A high dynamic funnel control method based on state predictor

Abstract

The application discloses a high-dynamic funnel control method based on a state predictor and belongs to the technical field of electromechanical control. The application mainly comprises the following three parts: firstly, a differential tracker is designed to arrange the dynamic process of a high-dynamic centrifuge system, to smoothly track a target curve, to prevent the high-dynamic centrifuge system from having excessive overshoot, to realize smooth transition of the dynamic process of the system, and to reduce the control difficulty of a subsequent controller; secondly, an adaptive funnel controller is designed, which is more simple in structure and non-singular, guarantees that the dynamic and steady-state responses of tracking errors are limited in a given funnel boundary, improves the dynamic response of the system, and reduces overshoot and regulation time; and finally, a state predictor is used to adjust the adaptive control process, so as to accelerate the convergence speed and smooth the convergence curve. The application can improve the dynamic performance of the centrifuge system under the conditions of high dynamic, high g value and high lift rate, and realize accurate control of the precision centrifuge system.

Description

TECHNICAL FIELD

[0001] The application relates to a high-dynamic centrifuge precision control method, in particular to a high-dynamic funnel control method based on a state predictor, and belongs to the technical field of electromechanical control. BACKGROUND

[0002] Missiles, carrier rockets and guided shells and other high-dynamic carriers have higher and higher requirements for the performance of high-dynamic inertial navigation systems, and higher requirements for the metrological calibration of high-dynamic inertial navigation systems. Accurate measurement and calibration through high-dynamic standard devices are key links to ensure that high-dynamic carriers accurately complete tasks. The main function of a high-dynamic centrifuge is to generate a load environment with a specific acceleration loading curve for high-precision calibration and simulation research of inertial instruments and for testing the dynamic characteristics of a tested piece under different acceleration change rates. The centrifuge adopts a rotating arm structure, and a high-power torque motor drives the rotating arm to rotate at a speed specified by a simulation curve, so as to generate an expected acceleration at a sample table on the rotating arm and realize dynamic acceleration characteristic testing of a tested piece on the sample table.

[0003] At present, the research on high-dynamic large-g-value (>1000 m / s 2 ) and high-lift-rate (>600 m / s 3 ) acceleration standard devices in China is still in the bottleneck stage, and there is a lack of effective high-dynamic metrological standard devices, which cannot meet the detection and calibration requirements of high-dynamic carrier inertial navigation systems, and there is a certain gap with the technical level of the United States and Russia. At present, the units engaged in the development of centrifuges for inertial navigation calibration in China mainly include Harbin Institute of Technology, Beijing Institute of Automation and Control Equipment of Aerospace General Corporation, Aviation Precision Machinery Institute and 304 Institute, etc. The Second Department of the Second Institute of Aerospace Science and Technology Group, the Thirty-third Institute of Aerospace Science and Technology Group and the China Academy of Engineering Physics have introduced related centrifuges from Russia. Due to time constraints, the service life has been exceeded, and in addition, the dynamic characteristics cannot meet the inertial product metrology requirements. At present, the calibration of inertial instruments in China is mostly limited to static tests, and dynamic characteristic calibration tests are still at the low-dynamic level, and there is a lack of acceleration calibration equipment for wide range, large g value and high dynamics.

[0004] Therefore, the development of high-dynamic, large-g-value and high-lift-rate acceleration standard devices has important value and significance for the calibration and evaluation of the dynamic performance of high-dynamic inertial navigation systems and meets the urgent needs of the type task. The key is to realize high-precision and high-stability control of the dynamic process of the system, which provides a strong guarantee for the improvement of the performance of the high-dynamic centrifuge system. SUMMARY

[0005] The technical problem to be solved by the high dynamic funnel control method based on a state predictor is to improve the dynamic performance of a centrifuge system and realize accurate control of a precision centrifuge system under the conditions of high dynamic, high g value and high lifting rate.

[0006] The object of the application can be achieved by the following technical solutions:

[0007] The high dynamic funnel control method based on a state predictor disclosed by the application mainly includes the following three parts: firstly, a differential tracker is designed to arrange the dynamic process of the high dynamic centrifuge system, smooth the target curve and prevent the high dynamic centrifuge system from having excessive overshoot; secondly, an adaptive funnel controller is designed to ensure that the dynamic and steady-state responses of the tracking error are limited within the given funnel boundary; and finally, a state predictor is used to adjust the adaptive control process, so as to accelerate the convergence speed and smooth the convergence curve.

