Flexible intelligent material driver output constraint control method considering butterfly hysteresis input

Abstract

The invention provides a flexible intelligent material driver output constraint control method considering butterfly-shaped hysteresis input for an output constraint flexible intelligent material driving system with butterfly-shaped hysteresis input, aims to realize high-precision control in different application scenes, and comprises the following steps of: on the basis of a traditional KP model, selecting a KP model; according to the invention, a new butterfly-shaped KP (Butterfly Kranoselskii-Pokrovskii, BKP) kernel is obtained through derivation, and the KKP (Butterfly Kranoselskii-Pokrovskii, BKP) kernel is used as a kernel of the KKP. A new BKP model is established to describe butterfly hysteresis in the flexible intelligent material driver by performing weighted stacking on the BKP core; an unknown time delay function in the system is approached by using a radial basis function neural network and a finite coverage lemma, and the time delay problem of the control system is solved; a high-gain K-filter is designed to overcome the problem that the state in the system cannot be measured, and the problem of output constraint control of the butterfly hysteresis system is solved by combining a barrier Lyapunov function and an adaptive dynamic surface output feedback control algorithm; a butterfly pseudo-inverse algorithm is designed, the requirement for solving a hysteresis inverse model is avoided, and butterfly hysteresis nonlinearity is weakened to a great extent. Compared with a traditional control scheme, the method has a better effect on tracking performance and tracking errors, the tracking errors are effectively reduced, the control precision is remarkably improved, and precise control over the intelligent material driving system is achieved.

Description

Technical Field

[0001] The present invention belongs to the technical field of intelligent material drive and nonlinear control, and proposes an output constraint control method for a flexible intelligent material driver considering butterfly hysteresis input, which is suitable for the precise control of flexible intelligent material drivers such as bionic robots and medical equipment. Background Art

[0002] Flexible smart material actuators (such as dielectric elastomer actuators) have excellent flexibility, ductility, human-like properties, and fast response speeds, giving them important application potential in fields such as bionic robotics and precision medicine. However, all smart material actuators have complex relationships between input and output, and face core challenges such as butterfly hysteresis nonlinearity, output over-limit risk, time delay, and unpredictable state. The existence of these problems can cause control system oscillation and performance degradation. In severe cases, it may even lead to control system divergence. Therefore, establishing accurate hysteresis models and designing effective control schemes to deal with hysteresis nonlinearity in control systems are of great significance to the development and application of flexible smart material actuators.

[0003] In existing technologies, traditional hysteresis models can only describe single-loop hysteresis characteristics and cannot accurately characterize the dual-loop coupling effects of butterfly hysteresis. Models based on differential equations can be partially improved, but their controller design is complex and relies on inverse model compensation, limiting their practical application. Existing methods address output constraints by utilizing barrier Lyapunov functions combined with effective controllers. However, for relatively high-order complex systems, the computational burden increases significantly and may even lead to differential explosion problems. Furthermore, traditional methods for dealing with time delays use the Lyapunov-Krasovsky function strategy, but this requires certain assumptions about the time delay function and lacks robustness.

[0004] In many physical systems, due to technical or measurement cost reasons, it is impossible to obtain the full state information of the controlled object. When only the system output is measurable, an output feedback control strategy is required to solve the control problem of nonlinear systems. Traditional output feedback control can partially address the problem of unmeasurable states by constructing fuzzy observers and linear observers, but it relies on the assumption of fixed control gains and is difficult to adapt to the time-varying characteristics of smart material parameters. When the system control gain is unknown, Kreissehneier filters (K-filters) are often used to estimate the unmeasurable state. However, considering the influence of output constraints increases the difficulty of controller design and analysis. Summary of the Invention

[0005] To solve the above problems, the present invention provides an output constraint control method for a flexible smart material actuator considering butterfly hysteresis input, which includes:

[0006] Based on the new BKP core, a butterfly hysteresis model of flexible smart material actuators is constructed;

[0007] For the system model of flexible smart material actuator, radial basis function neural networks (RBFNNs) and finite covering lemma are used to approximate the unknown function with time delay constant to rewrite the system model.

[0008] Converting the rewritten system model into a state-space model, and estimating the state vector in the state-space model based on the constructed state observer;

[0009] Based on the state observer, a temporary control signal is determined according to the obstacle Lyapunov function and the adaptive dynamic surface output feedback control algorithm;

[0010] Based on a butterfly pseudo-inverse algorithm, an actual control signal is determined according to the temporary control signal and the butterfly hysteresis model.

[0011] As a preferred option, the rewritten system model is:

[0012]

[0013] y=x1,i=1,…,n-1,

[0014] Among them, x represents the state, y∈R is the output of the system, and the output is constrained in a tight set, that is, in is a positive constant; the approximation error ε i Satisfy |ε i |≤ε m ; is the ridge function, defined as ζ k ∈R q and η i are the center and width of the ridge function, respectively, and η i >0; is the optimal weight vector, the approximation error d i (t) is the interference term; δ i0 ,i=1,…,n is any normal number.

