Control method and control device

Abstract

To provide a control method and a control program capable of further improving an energy efficiency and robustness.SOLUTION: A control method comprises the steps of: measuring a process variable of a target to be controlled; calculating an error value e(t) defined as a difference between a reference value and the process variable; calculating a manipulated variable u, using a sum of a product of a differential gain Ks and a differential s(t) of an error value related to a time, a product of a proportional gain Ke and the error value e(t), and a product of an integral gain KE and an integral E(t) of the error value related to a time; and controlling the target based on the manipulated variable u, wherein a state vector x(t) satisfies a prescribed formula.SELECTED DRAWING: Figure 1

Description

[Technical field]

[0001] The present invention relates to a control method and a control device. [Background technology]

[0002] Non-Patent Document 1 discloses an adaptive robot control algorithm consisting of a PD feedback part and a full dynamics feedforward compensation part, which estimates unknown dynamic parameters of the manipulator and the payload online. This algorithm is computationally simple because it effectively utilizes the structure of the manipulator dynamics.

[0003] Non-Patent Document 2 discloses global asymptotic stability of the entire system that requires the transfer function of a linear controller to be positively real.

[0004] Non-Patent Document 3 discloses a control framework for torque-controlled humanoid robots that efficiently minimizes tracking error using quadratic programming (QP) formulated as a multi-objective weighted task with constraints. [Prior art documents] [Non-patent literature]

[0005] [Non-Patent Document 1] J.-JE Slotine et al., "On the adaptive control of robot manipulators." The International Journal of Robotics Research, 6(3), 1987. [Non-Patent Document 2] ID Landau et al., "Applications of the Passive Systems Approach to the Stability Analysis of Adaptive Controllers for Robot Manipulators." International Journal of Adaptive Control and Signal Processing, 3, 1989. [Non-Patent Document 3] R. Cisneros Limon, M. Benallegue, A. Benallegue, M. Morisawa, H. Audren, P. Gergondet, A. Escande, A. Kheddar, F. Kanehiro, "Robust Humanoid Control Using a QP Solver with Integral Gains." IROS 2018: pp. 7472-7479. Summary of the Invention [Problem to be solved by the invention]

[0006] Traditional torque or current control is susceptible to modeling errors, for example when mass distribution and load loading are incorrect, and therefore high-gain position control is typically used, which leads to tracking errors in dynamic motion and dangerous conditions for surrounding humans and the environment, especially when unexpected contact occurs.

[0007] Therefore, the present invention has been made in consideration of the above problems, and an object of the present invention is to provide a control method and a control device that can further improve energy efficiency and robustness. [Means for solving the problem]

[0008] The present invention has been made based on the above findings, and the gist of the present invention is as follows.

[0009] [1] A control method comprising the steps of: Measuring a target process variable to be controlled; calculating an error value e(t) defined as the difference between a reference value and the process variable; Differential gain K s and the differential of the error value with respect to time s(t), the proportional gain K e and the error value e(t), and the integral gain K E and the integral of the error value with respect to time E(t), and controlling the target based on the manipulated variable u; The state vector x(t) defined as equation (1) is expressed as equation (2)

[0010]

number

[0011] Fulfilling t represents time, and α 0 and α 1 A way to represent a positive number. [2] The control method according to [1], further comprising the steps of: s satisfies equation (3), and the proportional gain K e satisfies equation (4), and the integral gain K E The product of satisfies equation (5), K s =λM+K a +C formula (3) K e = μM + λK a +L+λC Equation (4) K E = μK a +γλL+μC Equation (5) where λ, μ, and γ are positive scalars, γ is less than 1, and K a and L is a positive definite matrix and M is a mass matrix, the control method. [3] The control method according to [1] or [2], wherein the target has n joints, and each of the n joints has one position; The operational variable u is expressed by equation (6).