[0008] As preferred, the control index requirements of the high dynamic centrifuge system are designed according to the overall requirements of the control system. The control system needs to meet the main technical index requirements of the high dynamic high-speed centrifugal acceleration standard device, especially the high lifting rate of acceleration, that is, the motor power and rotating speed of the control system need to meet the technical index requirements, and the control strategy and hardware composition need to meet the dynamic and static precision requirements.

[0009] As preferred, an alternating current permanent magnet synchronous motor (PMSM) type motor is selected for the control system design. The induced electromotive force and winding current of the PMSM are both three-phase sine waves, and the rotor position is continuously detected by a high-resolution position sensor. The PMSM driven by a sine wave is much more complex than the BDCM control driven by a trapezoidal wave, but in the high-precision servo field, since the output torque of the PMSM is stable and the fluctuation torque is much smaller than that of the BDCM, a high-torque, high-precision and high-speed precision precision servo drive system is selected.

[0010] As preferred, in the control strategy of the direct current motor, the space angle between the excitation magnetic field and the armature magnetic potential is usually fixed as orthogonal by the brush and commutator, so the armature current and the electromagnetic torque are in a linear relationship, and the torque control of the direct current motor is realized by controlling the armature current, so the direct current motor is selected for the electric drive system. In the permanent magnet synchronous motor, the space angle between the excitation magnetic field and the armature magnetic potential changes with the load, so it is necessary to control the space angle and the amplitude of the armature current to simulate the permanent magnet synchronous motor as a direct current motor, so as to obtain good speed regulation performance, and since the phase and amplitude of the armature current need to be controlled at the same time, that is, vector control.

[0011] The high dynamic funnel control method based on a state predictor disclosed by the application includes the following steps:

[0012] Step 1: Analyze the friction nonlinearity of the high dynamic centrifuge system and establish a high dynamic centrifuge system model.

[0013] A continuously differentiable model is used to represent friction nonlinearity, i.e.

[0014]

[0015] Among them, α1, α2, α3, β1, β2, β3 are positive constants, is the system speed. The continuously differentiable model (1) includes static friction characteristics and sliding friction characteristics and is suitable for the design of smooth control laws.

[0016] First, the precision centrifuge system is modeled and equivalent to a motor drive system. The motor model can be expressed as:

[0017]

[0018] Where q is the centrifuge angle; is the centrifuge speed; J is the moment of inertia; R a is the armature circuit resistance; u is the control signal; T f ,T d ,T m is the friction torque, external interference torque and driving torque; L a is the total inductance of the armature winding; i a is the armature winding current; K T is the electromechanical conversion constant; K E is the back electromotive force constant.

[0019] In the actual system, due to L a / R a Very small, the differential current di a / dt is close to zero. Define the following system variables Then the state space expression of formula (2) is:

[0020]

[0021] Where K1 = K T / R a ,K2=K T K E / R a is a positive constant,

[0022] Step 2: Design a differential tracker to realize the dynamic process of regulating the system, smoothly track the target curve, and prevent the system from overshooting.

[0023] To solve the problem of excessive overshoot in high dynamic centrifuge system, a tracking differentiator is used to arrange the transition process of reference command.

[0024] Let the set value of the centrifuge angle be y d The transition process can be realized by a tracking differentiator (TD), which is designed as follows:

[0025]

[0026] wherein

[0027] wherein y = v1 - y d + hv2; h is the system sampling step; r0 is the speed factor; v1, v2 are the outputs of the tracking differentiator; a, y are system variables; d, r are adjustable parameters.

[0028] According to the design principle of the tracking differentiator, the fast and slow of the transition process and the overshoot are arranged by adjusting the parameter r0, and the noise in the tracking signal is filtered by adjusting h.

[0029] Step three: design an adaptive funnel controller to ensure that the dynamic and steady-state responses of the tracking error of the system are limited within the given funnel boundary.

[0030] Further, based on the new reference command of the differential tracking device output, an adaptive funnel controller is designed to ensure that the dynamic and steady-state responses of the tracking error of the system are limited within the given funnel boundary.