[0015] Preferably, using radial basis function neural networks (RBFNNs) and the finite covering lemma to approximate an unknown function with a time delay constant includes:

[0016] Radial basis function neural networks (RBFNNs) are used to approximate the unknown smooth function f i,i=1,...,n,for ε m > 0, so that the following RBFNNs are established:

[0017]

[0018] Among them, the approximation error ε i Satisfy |ε i |≤ε m ; is the ridge function, defined as ζ k ∈R q and η i are the center and width of the ridge function, respectively, and η i >0;θ i * is the optimal weight vector, the approximation error

[0019] The time delay constant τ and the state x i are unknown and when the unknown function f i (ξ i ) contains a time delay, i.e. i =(x i ,x i (t-τ i )), radial basis neural networks (RBFNNs) cannot directly approximate the unknown function f i (x i ,x i (t-τ i ));

[0020] Assume f(ξ):Ω ξ →R is a smooth function where Let ξ=(ξ(t),ξ(t-τ)) be continuous, τ∈[0,τ M ] is the time delay constant, in [0,τ M ] there exists a finite region on the surface of the t-independent region, for which δ0>0, 0<t1<t2<…<t m ≤τ M If true, then there exists a point make for holds; and assuming that the interference term d i (t), i=1,...,n, satisfying in is an unknown constant;

[0021] Existence point τ 1 / 1 ,…τ n / n ,∈{t1,…,t m}, so that the following equation holds true:

[0022]

[0023] use Approach The following equation holds true Among them, ε i >0 indicates the approximation error of RBFNNs, is x1,...,x i ,i=1,...,n estimated value;

[0024] according to and The system model is rewritten.

[0025] As a preference, the state space model after the rewritten system model conversion is:

[0026]

[0027]

[0028] in, x:=[x1,x2,...x n ] T ,e1=[1,0,...,0], b=[0,...,b0] T , D=[d1(t),...,d n (t)] T ,ε=[ε1,...,ε n ] T ,δ0=[δ 10 ,...,δ n0 ] T .

[0029] make

[0030]

[0031] Where A0 is the Hurwitz matrix of vector q, and Where q=[q1,...,q n ] T ; Then, the state space model is further rewritten as:

[0032]

[0033] Preferably, the state observer is expressed as:

[0034]

[0035] where e n =[0,...,0,1] T , and e n ∈R n Φ=diag{1,k,…,k n-1}, and k>1 is a design parameter;

[0036] The estimated state vector is expressed as:

[0037]

[0038] The actual state estimate is expressed as:

[0039]

[0040] in is an estimate of b0, is θ * estimated value.

[0041] Preferably, the step of determining the temporary control signal includes:

[0042] Define the first, second, ... nth surface errors in sequence and determine the temporary control signal w(t) as:

[0043]

[0044] and The adaptive law is designed as:

[0045]

[0046] Preferably, the BKP core is expressed as:

[0047]

[0048] Where s is the intersection point of the BKP kernel, and ρ1 and ρ2 are thresholds. Observing the butterfly hysteresis phenomenon, it is obvious that the butterfly hysteresis loop is composed of two loops on the left and right sides;

[0049] The ridge function on the left is defined as:

[0050]

[0051] The ridge function on the right is defined as:

[0052]

[0053] Where a is the slope, and a>0, k L and k R Represents design parameters.

[0054] Preferably, based on a butterfly pseudo-inverse algorithm, the step of determining the actual control signal according to the temporary control signal and the butterfly hysteresis model includes:

[0055] Determine the approximately optimal signal u based on the butterfly pseudo-inverse algorithm * (t), so that the following equation holds true

[0056]

[0057] The actual input range of the butterfly hysteresis is defined as [u -max ,u +max ];

[0058] According to the BKP kernel, w(t) is determined in [u min ,u +max ] is monotonically increasing, and in [u -max ,u min ] is monotonically decreasing;

[0059] For u(t)∈[u -max ,u max ],definition:

[0060]

[0061] And make in, is the upper bound of μ(t,ρ1,ρ2);

[0062] According to the BKP core and Under the premise of boundedness, compare the peak values ​​of the left and right double rings, that is, N -max and N +max The size of

[0063] Define a new variable w l (t), the corresponding input is u l (t), where l∈[u -max -u min ,u +max -u min ]; let u0(t)=u min

[0064] u l (t)=u0(t)+l

[0065] If N +max ≥N -max , then execute event 1 to determine the actual control signal u(t), otherwise execute event 2 to determine the actual control signal u(t).