[0012]

number

[0013] is defined as where q is the joint position,

[0014]

number

[0015] is the joint velocity,

[0016]

number

[0017] is the joint acceleration, C is the Coriolis matrix, G is the target gravity vector, and J i is the Jacobian matrix of joint point i, and F i is the generalized force at joint point i, where i is a value between 0 and n. [4] A control device comprising: a sensor unit configured to sense a target process variable to be controlled; a memory unit configured to store the reference value to be input; Differential gain K s and the differential s(t) of the error value e(t) with respect to time, and the proportional gain K e and the error value e(t), and the integral gain K E and a calculation unit configured to calculate the manipulated variable u using a sum of products of and an integral E(t) of the error value with respect to time; a control unit configured to control the target based on the manipulated variable u; The state vector x(t) defined as equation (1) is expressed as equation (2)

[0018]

number

[0019] Fulfilling where e(t) is defined as the difference between the reference value and the process variable, t represents time, and α 0 and α 1 represents a positive number,controller. [5] [4] The control device according to the present invention, s satisfies equation (3), and the proportional gain K e satisfies equation (4), and K E satisfies equation (5), K s =λM+K a +C formula (3) K e = μM + λK a +L+λC Equation (4) K E = μK a +γλL+μC Equation (5) where λ, μ, and γ are positive scalars, γ is less than 1, and K a and L is a positive definite matrix and M is a mass matrix,controller. [6] The control device according to [4] or [5], wherein the target has n joints, and each of the n joints has one position; The operational variable u is expressed by equation (6).

[0020]

number

[0021] is defined as where q is the joint position,

[0022]

number

[0023] is the joint velocity,

[0024]

number

[0025] is the joint acceleration, C is the Coriolis matrix, G is the target gravity vector, and J i is the Jacobian matrix of joint point i, and F i is the generalized force at joint point i, where i is a value between 0 and n, the controller. Effect of the Invention

[0026] As described above, according to the present invention, it is possible to provide a control method and a control device that can further improve energy efficiency and robustness. [Brief description of the drawings]

[0027] [Figure 1] 4 is a flowchart showing an example of the flow of a control method according to an embodiment of the present invention. [Diagram 2] FIG. 2 illustrates components of a control device on which a control device may be mounted according to one embodiment. [Diagram 3] FIG. 1 shows a robot with joints to be controlled according to an example of the present invention. [Figure 4] FIG. 13 illustrates the root mean square (RMS) error of joint velocity (vq) in radians / sec and position (q) in radians with respect to time in milliseconds for the perfect model under kinematic feedback and PID based passivity in accordance with an example of the present invention. [Diagram 5] FIG. 13 illustrates the RMS error of joint velocity (vq) in radians / sec and position (q) in radians with respect to time (ms) for the bias model under kinematic feedback and PID based passivity in accordance with a comparative example of the present invention. [Figure 6] FIG. 2 is a block diagram of a controller. DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENTS

[0028] Hereinafter, an embodiment of the present disclosure will be described in detail with reference to the accompanying drawings. In addition, in this specification and the drawings, the same components having substantially the same functions and configurations are designated by the same reference numerals, and duplicated descriptions are omitted.

[0029] 1 is a flowchart showing an example of a flow of a control method according to an embodiment of the present invention. As shown in FIG. 1, the control method according to the embodiment of the present invention is characterized by: (a) measuring a target process variable to be controlled; (b) calculating an error value e(t), defined as the difference between a reference value and the process variable; (c) Differential gain K s and the differential of the error value with respect to time s(t), the proportional gain K e and the error value e(t), and the integral gain K E and the integral of the error value with respect to time E(t), (d) controlling the target based on the manipulated variable u; The state vector x(t) defined as equation (1) is expressed as equation (2)

[0030]

number

[0031] Fulfilling t represents time, and α 0 and α 1 represents a positive number.

