted, noise used in the encryption process leaks in, resulting in a number that is even larger than the actuator specifications.

[0119] As can be seen from Figure 10B, it was confirmed that the encryption control system for comparison cannot detect replay attacks, whereas the encryption control system for the control device 10 can detect replay attacks in real time. This is because the public key and private key are updated at every step. Since the decryption process uses a key different from the key used in the encryption process, noise leaks when the encrypted signal is decrypted.

[0120] As described above, real-time threshold-based cyber-attack detection can be easily incorporated into a control system involving the control device 10, in which encryption of control parameters and communication signals is used.

[0121] In the control device 10 of this embodiment, as described above, the estimated cogging function unit 51 linearizes the dynamics of the linear motor 1 prior to encryption processing using the above-described formula (1). This makes it possible to encrypt the dynamics (control parameters and communication signals) of the linear motor 1, which are nonlinear and cannot be encrypted.

[0122] In this embodiment, the control device 10 controls the linear motor 1 using the encrypted control parameters and communication signals, and therefore, it is possible to prevent the control information from being leaked to the outside of the control device 10 and the control parameters and the like from being tampered with.

[0123] Furthermore, in this embodiment, the control device 10 uses the homomorphic encryption method as described above, and due to the characteristics of homomorphic encryption, it is possible to perform calculations using encrypted parameters and communication signals using a public key without having a private key, so the control device 10 can control the linear motor 1 using the encrypted parameters and communication signals.

[0124] Furthermore, the control device 10 in this embodiment uses a homomorphic encryption scheme in which the public key and private key are updatable, so that attacks on the control system can be quickly detected and dealt with, as described above.

[0125] The disclosed embodiments should be considered in all respects as illustrative and not restrictive. The scope of the present disclosure is defined by the claims, not by the above description, and is intended to include all modifications within the meaning and scope of the claims.

[0126] The matters described in each embodiment can be combined with each other. Furthermore, the independent claims and dependent claims described in the claims can be combined with each other in any and all combinations, regardless of the reference format. Furthermore, the claims use a format in which a claim references two or more other claims (multiple claim format), but this is not limited to this. A multiple claim (multi-multi claim) that references at least one other multiple claim may also be used. [Explanation of symbols]

[0127] 1. Linear motor 2 Mover 10 Control device 41 Cogging function section (output processing section) 51 Estimated cogging function part 61 Disturbance Observer 80 Encryption section

Claims

1. A control device for a linear motor, an encryption unit that encrypts parameters and communication signals related to control of the linear motor, A control device that controls the linear motor using encrypted parameters and communication signals.

2. The objects to be encrypted by the encryption unit include:

2. The control device according to claim 1, wherein the information includes a target position of the mover, and a detected position and moving speed of the mover.

3. The control device according to claim 1 , further comprising a damping processing unit that damps nonlinearity of the dynamics of the linear motor before encryption by the encryption unit.

4. The control device according to claim 1 , wherein the encryption unit performs encryption using homomorphic encryption.

5. The control device according to claim 4 , wherein the encryption unit performs encryption using a homomorphic encryption method in which the key used is updatable.

6. the damping processing unit performs the nonlinear damping using an estimated cogging force function; The estimated cogging force function (^f cog 4. The control device according to claim 3, wherein: [Equation 1] where k∈Z ≧０ is the step, θ(y p ): = 2πy p / β+δ, and y p is the displacement of the mover, α is the amplitude of the cogging force, β is the length of one cycle of the cogging force, and δ is the initial phase of the cogging force.

7. The control device according to claim 1 , further comprising an output processing unit that outputs a cogging force when position information of the mover of the linear motor is input.

Images