[0066] Preferably, the event 1 includes:

[0067] If w min (t)>w(t), then u * (t) = u min ;

[0068] If w +max (t)<w(t), then u * (t) = u +max ;

[0069] If w min (t)≤w(t)≤w +max (t),u * (t) is calculated using the following steps:

[0070] Step (1): Assume that the input range is divided into n equal parts, define Corresponding for

[0071]

[0072] Step (2): Calculation and

[0073] Step (3): When Then lock the interval,

[0074] Step (4): Let l increase from zero to

[0075] Step (5): Calculate w l (t), if w(t)>w l (t), then keep increasing l and repeat step (5) until w(t)≤w l (t), then execute step (6);

[0076] Step (6): Stop increasing l and set l at this moment to l x , then solve for

[0077] The actual control signal u(t) is solved using the butterfly pseudo-inverse algorithm as shown below:

[0078] u(t)=u * (t)

[0079] The event 2 includes:

[0080] If w min (t)>w(t), then u * (t) = u min;

[0081] If w -max (t)<w(t), then u * (t) = u -max ;

[0082] If w -max (t)≤w(t)≤w min (t), divide the input range into n equal parts, and solve

[0083] The actual control signal u(t) is solved using the butterfly pseudo-inverse algorithm as shown below:

[0084] u(t)=u * (t)

[0085] Compared with the prior art, the present invention has the following beneficial effects:

[0086] The present invention aims to achieve high-precision control in different application scenarios. Based on the traditional KP model, a new butterfly KP (Butterfly Krasnoselskii-Pokrovskii, BKP) kernel is derived. By weighted superposition of the BKP kernel, a new BKP model is established to describe the butterfly hysteresis in the flexible intelligent material actuator; the unknown time delay function in the system is approximated by the radial basis neural network and the finite covering lemma to solve the time delay problem of the control system; a high-gain K-filter is designed to overcome the problem of unmeasurable state in the system, and the output constraint control problem of the butterfly hysteresis system is overcome by combining the barrier Lyapunov function with the adaptive dynamic surface output feedback control algorithm; a butterfly pseudo-inverse algorithm is designed to avoid the need to solve the hysteresis inverse model, and greatly reduce the butterfly hysteresis nonlinearity. Compared with the traditional control scheme, it has better results in tracking performance and tracking error, effectively reduces the tracking error, significantly improves the control accuracy, and realizes the precise control of the intelligent material drive system. BRIEF DESCRIPTION OF THE DRAWINGS

[0087] Figure 1 This is a principle block diagram of a flexible intelligent material driver output constraint control method considering butterfly hysteresis input provided by the present invention;

[0088] Figure 2 The input-output relationship of the BKP hysteresis model provided by the present invention;

[0089] Figure 3 The BKP core input-output relationship corresponding to the BKP hysteresis model provided by the present invention;

[0090] Figure 4The prediction accuracy of the BKP model designed by the present invention;

[0091] Figure 5 Comparison of the tracking performance and tracking error of the control scheme provided by the present invention with other control schemes for triangular wave signals;

[0092] Figure 6 Comparison of the tracking performance and tracking error of the control scheme provided by the present invention with other control schemes for square wave signals;

[0093] Figure 7 Comparison of the control performance of the control scheme provided by the present invention with other control schemes for composite signal tracking control;

[0094] Figure 8 The control scheme provided by the present invention is compared with other control schemes for composite signal tracking control error. DETAILED DESCRIPTION

[0095] It should be noted that: the technical solution of the present invention is described in detail below through the accompanying drawings and specific embodiments. It should be understood that the embodiments of the present invention and the specific features in the embodiments are detailed descriptions of the technical solution of the present invention, rather than limitations on the technical solution of the present invention. In the absence of conflict, the embodiments of the present invention and the technical features in the embodiments can be combined with each other. The term "and / or" is merely a description of the association relationship of associated objects, indicating that there can be three relationships. For example, A and / or B can represent three situations: A exists alone, A and B exist at the same time, and B exists alone. In addition, the character " / " generally indicates that the related objects before and after are in an "or" relationship.

[0096] The present invention provides a butterfly hysteresis adaptive neural network pseudo-inverse dynamic surface control method, the main steps of which are as follows:

[0097] Establishment of a butterfly hysteresis model: Based on the hysteresis characteristics of flexible smart material actuators, a new butterfly Krasnoselskii-Pokrovskii (BKP) kernel was derived from the traditional Krasnoselskii-Pokrovskii (KP) model. By performing a weighted superposition of the BKP kernel, a new BKP model was established to describe the butterfly hysteresis in flexible smart material actuators.

[0098] Adaptive Neural Network Control Based on Barrier Lyapunov Functions: Using radial basis function neural networks and the finite covering lemma, this approach approximates an unknown function with a time-delay constant in the system, resolving the time delay issue in the control system. A high-gain K-filter is then designed to overcome the unmeasurable state problem in the system. By combining the barrier Lyapunov function with an adaptive dynamic surface output feedback control algorithm, the system's actual output accurately tracks the desired signal, and all signals in the closed-loop system are semi-globally ultimately bounded.