[0031] First, d(t) is used to represent the Euclidean distance between the funnel boundary and the error as follows

[0032]

[0033] wherein is the funnel function, and e(t) is the tracking error.

[0034] The funnel boundary is determined by an arbitrarily selected, continuous, positive function The reciprocal determines that Therefore, the funnel function is defined as

[0035]

[0036] As can be seen from equation (6), the initial error value e(t0) is contained in the funnel boundary, and as time increases, e(t) is also contained in the funnel boundary. Therefore, the control gain τ(t) in the funnel control is designed as

[0037]

[0038] Therefore, the control gain τ(t) is increased when the tracking error e(t) is close to the boundary zero; on the contrary, the control gain τ(t) is decreased when the tracking error e(t) is beyond the boundary the control gain τ(t) is decreased accordingly.

[0039] Based on the funnel function (6), the adaptive funnel controller is designed as follows:

[0040] Define the error variable as follows:

[0041]

[0042] where v1 is the output of the tracking differentiator, α is the virtual control variable, i = 1, 2 are the funnel performance functions, whose parameters The initial condition needs to be satisfied

[0043] The virtual control signal of the system and the actual control signal are designed as:

[0044]

[0045] where c1, c2 are normal numbers, v2 is the output of the tracking differentiator, is the estimated value of w.

[0046] The adaptive law of is designed as

[0047]

[0048] where σ > 0 is the adjustment coefficient, and Γ is a positive definite matrix.

[0049] Finally, a state predictor is used to adjust the adaptive control process, which plays a role in accelerating the convergence speed and smoothing the convergence curve.

[0050] Step four: increase the state predictor in the adaptive law obtained in step three, use the prediction error and the tracking error to jointly adjust the adaptive law, improve the dynamic performance of the centrifuge system under the conditions of high dynamic, large g value, and high lift rate, and realize the precise control of the precise centrifuge system.

[0051] The state predictor is designed as follows:

[0052]

[0053] where l1, l2 are normal numbers, is the predicted state of x1, x2, is the state prediction error.

[0054] Then, according to the state predictor, the parameter adaptive law (10) is adjusted to

[0055]

[0056] The state predictor designed in the application is introduced into the adaptive funnel controller, the stability of the system can still be ensured, high-frequency oscillation of the system signal can be avoided, the convergence rate of the adaptive parameter can be accelerated, and the approaching curve can be smoothed, the dynamic performance of the centrifuge system is improved under the conditions of high dynamics, large g value and high lift rate, and accurate control of the precise centrifuge system is realized.

[0057] Beneficial effects:

[0058] 1. The high-dynamic funnel control method based on the state predictor disclosed in the application can eliminate excessive overshoot, realize smooth transition of the dynamic process of the system, and reduce the control difficulty of the subsequent controller, because the system state will experience a rapid change process during the start-up and braking stages of the high-dynamic centrifuge, and overshoot can easily lead to loss of control of the system.

[0059] 2. The high-dynamic funnel control method based on the state predictor disclosed in the application can guarantee that the dynamic and steady-state responses of the system are constrained within a given range, improve the dynamic response of the system, and reduce overshoot and regulation time, because the adaptive funnel controller designed in the application is more simple in structure and non-singular compared with the predetermined performance control.

[0060] 3. The high-dynamic funnel control method based on the state predictor disclosed in the application can avoid high-frequency oscillation of the system signal, accelerate the convergence rate of the adaptive parameter, and smooth the approaching curve, because the existing adaptive law regulation method mostly uses tracking error for direct regulation, and large initial tracking error and fast adaptive process can cause high-frequency oscillation of the control signal.

[0061] 4. The high-dynamic funnel control method based on the state predictor disclosed in the application can improve the dynamic performance of the system and realize precise control of the centrifuge under high dynamics by arranging, regulating and setting the dynamic process of the precise centrifuge system. BRIEF DESCRIPTION OF DRAWINGS

[0062] Figure 1 It is a standard device structure diagram of the high-dynamic centrifuge.

[0063] Figure 2 It is a control principle diagram of the high-dynamic centrifuge system.

[0064] Figure 3 It is a performance diagram of the differential tracker: (a) transition process curve; (b) approaching error.