[0032] (Step of measuring the target process variable to be controlled) In an embodiment of the present invention, a process variable of a target to be controlled is measured. The process variable and the target are not limited. The target can have n joints. Each of the n joints can have one position. The target can be a robot. A sensor for measuring the process variable of the target can be used as the measurement device. In an embodiment of the present invention, the sensor is a joint position sensor. In addition, the sensor can further include a torque sensor, a pressure sensor, an inertial sensor, or a similar sensor.

[0033] (Step of calculating the error value e(t), which is defined as the difference between the reference value and the process variable) In an embodiment of the present invention, the error value e(t) is calculated by using a reference value and a process variable. The reference value is a preset value. The error value e(t) is defined as the difference between the reference value and the process variable.

[0034] (Step of calculating the feedback operation variable u) In an embodiment of the present invention, the feedback manipulated variable u f is the differential gain K s and the differential of the error value with respect to time s(t), the proportional gain K e and the error value e(t), and the integral gain K E and the integral of the error value with respect to time E(t). f is the formula

[0035]

number

[0036] It can be expressed as:

[0037] Differential gain K s Preferably, the proportional gain K satisfies the formula (3). e preferably satisfies equation (4), and the integral gain K E The product satisfies equation (5). K s =λM+K a +C formula (3) K e = μM + λK a +L+λC Equation (4) K E = μK a +γλL+μC Equation (5) where λ, μ, and γ are positive scalars, γ is less than 1, and K a and L is a positive definite matrix and M is the mass matrix of the joint.

[0038] When the target has n joints, each of the n joints has one position, and the manipulated variable u is preferably expressed by the following equation (6):

[0039]

number

[0040] It is defined as: where q is the joint position,

[0041]

number

[0042] is the joint velocity,

[0043]

number

[0044] is the joint acceleration, C is the Coriolis matrix, G is the target gravity vector, and J i is the Jacobian matrix of joint point i, and F i is the generalized force at joint point i, where i runs between 0 and n.

[0045] (Step of controlling the target based on the manipulated variable u) In an embodiment of the present invention, the target is controlled based on the manipulated variable u.

[0046] According to an embodiment of the present invention, the manipulated variable u is the integral gain K E and the integral E(t) of the error value with respect to time. It is therefore possible to correct modeling errors at low frequencies and have a safer compliant behavior in case of unexpected contact.

[0047] Further, according to an embodiment of the present invention, the state vector x(t) defined as equation (1) can be expressed as equation (2)

[0048]

number

[0049] Fulfilling t represents time, and α 0 and α 1 represents a positive number. Therefore, the state vector x(t) converges in a first-order exponential manner. For this reason, the convergence proof provides a guarantee of fast convergence.

[0050] When a robot has n joints, each has one position represented by a real number. The vector of these joint positions is denoted as q. Each of these joints is actuated by a torque generator. The vector of these torques is denoted as τ. One important factor to note is that τ and q are vectors with the same size. The robot moves F at node i. i The time differential operator d / dt is expressed as dot

[0051]

number

[0052] and is expressed as d 2 / dt 2 is two dots

[0053]

number

[0054] It is expressed as: q,

[0055]

number

[0056] ,

[0057]

number

[0058] , τ, and F i The equations of motion that link the two are called Lagrangian mechanics,

[0059]

number

[0060] and The symbols may be defined as follows: q=q(t): current joint position q r =q r (t): Reference joint position

[0061]

number

[0062] : Current joint speed

[0063]

number

[0064] : Reference joint velocity

[0065]

number

[0066] : Current joint acceleration

[0067]

number

[0068] : Reference joint acceleration M=M(q): mass matrix / inertia matrix e=qq r :Joint position error

[0069]

number

[0070] :dM / dt=C+C t The Coriolis matrix such that

[0071]

number

[0072] :Joint velocity error G=G(q): Gravity vector of the robot

[0073]

number

[0074] :Integral of joint position error J i = J i (q): Jacobian matrix of node i λ, μ, γ: positive scalars (γ<1) F i =F i (t): Generalized force at junction i K a , L: positive definite matrix