[0099] Butterfly pseudo-inverse algorithm: A butterfly pseudo-inverse algorithm is designed to suppress the butterfly hysteresis nonlinearity in the system. This algorithm does not require the construction of a hysteresis inverse model, but is a mechanism to extract the actual control signal from the temporary hysteresis controller, thereby alleviating the butterfly hysteresis nonlinearity in the flexible smart material actuator.

[0100] Through these three key steps, the solution of the present invention is dedicated to solving the challenge of output constraint control of butterfly hysteresis time-delay nonlinear systems in smart material actuators, and provides an innovative and comprehensive solution for high-precision control in different application scenarios. The invention content is mainly divided into several parts:

[0101] (1) Establishment of butterfly hysteresis model

[0102] The Krasnoselski-Pokrovski (KP) model is an effective tool for describing the hysteresis characteristics of smart material actuators. The KP model is defined as:

[0103]

[0104] Where w(t) is the output of the KP model; u(t) is the input vector; μ(ρ) represents the density function, ρ=(ρ1,ρ2)∈T0; ρ is T0={-T b ≤ρ1≤ρ2≤T b}, T0 is the integration range, T b is the boundary of T0, and T b >0;κ ρ,a [u,γ ρ,a ](t) is the KP kernel, defined as

[0105]

[0106] where r(J) is the ridge function, defined as

[0107]

[0108] Where a is the slope of the ridge function r(J), and a>0. ρ,a (t) is defined as γ ρ,a (t) = κ ρ,a[u(t),γ ρ,a (t i )], its initial value is γ ρ,a (0) = κ ρ,a [u(t),γ -1 ], where γ -1 represents the initial value of the KP kernel. Since the traditional KP model can only describe the hysteresis phenomenon of a single loop and cannot describe the butterfly hysteresis phenomenon existing in the smart material actuator, an improved KP model is designed to describe the butterfly hysteresis in the smart material actuator. Different from the KP kernel in the traditional KP model in formula (2), a new BKP kernel is derived as follows:

[0109]

[0110] Where s is the intersection of the BKP kernel, and ρ1 and ρ2 are thresholds. Observing the butterfly hysteresis phenomenon, it is obvious that the butterfly hysteresis loop is composed of two loops on the left and right sides. The ridge function on the left is defined as:

[0111]

[0112] The ridge function on the right is defined as:

[0113]

[0114] Where a is the slope, and a>0, k L and k R Denotes the design parameters. Considering the BKP kernel in formula (4), a new BKP model is constructed based on the structure of the traditional KP model as follows:

[0115]

[0116] where K B [u](t) is the output of the BKP model, and μ(t,ρ1,ρ2) is the density function. represents the initial value of the BKP kernel, yes The initial value of is defined as:

[0117]

[0118] (2) Adaptive neural network control based on obstacle Lyapunov function

[0119] Consider the following nonlinear time-delay system with butterfly hysteresis and a smart material actuator such as a dielectric elastomer actuator:

[0120]

[0121] in, is the unmeasurable state in the system; y∈R is the output of the system, and the output is constrained in a tight set, that is, in is a positive constant; represents an unknown continuous time delay function, which exists in a sufficiently large compact set, ι i is the delay constant; d i (t) is the external disturbance; b0 is the unknown control coefficient, w(t)∈R is the output of the butterfly hysteresis model, which is expressed as follows

[0122] w(t)=P b (u(t)) (10)where P b (·) represents the output of the butterfly hysteresis operator, and u∈R represents the input of the model.

[0123] Before designing the controller, the following assumptions need to be made about the system (9):

[0124] Assumption 1: Reference signal y r is a smooth function that satisfies in is a positive number. For t>0, the vector is bounded, where Υ is a known compact set. This assumption ensures that the system state will not become untraceable due to sudden changes in the reference trajectory.

[0125] Assumption 2: Constant ι i >0, i=1,...,n, and 0≤ι i ≤ι M , where ι M for ι i This assumption defines the delay constant, which facilitates the subsequent processing of the delay.

[0126] Hypothesis 3: Disturbance d i (t), i=1,...,n, satisfying in is an unknown constant. This assumption limits the range of disturbances to avoid system out of control due to unbounded disturbances.

[0127] Step 1: Solve the time delay problem. Use radial basis function neural networks (RBFNNs) and the finite covering lemma to approximate the unknown function with time delay constant in the control system.