[0065] Figure 4 Tracking performance plot for state predictor based adaptive funnel control: (a) output curve; (b) tracking error. DETAILED DESCRIPTION

[0066] The state predictor based high dynamic funnel control method disclosed in the embodiment mainly includes the following three parts: first, a differential tracker is designed to arrange the dynamic process of the system, smooth the tracking target curve, and prevent the system from having excessive overshoot; second, an adaptive funnel controller is designed to ensure that the dynamic and steady-state responses of the system are limited within the given funnel boundary; and third, a state predictor is used to adjust the adaptive control process, so as to accelerate the convergence speed and smooth the convergence curve.

[0067] The state predictor based high dynamic funnel control method disclosed in the embodiment specifically includes the following steps:

[0068] Step 1: Analyze the friction nonlinearity of the high dynamic centrifuge system, and establish a high dynamic centrifuge system model.

[0069] A conventional friction model is discontinuous or piecewise continuous, which will cause difficulty in designing a smooth control law. Therefore, the present application uses a continuous differentiable model to represent the friction nonlinearity, that is,

[0070]

[0071] where α1, α2, α3, β1, β2, β3 are normal numbers, is the system speed. The continuous differentiable model (13) contains static friction characteristics and sliding friction characteristics, and is suitable for the design of a smooth control law.

[0072] First, the precise centrifuge system is modeled and equivalent to a motor-driven system, and the motor model is represented as:

[0073]

[0074] In the formula, q is the centrifuge rotation angle; is the centrifuge speed; J is the moment of inertia; R a is the armature circuit resistance; u is the control voltage; T f ,T d ,T m is the friction torque, external disturbance torque and driving torque; L a is the total inductance of the armature winding; i a is the armature winding current; K T is the electromechanical conversion constant; K E is the back electromotive force constant.

[0075] In practical systems, L a / R a is very small, the differential di a / dt of the current is close to zero. Define the system variable The system state space expression can be written as

[0076]

[0077] where K1=K T / R a , K2=K T K E / R a are normal numbers,

[0078] The control objective is to design the control law u such that the system tracking error is uniformly bounded and the dynamic process quality of the system is guaranteed.

[0079] Step two, in view of the problem of excessive overshoot that is prone to occur in the dynamic process of the system, a tracking differentiator is used to arrange the transition process of the reference command.

[0080] Let the centrifuge rotation angle set value be y d The transition process can be realized by a tracking differentiator (TD), which can be designed as follows:

[0081]

[0082] where where y=v1-y d +hv2; h is the system sampling step; r0 is the speed factor; a, y are system variables; d, r are adjustable parameters.

[0083] According to the design principle of the tracking differentiator, the fast and slow and overshoot of the transition process can be arranged by adjusting the parameter r0, and the noise in the tracking signal can be filtered by adjusting h.

[0084] Step three, based on the new reference command output by the tracking differentiator, an adaptive funnel controller is designed to ensure that the dynamic and steady-state responses of the tracking error of the system are limited within the given funnel boundary.

[0085] Funnel control is a control method proposed by Ilchmann et al., which can guarantee that the tracking error is limited within a given range by selecting a funnel function. First, let d(t) represent the Euclidean distance between the funnel boundary and the error as follows

[0086]

[0087] where is a funnel function, e(t) is the tracking error.

[0088] The funnel boundary is defined by an arbitrary chosen, continuous, positive function The inverse decision, i.e. Therefore, the funnel variable is defined as

[0089]

[0090] From the above equation, it can be seen that when the initial error e(t0) is contained in the funnel boundary, then e(t) is also contained in the funnel boundary when t≥0. Therefore, the control gain τ(t) in the funnel control can be designed as

[0091]

[0092] Therefore, when the tracking error e(t) is close to the boundary zero, the control gain τ(t) should be increased; on the contrary, when the tracking error e(t) exceeds the boundary The control gain τ(t) should be decreased accordingly.

[0093] The funnel boundary function is designed as follows:

[0094]

[0095] where and β are positive constants and satisfy and The parameter β determines the convergence rate of the error, represents the maximum boundary of the initial error, and represents the steady-state error boundary.

[0096] The improved funnel function is used to design the controller as follows

[0097]

[0098] This function satisfies the limit of the initial condition, and the new variable z(t) is not limited by the order of the system, so the improved funnel function has a wider application in practice.