[0075] The robot is moved along a time-dependent prescribed reference trajectory q r If it is desired to trace the above reference trajectory, then the derivative

[0076]

number

[0077] and

[0078]

number

[0079] The problem is how to generate the torque τ. According to the above reference trajectory, when t becomes infinity, q becomes q r It is difficult to guarantee that the convergence of

[0080]

number

[0081] but

[0082]

number

[0083] As t approaches infinity,

[0084]

number

[0085] but

[0086]

number

[0087] It is difficult to obtain the desirable property of converging to

[0088] Meanwhile, the control method according to the embodiment of the present invention can solve the above-mentioned problems.

[0089] A control method according to an embodiment of the present invention includes a PID (Proportional-Integral-Derivative) control method based on passivity, which is the property of a system not to generate energy in excess of that introduced by input sources and external sources.

[0090] The energy of the system is given by the formula

[0091]

number

[0092] It is expressed as P is the potential gravitational energy. The time derivative of energy is the mechanical power, given by the formula

[0093]

number

[0094] is given by Next,

[0095]

number

[0096] If , we obtain the following equation:

[0097]

number

[0098] In the second section

[0099]

number

[0100] is added, yielding the following formula:

[0101]

number

[0102] matrix

[0103]

number

[0104] is skew-symmetric. This means that for any vector

[0105]

number

[0106] About

[0107]

number

[0108] This means that you can get

[0109]

number

[0110] In this system, passivity

[0111]

number

[0112] Therefore, we can benefit from the fact that this payoff matrix K s , K e , and KE can be expressed as follows: K s =λM+K a +C formula (3) K e = μM + λK a +L+λC Equation (4) K E = μK a +γλL+μC Equation (5) This is the formula

[0113]

number

[0114] Gives. where these gains are q and

[0115]

number

[0116] depends on and therefore varies over time.

[0117] The control method according to the embodiment of the present invention has Lyapunov stability, which is one of various types of stability or convergence for the solution of a differential or difference equation describing a dynamical system. e The solution that starts from near the equilibrium point x e When the equilibrium point x e is Lyapunov stable. More precisely, the equilibrium point x e is Lyapunov stable, and the equilibrium point x e All solutions starting from near the equilibrium point x e When it converges to the equilibrium point x e is asymptotically stable.

[0118] Any solution starting from any point in the state space is an equilibrium point x e When it converges to the equilibrium point x e is globally asymptotically stable (condition 1). State space R n If the solution starts at time t=0 at any point in

[0119]

number

[0120] Two positive numbers α such that 0 and α 1 When exists, state x is an equilibrium point x e (Condition 2).

[0121]

number

[0122] There exists a constant positive definite matrix H such that

[0123]

number

[0124] Two other positive definite matrices H 0 (t)>H and H 1 (t)>H exists and there exists a state space R n A solution starting anywhere in

[0125]

number

[0126] (condition 3), we have

[0127] State x is equilibrium point x e Condition 3 is a slightly stronger condition than condition 1, and is called first-order global exponential convergence. The control method according to the embodiment of the present invention preferably satisfies first-order global exponential convergence.

[0128] If the state vector x is

[0129]

number

[0130] When defined as formula

[0131]

number

[0132] is the formula

[0133]

number

[0134] is replaced in the closed-loop dynamics

[0135]

number

[0136] is obtained, this is,

[0137]

number

[0138] Gives. This is the autonomous state dynamics

[0139]

number

[0140] Given I 3×3 is a 3×3 identity matrix, and 0 3×3 is a 3 × 3 zero matrix.