[0128] First, radial basis function neural networks (RBFNNs) are used to approximate the unknown smooth function f i ,i=1,...,n,for ε m >0, by reasonably choosing η i and ζ k,k=1,2...,N, so that the following RBFNNs are established

[0129]

[0130] Among them, the approximation error ε i Satisfy |ε i |≤ε m ; is the ridge function, defined as ζ k ∈R q and η i are the center and width of the ridge function, respectively, and η i >0; is the optimal weight vector. From formula (11), we can see that the approximation error

[0131] According to the definition of RBFNNs, because the time lag constant τ and the state x i are all unknown. When the unknown continuous function f i (ξ i ) contains a time delay, i.e. i =(x i ,x i (t-τ i )), RBFNNs cannot directly approximate the unknown function f i (x i ,x i (t-τ i )). Therefore, it is necessary to combine the finite cover theorem with RBFNNs to approximate the unknown function f i (x i ,x i (t-τ i )).

[0132] Lemma 1: Assume f(ξ):Ω ξ →R is a smooth function where Let ξ=(ξ(t),ξ(t-τ)) be continuous, τ∈[0,τ M ] is the time delay constant, in [0,τ M ] there exists a finite region on the surface of the t-independent region, for which δ0>0, 0<t1<t2<...<t m ≤τ M If true, then there exists a point make

[0133]

[0134] for Established.

[0135] Considering Lemma 1 and Assumption 3, there exists a point τ 1 / 1 ,...τ n / n ,∈{t1,...,t m}, so that the following equation holds true:

[0136]

[0137] where t1,...,t m As introduced in Lemma 1, δ i0 , i=1,...,n is any positive constant, then we can use formula (11) to approximate That is, the following equation holds true

[0138]

[0139] Among them, ε i >0 indicates the approximation error of RBFNNs, is x1,...,x i ,i=1,...,n estimated values. In addition, It will be given in formula (22).

[0140] According to formula (13) and formula (14), formula (9) can be rewritten as

[0141]

[0142] Then, convert Equation (15) into the following state space form:

[0143]

[0144] in, x:=[x1,x2,...x n ] T ,e1=[1,0,...,0], b=[0,...,b0] T , D=[d1(t),...,d n (t)] T ,ε=[ε1,...,ε n ] T ,δ0=[δ 10 ,...,δ n0 ] T .

[0145] make

[0146]

[0147] Where A0 is the Hurwitz matrix of vector q, and Where q=[q1,...,q n ] T Then, formula (16) can be rewritten as:

[0148]

[0149] Step 2: Design a state observer. The unmeasurable state x in formula (18) is estimated by constructing a high-gain K state observer.

[0150] The observer looks like this:

[0151]

[0152] where e n =[0,...,0,1] T , and e n ∈R n Φ=diag{1,k,...,k n-1}, and k>1 is a design parameter. The estimated state vector is expressed as:

[0153]

[0154] Define the observer error as but

[0155] =A-kΦq1+B0 (21)

[0156] Where B0 is defined in formula (17), and ∈1 represents the first term of ∈.

[0157] Since b0 and θ in formula (20) * is unknown, the actual state estimation can be expressed as:

[0158]

[0159] in is an estimate of b0, is θ * estimated value.

[0160] Step 3: Design a temporary hysteresis controller. Based on the high-gain K state observer of formula (19), the temporary hysteresis controller is designed by combining the barrier Lyapunov function with the adaptive dynamic surface output feedback control algorithm.

[0161] Step 1: Define the first surface error as

[0162] S1=yy r (23) where yr is the reference signal. Considering formula (19), the derivative of S1 is

[0163]

[0164] According to the definition of observation error ∈, we can get

[0165]

[0166] Where ∈2 is the second term of the observation error ∈. (2) is the second term of Ξ. Then the following equation exists:

[0167]

[0168] in, is a virtual control signal, which is designed as:

[0169]

[0170] in yes The estimated value of Design the virtual control signal as

[0171]

[0172] where l1 is a positive design parameter, is θ * estimated value. Is a positive constant. Define a compact set and The adaptive law is designed as

[0173]

[0174]

[0175] Let z2 pass through a first-order low-pass filter

[0176]

[0177] in, and ι2 are the input and positive delay constants of the above low-pass filter respectively.

[0178] Step 2: Define the second surface error as

[0179] S2=v (0,2) -z2 (32)

[0180] Considering formula (19), the derivative of S2 is

[0181]

[0182] in, is the virtual control signal. According to formula (33), the designed virtual control signal is:

[0183]

[0184] Among them, l2 is a designed positive constant, is an estimate of b0, Designed to:

[0185]

[0186] Let z3 pass through a first-order low-pass filter:

[0187]

[0188] in, and ι3 are the input and positive time constant of the above low-pass filter respectively.