[0099] Based on the funnel function (21), the adaptive funnel controller is designed as follows:

[0100] Define the error variable as follows:

[0101]

[0102] where v1 is the output of the differential tracker, α is the virtual control variable, is the funnel performance function, and its parameters should satisfy the initial condition

[0103] First step: Derivation of transformed tracking error z1

[0104]

[0105] Consider the following Lyapunov function Its derivative is

[0106]

[0107] where The virtual control signal can be designed as

[0108]

[0109] where c1 is a positive constant.

[0110] Substitute the virtual control (25) into (24) to get

[0111]

[0112] Second step: Derivation of transformed tracking error z2

[0113]

[0114] Select the second Lyapunov function Its derivative is

[0115]

[0116] where is the estimate of w. The actual control signal is designed as

[0117]

[0118] where c2 is a positive constant. Its adaptive law can be designed as

[0119]

[0120] where σ > 0 is the tuning coefficient.

[0121] Substitute the control law (29) and its adaptive law (30) into (28) and use Young's inequality to get

[0122]

[0123] where λ = min{2c1-1, 2c2-1, 3Γ -1 σ / 2}, ε = σw 2 .

[0124] Integrating (31) on both sides, we have

[0125]

[0126] This shows that all signals of the closed-loop system are ultimately uniformly bounded.

[0127] Step four, increase state predictor in adaptive funnel control, utilize prediction error and tracking error to jointly adjust adaptive law, improve dynamic performance of centrifuge system under high dynamic, high g value, high lift rate condition, realize accurate control of precise centrifuge system.

[0128] The designed state predictor is as follows:

[0129]

[0130] Wherein l1, l2 are normal numbers, Is the predicted state of x1, x2, Is the state prediction error.

[0131] Then according to the state predictor, the parameter adaptive law (30) can be adjusted to

[0132]

[0133] Consider the following Lyapunov function

[0134]

[0135] Its derivative is

[0136]

[0137] Wherein Λ=min{2c1-1,2c2-1,3Γ -1 σ / 2,2l1,2l2}, ε=σw 2 .

[0138] Integrating (36) on both sides, we have

[0139]

[0140] This shows that all signals of the closed-loop system are ultimately uniformly bounded.

[0141] The state predictor designed in the application is introduced into the adaptive funnel controller, the stability of the system can still be guaranteed, and high-frequency oscillation of the system signal can be avoided, the convergence rate of the adaptive parameter can be accelerated, and the approximation curve can be smoothed.

[0142] From Figure 3As can be seen from the figures, the transition process of the reference signal is arranged by using the tracking differentiator, which plays a role in smoothing the curve, thereby enabling smooth transition of the high dynamic centrifuge in the start and braking conversion stage. Figure 4 The tracking performance diagram of the adaptive funnel control based on the state predictor is given, from which Figure 4 As can be seen from (a), in the case of signal mutation, the output curve can still better track the reference signal; Figure 4 (b) also shows the effectiveness of the designed adaptive funnel control, which can ensure that the dynamic and steady-state response of the system is limited within a given range. Therefore, the high dynamic funnel control based on the state predictor can improve the dynamic process quality of the system and meet the requirements of fast and accurate control performance.

[0143] Other embodiments of the application will be apparent to those skilled in the art from consideration of the specification and practice of the application disclosed herein. It is intended that the specification and examples be considered as exemplary only, with the true scope of the application being indicated by the following claims.

[0144] It should be understood that the application is not limited to the precise construction that has been described above and shown in the accompanying drawings, and that various modifications and changes can be made by those skilled in the art without departing from the scope of the application. The embodiments of the application described above are not intended to be limiting of the scope of the application.