[0141] where this is an autonomous linear dynamics with a time-varying matrix, x e = (0 0 0) is an equilibrium point of the system. If the global asymptotic stability of this equilibrium point is obtained, then when t goes to infinity, q becomes q r It is important to be able to guarantee that as t goes to infinity,

[0142]

number

[0143] but

[0144]

number

[0145] As t approaches infinity,

[0146]

number

[0147] but

[0148]

number

[0149] It is possible to obtain the desirable property that it converges to

[0150] K s , K e , and K E When the values ​​of are replaced by the values ​​from equations (3), (4), and (5), respectively,

[0151]

number

[0152] A constant positive definite matrix H in, and

[0153]

number

[0154] The other two positive definite matrices H 0 (t)>H, H 1 (t)>H exists,

[0155]

number

[0156] and when this satisfies condition 3, this implies that condition 2 is also satisfied, which means that the system is globally exponentially stable.

[0157] The control method according to the embodiment of the present invention can achieve theoretical proof of first-order exponential convergence in the velocity error, position error, and integral of the position error, where the error converges to zero. The position error is usually simply called the error. When the position error converges to zero, this means that in the case of a perfect system, the tracking is good and the dynamics is stable. When the velocity error converges to zero, it means that the moving object tracking is good and there is no delay. When the integral of the position error converges to zero, it means that there is no steady-state error when there is a small mismatch between the model and reality.

[0158] The presence of the integral of the position error allows the system to have no static errors, the steady-state errors being the result of zero-frequency disturbances. Similarly, when there is a low-frequency disturbance, this integral term will also compensate for it, since the integral amplifies the low-frequency components. This term allows us to keep a low gain without steady-state errors, allowing more compliance and generally being safer in the case of interaction between robots and humans.

[0159] Next, a control device according to an embodiment of the present invention will be described in detail with reference to the accompanying drawings.

[0160] 2 is a diagram showing components of a control device in which the control device according to the present embodiment is installed. As shown in FIG. 2, the control device 100 according to the present embodiment includes a sensor unit 200, a memory unit 300, a calculation unit 400, and a control unit 500.

[0161] (Sensor unit) The sensor unit 200 according to the embodiment of the present invention senses a process variable of a target to be controlled. For example, the sensor unit 200 may be realized by a joint position sensor. In addition, the sensor unit 200 may further include a torque sensor, a pressure sensor, an inertial sensor, or a similar sensor.

[0162] (Memory Unit) The memory unit 300 according to an embodiment of the present invention stores the reference value to be input. For example, the memory unit 300 can be realized by a read-only memory (ROM), a random access memory (RAM), a hard disk drive (HDD), a flash memory, or the like.

[0163] (Computational Unit) The calculation unit 400 according to the embodiment of the present invention calculates the differential gain K s and the differential s(t) of the error value e(t) with respect to time, and the proportional gain K e and the error value e(t), and the integral gain K E and the integral of the error value with respect to time E(t) is used to calculate the manipulated variable u. For example, the calculation unit 400 may be an arithmetic logic unit (ALU).

[0164] The calculation unit 400 according to the embodiment of the present invention calculates the differential gain K s satisfies equation (3), and the proportional gain K e satisfies equation (4), and the integral gain K ECalculate the operational variable u so that the product satisfies equation (5). K s =λM+K a +C formula (3) K e = μM + λK a +L+λC Equation (4) K E = μK a +γλL+μC Equation (5) where λ, μ, and γ are positive scalars, γ is less than 1, and K a and L is a positive definite matrix and M is a mass matrix.

[0165] When the target has n joints, each of the n joints has one position, and the manipulated variable u is preferably expressed by the following equation (6):

[0166]

number

[0167] It is defined as: where q is the joint position,

[0168]

number

[0169] is the joint velocity,

[0170]

number

[0171] is the joint acceleration, C is the Coriolis matrix, G is the target gravity vector, and J i is the Jacobian matrix of joint point i, and F i is the generalized force at joint point i, where i is a value between 0 and n. A control method is provided.