[0189] Step i (3≤i≤n-1): Define the i-th surface error as

[0190] S i =v (0,i) -z i (37)

[0191] Considering formula (19), S i The derivative of

[0192]

[0193] in, Is the virtual control signal. According to formula (38), the virtual control signal is designed for:

[0194]

[0195] Among them, l i is a designed normal number. Let z i+1 Through a first-order low-pass filter:

[0196]

[0197] in, and ι i+1 are the input and positive time constant of the above low-pass filter respectively.

[0198] Step n: Define the nth surface error as

[0199] S n =v(0,n) -z n (41)

[0200] Considering formula (19), S n The derivative of

[0201]

[0202] According to formula (42), the temporary control signal w(t) is designed as:

[0203]

[0204] and The adaptive law is designed as:

[0205]

[0206] Among them, l n is a positive design parameter.

[0207] (3) Butterfly pseudo-inverse algorithm

[0208] The actual control signal u is coupled to the temporary hysteresis controller of formula (43), that is,

[0209]

[0210] Therefore, it is crucial to solve u from the double integral function of w(t). The butterfly pseudo-inverse algorithm aims to design a search mechanism to find an approximately optimal signal u * (t), so that the following equation holds true

[0211]

[0212] First, define the actual input range of butterfly hysteresis as [u -max ,u +max ], considering the BKP kernel κ in formula (7) Bρ,a [u,γ Bρ,a (t)], we can get w(t) in [u min ,u +max ] is monotonically increasing, and in [u -max ,u min ] is monotonically decreasing. For u(t)∈[u -max ,u max ],definition:

[0213]

[0214] Among them, u min =s, s is the design parameter defined in formula (4).

[0215] Secondly, let

[0216]

[0217] in, is the upper bound of μ(t,ρ1,ρ2) in formula (7). Bρ,a [u -max ,γ Bρ,a ](t) definition and Under the premise of the boundedness, we can compare the peak values ​​of the left and right double rings, that is, N -max and N +max The size of . It can be inferred that:

[0218]

[0219] Again, define a new variable w l (t), the corresponding input is u l (t), where l∈[u -max -u min ,u +max -u min ].

[0220] Let u0(t) = u min , the following formula exists:

[0221]

[0222] u l (t)=u0(t)+l (51)

[0223] If N +max ≥N -max , then execute event 1, otherwise execute event 2.

[0224] Event 1:

[0225] If w min (t)>w(t), then u * (t) = u min .

[0226] If w +max (t)<w(t), then u * (t) = u +max .

[0227] If w min (t)≤w(t)≤w +max (t),u * (t) can be found in the following steps.

[0228] Step (1): Assume that the input range is divided into n equal parts, define Corresponding for

[0229]

[0230] Step (2): Calculation and

[0231] Step (3): When Then lock this interval, let

[0232] Step (4): Let l increase from zero to

[0233] Step (5): Calculate w l (t), if w(t)>w l (t), then keep increasing l and repeat step (5) until w(t)≤w l (t), then execute step (6).

[0234] Step (6): Stop l from increasing and set e at this moment to e x , then solve for u * (t) is

[0235]

[0236] Event 2:

[0237] If w min (t)>w(t), then u * (t) = u min .

[0238] If w -max (t)<w(t), then u * (t) = u -max .

[0239] If w -max (t)≤w(t)≤w min (t),u * The solution steps for (t) are similar to those for event 1.

[0240] Finally, the actual control signal u(t) is solved using the butterfly pseudo-inverse algorithm as shown below:

[0241] u(t)=u * (t) (54)

[0242] In a specific embodiment, this embodiment proposes a butterfly hysteresis adaptive neural network pseudo-inverse dynamic surface control scheme, derives a new BKP kernel based on the traditional KP model, and designs a temporary controller by combining the obstacle Lyapunov function and the adaptive dynamic surface output feedback control algorithm, which is finally verified by a dielectric elastomer flexible intelligent material driver.

[0243] In order to verify the effectiveness of the proposed control scheme, a dielectric elastomer drive motion control experimental platform was built with the dielectric elastomer drive as the controlled object, and the designed control scheme was applied to the experimental platform. By comparing the control conditions of the proposed control scheme, the backstepping control scheme and the proposed control scheme without considering hysteresis compensation on the dielectric elastomer drive motion experimental platform, the superior control performance of the proposed control scheme was verified.

[0244] During the construction process, a circular elastomer was fixed to a rigid frame, and a heavy circular mechanical load was placed on the elastomer film. The dielectric elastomer film was biaxially pre-stretched 3x3 times using VHB-4910 film produced by Minnesota Mining and Manufacturing Company and fixed to a circular polymethyl methacrylate frame. 846-80g of carbon conductive grease was evenly coated on both sides of the dielectric elastomer film. The dielectric elastomer film had an inner diameter of 40mm and an outer diameter of 60mm. The specific operating principle of the dielectric elastomer actuator experimental platform is that Matlab software on the host computer sends the designed control signal to the PCIE-6361NI board. After conversion by the NI board, the analog signal is transmitted to the TERK 10 / 40AHS voltage amplifier. The amplified voltage acts on the annular dielectric elastomer actuator system, controlling the precise movement of the dielectric elastomer. The displacement of the annular dielectric elastomer actuator system is measured using an LK-H152 laser displacement sensor, and the measured data is transmitted back to the host computer.