Claims

1. A highly dynamic funnel control method based on a state predictor, characterized by: The steps include: Step 1: Analyze the friction nonlinearity of the high dynamic centrifuge system and establish a high dynamic centrifuge system model; A continuously differentiable model is used to represent friction nonlinearity, i.e. Among them, α1, α2, α3, β1, β2, β3 are positive constants, is the system speed; the continuously differentiable model (1) includes static friction characteristics and sliding friction characteristics and is suitable for the design of smooth control laws; First, the precision centrifuge system is modeled and equivalent to a motor drive system. The motor model can be expressed as: Where q is the centrifuge angle; is the centrifuge speed; J is the moment of inertia; R a is the armature circuit resistance; u is the control signal; T f ,T d ,T m is the friction torque, external interference torque and driving torque; L a is the total inductance of the armature winding; i a is the armature winding current; K T is the electromechanical conversion constant; K E is the back electromotive force constant; In the actual system, due to L a / R a Very small, the differential current di a / dt is close to zero; define the following system variables Then the state space expression of formula (2) is: Where K1 = K T / R a ,K2=K T K E / R a is a positive constant, Step 2: Design a differential tracker to realize the dynamic process of the regulation system, smoothly track the target curve, and prevent the system from overshooting. Aiming at the problem of excessive overshoot that is easy to occur in the dynamic process of high dynamic centrifuge system, a tracking differentiator is used to arrange the transition process of reference instruction. Assume that the centrifuge angle setting value is y d , the transition process can be realized by the tracking differentiator (TD), and the tracking differentiator is designed as follows: in in y=v1-y d +hv2; h is the system sampling step; r0 is the speed factor; v1, v2 are the tracking differentiator outputs; a, y are system variables; d, r are adjustable parameters; According to the design principle of the tracking differentiator, the speed and overshoot of the transition process are arranged by adjusting the parameter r0, and the noise in the tracking signal is filtered by adjusting h. Step 3: Design an adaptive funnel controller to ensure that the system's tracking error dynamic and steady-state responses are confined within the given funnel boundaries; Based on the new reference command output by the differential tracker, an adaptive funnel controller is designed to ensure that the dynamic and steady-state tracking error responses of the system are confined within the given funnel boundaries. First, d(t) is used to represent the Euclidean distance between the funnel boundary and the error as follows in is the funnel function, e(t) is the tracking error; The funnel boundary is an arbitrarily chosen, continuous, positive function The countdown decision, that is Therefore, the funnel function is defined as From Equation (6), it can be seen that the initial error value e(t0) is contained within the funnel boundary. As time increases, e(t) is also always contained within the funnel boundary. Therefore, the control gain τ(t) in the funnel control is designed to be Therefore, when the tracking error e(t) is close to the boundary zero, the control gain τ(t) should be increased; on the contrary, when the tracking error e(t) exceeds the boundary The control gain τ(t) should be reduced accordingly; Based on the funnel function (6), the adaptive funnel controller is designed as follows: Define the following error variables: Where v1 is the output of the tracking differentiator, α is the virtual control quantity, is the funnel performance function, whose parameters Initial conditions must be met The system's virtual control signal and actual control signal are designed as follows: Where c1 and c2 are positive constants. v2 is the tracking differentiator output, is the estimated value of w; The adaptive law is designed as Where σ>0 is the adjustment coefficient, Γ is a positive definite matrix; The state predictor is used to adjust the adaptive control process, which plays a role in accelerating the convergence speed and smoothing the convergence curve; Step 4: Add a state predictor to the adaptive law obtained in step 3, and use the prediction error and tracking error to jointly adjust the adaptive law. This improves the dynamic performance of the centrifuge system under high dynamic, high g-value, and high lift rate conditions, and achieves precise control of the precision centrifuge system. The design state predictor is as follows: Among them, l1 and l2 are positive constants. is the predicted state of x1, x2, is the state prediction error; According to the state predictor, the parameter adaptive law (10) is adjusted to Introducing the designed state predictor into the adaptive funnel controller can still ensure the stability of the system, avoid high-frequency oscillation of the system signal, accelerate the convergence rate of the adaptive parameters, and smooth the approximation curve. Under high dynamic, large g-value, and high rise and fall rate conditions, the dynamic performance of the centrifuge system can be improved, and precise control of the precision centrifuge system can be achieved.

2. The high-dynamic funnel control method based on a state predictor according to claim 1, characterized in that: According to the overall needs of the control system, the control index requirements of the high dynamic centrifuge system are designed; the control system needs to meet the main technical index requirements of the high dynamic high-speed centrifugal acceleration standard device.

3. The high-dynamic funnel control method based on a state predictor according to claim 1, characterized in that: The AC permanent magnet synchronous motor (PMSM) is selected for control system design.

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