[0172] (Control Unit) The control unit 500 according to the embodiment of the present invention controls a target based on the manipulated variable u. For example, the control unit 500 may be realized by a processor such as a central processing unit (CPU) or a graphics processing unit (GPU) that executes a program (software). In addition, some or all of these components may be realized by hardware (including a circuit unit, a circuit) such as a large-scale integrated circuit (LSI), an application-specific integrated circuit (ASIC), or a field programmable gate array (FPGA), or may be realized by cooperation of software and hardware.

[0173] The above described embodiment can be expressed as follows. A control device comprising a storage device for storing a program and a processor, the processor executing the program to measure a process variable of a target to be controlled, calculate an error value e(t) defined as a difference between a reference value and the process variable, and calculate a differential gain K s and the differential of the error value with respect to time s(t), the proportional gain K e and the error value e(t), and the integral gain K E and an integral E(t) of the error value with respect to time, and calculating an operation variable u using the sum of the products of the operation variable u and the integral E(t) of the error value with respect to time, and controlling the target based on the operation variable u, and the state vector x(t) defined as equation (1) is calculated by:

[0174]

number

[0175] where t represents time and α 0 and α 1 represents a positive number,controller. EXAMPLES

[0176] Next, examples of the present invention will be described. The conditions in the examples are examples of conditions adopted to confirm the feasibility and effects of the present invention, but the present invention is not limited to these examples of conditions. Various conditions can be adopted in the present invention as long as the object of the present invention is achieved without departing from the gist of the present invention.

[0177] FIG. 3 shows a robot with joints to be controlled according to an example of the present invention. In the example, the joint torque is

[0178]

number

[0179] is set to.

[0180] Thus, we have obtained a torque with the following characteristics: When there are no disturbances and the desired trajectory starts from the current trajectory,

[0181]

number

[0182] ,

[0183]

number

[0184] , q=q r is obtained. Thus, in perfect conditions, the control method according to the embodiment does not degrade the performance of the system. In the presence of disturbances or when the desired trajectory starts from a state different from the current trajectory, convergence of s, e, and E to zero is obtained in first-order exponential dynamics. Thus, the system is robust to perturbations. This convergence exploits the natural passivity of the system and is therefore quite robust to modeling errors. This formulation is suitable for adaptive control.

[0185] FIG. 4 shows the RMS error of joint velocity (vq) in radians / sec and position (q) in radians over time in milliseconds for the perfect model under kinematic feedback and passivity-based PID according to an example of the present invention. FIG. 5 shows the RMS error of joint velocity (vq) in radians / sec and position (q) in radians over time (ms) for the biased model under kinematic feedback and passivity-based PID according to a comparative example of the present invention. FIG. 4 and FIG. 5 show the root mean square (RMS) error for joint velocity error ||s|| and joint position error ||e|| over sampled time. The axes are x-axis: sample time [ms], y-axis: joint velocity [rad / s] on the left and joint angle [rad] on the right. The classical PID (kf) signal is in pink and the passivity-based PID signal is in green. A simulation model of the manipulator arm Sawyer (by Rethink Robotics) tracks a desired trajectory. Two different algorithms are tested, the first is a traditional PID control called kinematic feedback (kf) and the second is a passivity-based PID expressed as integral (ip) based on passivity. Figure 5 shows the RMS error in tracking the desired joint trajectory with respect to sampled time. In perfect conditions, the errors are both zero as well, as shown in Figure 4.

[0186] However, as shown in Figure 5, when modeling errors were added, for example by adding a bias to the torque, the joint error of the conventional controller increased, while the passivity-based one kept the error very close to zero.

[0187] As shown in the right of Fig. 5, the control scheme is known from the state of the art (Slotine 1987) (Landau 1989) for PD control, but has never been used for PID control. Fig. 6 shows the block diagram of the controller. The reference acceleration generator is the unit that generates the desired position, velocity, and acceleration. The torque / current control is used to generate the acceleration of the motion using the inverse dynamics. Passivity-based PID improves on the usual inverse dynamics by adding correction terms that improve the robustness of the system. As shown in the example, when the system is perfect, there are no errors, so the additional terms are zero and do not affect the inverse dynamics. These terms appear to be corrected only when the system does not behave perfectly like the model. The global exponential convergence ensures that the control is stable and has good performance.