[0245] During the specific implementation process, the open-loop experiment of dielectric elastic drive motion was first carried out to verify the prediction accuracy of the established BKP model. A sinusoidal voltage excitation experiment was used, with the voltage amplitude set to -5kV to 5kV and the frequency coverage to 0.5 to 5Hz. In combination with the constant voltage hold experiment, the displacement response data under different voltage conditions were obtained. The input signal was u(t) = 4.5sin(0.6*2πt), and the density function satisfied ρ1,ρ2∈[-5,5]. This process not only verifies that the curve of the proposed BKP model is highly consistent with the experimental data from the dielectric elastomer, but also shows that the proposed BKP model can accurately describe the butterfly hysteresis phenomenon in the dielectric elastomer, and the prediction accuracy of the BKP model is high. In the control experiment, for the basis function of RBFNNs Select 7 central nodes and evenly distribute them in the range [-1,1]. The width of each basis function is ηj =1,j=1,...,7. Where k = 1, 2, t1 = 0.25, t2 = 0.45, t3 = 0.65, t4 = 0.85, t5 = 1.05. The initial value of the weight function is set to For a high-gain K state observer, set the parameter to Φ -1 =diag{0,1 / k},q=[q1,q2] T =[5,3] T , k = 5, the initial values ​​are set to ζ(0) = 0, v(0) = 0, Ξ(0) = 0. The reference trajectory is selected as y r (t)=0.5sin(0.2πt)+0.5cos(0.3πt)+3(mm). The output constraint is set as The parameter design is l1=18, l2=7, γ θ =0.6,γ b =0.1,γ r =0.3,σ b =0.2, σ θ =0.1,σ r =0.8. Experimental results show that the proposed butterfly hysteresis pseudo-inverse algorithm can effectively reduce the tracking error to a relatively small value, with a control accuracy of maximum absolute error (MAE) of 2.24% and normalized root mean square error (NRMSE) of 0.91%. The proposed adaptive neural network dynamic surface control scheme has a smaller error than the traditional backstepping control scheme, and the NRMSE value is 2% lower than that of the traditional backstepping control scheme, indicating that the proposed control scheme has better control effect.

[0246] The present invention solves the problem that traditional models cannot describe the butterfly hysteresis phenomenon in smart material actuators by constructing a new BKP model of butterfly hysteresis. By designing a butterfly pseudo-inverse algorithm, the need to solve the hysteresis inverse model is avoided, and the butterfly hysteresis nonlinearity is greatly weakened. The proposed control algorithm overcomes the output constraint control problem of the butterfly hysteresis system, providing a new technical path for the precise drive and intelligent control of bionic robots in the industrial, manufacturing, medical and military fields.

[0247] It will be understood by those skilled in the art that embodiments of the present invention may be provided as methods, systems, or computer program products. Thus, the present invention may take the form of an entirely hardware embodiment, an entirely software embodiment, or an embodiment combining software and hardware. Furthermore, the present invention may take the form of a computer program product implemented on one or more computer-usable storage media (including but not limited to magnetic disk storage, CD-ROM, optical storage, etc.) containing computer-usable program code.

[0248] The present invention is described with reference to flowcharts and / or block diagrams of methods, devices (systems), and computer program products according to embodiments of the present invention. It should be understood that each process and / or block in the flowcharts and / or block diagrams, as well as combinations of processes and / or blocks in the flowcharts and / or block diagrams, can be implemented by computer program instructions. These computer program instructions can be provided to a processor of a general-purpose computer, a special-purpose computer, an embedded processor, or other programmable data processing device to produce a machine, so that the instructions executed by the processor of the computer or other programmable data processing device generate instructions for implementing the processes in the flowcharts and / or block diagrams. Figure 1 a process or multiple processes and / or boxes Figure 1 A device that provides the functions specified in a block or multiple blocks.

[0249] These computer program instructions may also be stored in a computer readable memory that can direct a computer or other programmable data processing device to work in a specific manner, so that the instructions stored in the computer readable memory produce an article of manufacture comprising an instruction device, which implements the process Figure 1 a process or multiple processes and / or boxes Figure 1 The function specified in one or more boxes.

[0250] These computer program instructions can also be loaded onto a computer or other programmable data processing device so that a series of operational steps are executed on the computer or other programmable device to produce a computer-implemented process, thereby providing the instructions executed on the computer or other programmable device for implementing the process. Figure 1 a process or multiple processes and / or boxes Figure 1 The steps for the function specified in one or more boxes.