[0188] Although preferred embodiments of the present invention have been described and illustrated above, it should be understood that these are illustrative of the present invention and should not be considered as limiting. Additions, omissions, substitutions, and other modifications may be made without departing from the spirit or scope of the present invention. Thus, the present invention should not be considered as limited by the foregoing description, but only by the scope of the appended claims. The control device according to the embodiments of the present invention can be a robot with either hydraulic or electric actuators. [Industrial Applicability]

[0189] According to the present invention, it is possible to provide a control method and a control device that can further improve energy efficiency and robustness, and therefore the present invention has high industrial applicability. [Explanation of symbols]

[0190] 100 Control device 200 Sensor Unit 300 memory units 400 Computational Units 500 Control Unit

Claims

1. 1. A control method comprising: Measuring a target process variable to be controlled; calculating an error value e(t) defined as the difference between a reference value and the process variable; Differential gain K ｓ and the differential s(t) of the error value with respect to time, and a proportional gain K ｅ and the error value e(t), and the integral gain K Ｅ and an integral E(t) of said error value with respect to time; controlling the target based on the manipulated variable u; The state vector x(t) defined as equation (1) is expressed as equation (2) [0010] Fulfilling t represents time, and α ０ and α １ represents a positive number,control method.

2. The differential gain K ｓ satisfies the formula (3), and the proportional gain K ｅ satisfies equation (4), and the integral gain K Ｅ The product of these satisfies equation (5), K ｓ = λM + K ａ + C Equation (3) K ｅ = μM + λK ａ + L + λC Equation (4) K Ｅ =μK ａ +γλL+μC Formula (5) λ, μ, and γ are positive scalars, γ is less than 1, and K ａ and L is a positive definite matrix and M is a mass matrix.

3. the target has n joints, each of the n joints having a position; The operation variable u is expressed by the following equation (6): [0025] is defined as where q is the joint position, [0030] is the joint velocity, [0045] is the joint acceleration, C is the Coriolis matrix, G is the target gravity vector, and J ｉ is the Jacobian matrix of joint point i, and F ｉ 3. The method of claim 1, wherein: i is a generalized force at said joint point i, where i is a value between 0 and n.

4. A control device, a sensor unit configured to sense a target process variable to be controlled; a memory unit configured to store the reference value to be input; Differential gain K ｓ and the differential s(t) of the error value e(t) with respect to time, and the proportional gain K ｅ and the error value e(t), and the integral gain K Ｅ and a calculation unit configured to calculate an manipulated variable u using a sum of products of and an integral E(t) of said error value with respect to time; a control unit configured to control the target based on the manipulated variable u; The state vector x(t) defined as equation (1) is expressed as equation (2) [0050] Fulfilling e(t) is defined as the difference between the reference value and the process variable, where t represents time, and α ０ and α １ represents a positive number,controller.

5. The differential gain K ｓ satisfies the formula (3), and the proportional gain K ｅ satisfies equation (4), and K Ｅ satisfies equation (5), K ｓ = λM + K ａ + C Equation (3) K ｅ = μM + λK ａ + L + λC Equation (4) K Ｅ =μK ａ +γλL+μC Formula (5) λ, μ, and γ are positive scalars, γ is less than 1, and K ａ and L is a positive definite matrix and M is a mass matrix.

6. the target has n joints, each of the n joints having a position; The operation variable u is expressed by the following equation (6): [006] is defined as where q is the joint position, [0070] is the joint velocity, [0080] is the joint acceleration, C is the Coriolis matrix, G is the target gravity vector, and J ｉ is the Jacobian matrix of joint point i, and F ｉ 6. The control device according to claim 4 or 5, wherein: i is a generalized force at said joint point i, where i is a value between 0 and n.

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