[0251] The embodiments of the present invention are described above in conjunction with the accompanying drawings, but the present invention is not limited to the above-mentioned specific implementation methods. The above-mentioned specific implementation methods are merely illustrative and not restrictive. Under the guidance of the present invention, ordinary technicians in this field can also make many forms without departing from the scope of protection of the purpose of the present invention and the claims, which are all protected by the present invention.

Claims

1. A method for output constraint control of a flexible smart material actuator considering butterfly hysteresis input, characterized in that: include: Based on the new BKP core, a butterfly hysteresis model of flexible smart material actuators is constructed; For the system model of flexible smart material actuator, radial basis function neural networks (RBFNNs) and finite covering lemma are used to approximate unknown functions with time delay constants to rewrite the system model. Converting the rewritten system model into a state-space model, and estimating the state vector in the state-space model based on the constructed state observer; Based on the state observer, a temporary control signal is determined according to the obstacle Lyapunov function and the adaptive dynamic surface output feedback control algorithm; Based on a butterfly pseudo-inverse algorithm, an actual control signal is determined according to the temporary control signal and the butterfly hysteresis model.

2. The method for controlling output constraints of a flexible intelligent material actuator considering butterfly hysteresis input according to claim 1, characterized in that: The rewritten system model is: y=x1,i=1,…,n-1, Among them, x represents the state, y∈R is the output of the system, and the output is constrained in a tight set, that is, in is a positive constant; the approximation error ε i Satisfy |ε i |≤ε m ; is the ridge function, defined as ζ k ∈R q and η i are the center and width of the ridge function, respectively, and η i >0; is the optimal weight vector, the approximation error d i (t) is the interference term; δ i0 ,i=1,...,n is any positive constant.

3. The method for controlling output constraints of a flexible intelligent material actuator considering butterfly hysteresis input according to claim 2, characterized in that: Approximating unknown functions with time-delay constants using radial basis function neural networks (RBFNNs) and the finite covering lemma includes: Radial basis function neural networks (RBFNNs) are used to approximate the unknown smooth function f i ,i=1,...,n,for ε m > 0, so that the following RBFNNs are established: Among them, the approximation error ε i Satisfy |ε i |≤ε m ; is the ridge function, defined as ζ k ∈R q and η i are the center and width of the ridge function, respectively, and η i >0; is the optimal weight vector, the approximation error The time delay constant τ and the state x i are unknown and when the unknown function f i (ξ i ) contains a time delay, i.e. i =(x i ,x i (t-τ i )), radial basis neural networks (RBFNNs) cannot directly approximate the unknown function f i (x i ,x i (t-τ i )); Assume f(ξ):Ω ξ →R is a smooth function where Let ξ=(ξ(t),ξ(t-τ)) be continuous, τ∈[0,τ M ] is the time delay constant, in [0,τ M ] there exists a finite region on the surface of the t-independent region, for which δ0>0, 0<t1<t2<...<t m ≤τ M If true, then there exists a point make for holds; and assuming that the interference term d i (t), i=1,...,n, satisfying in is an unknown constant; Existence point τ 1 / 1 ,...τ n / n ,∈{t1,...,t m }, so that the following equation holds true: use Approach The following equation holds true Among them, ε i >0 indicates the approximation error of RBFNNs, is x1,...,x i ,i=1,...,n estimated value; according to and The system model is rewritten.

4. The method for controlling output constraints of a flexible intelligent material actuator considering butterfly hysteresis input according to claim 2, characterized in that: The state space model after the rewritten system model conversion is: Among them, x:=[x1,x2,...x n ] T ,e1=[1,0,...,0], b=[0,...,b0] T ,D=[d1(t),...,d n (t)] T ,ε=[ε1,...,ε n ] T ,δ0=[δ 10 ,...,d n0 ] T make B0=δ0+ε+D; Where A0 is the Hurwitz matrix of vector q, and Where q=[q1,...,q n ] T ; Then, the state space model is further rewritten as:

5. The method for controlling output constraints of a flexible intelligent material actuator considering butterfly hysteresis input according to claim 4, characterized in that: The state observer is expressed as: where e n =[0,...,0,1] T , and e n ∈R n Φ=diag{1,k,...,k n-1 }, and k>1 is a design parameter; The estimated state vector is expressed as: The actual state estimate is expressed as: in is an estimate of b0, is θ * estimated value.

6. The method for controlling output constraints of a flexible intelligent material actuator considering butterfly hysteresis input according to claim 5, characterized in that: The step of determining the temporary control signal includes: Define the first, second, ... nth surface errors in sequence and determine the temporary control signal w(t) as: and The adaptive law is designed as:

7. The method for controlling output constraints of a flexible intelligent material actuator considering butterfly hysteresis input according to claim 5, characterized in that: The BKP core is expressed as: Where s is the intersection point of the BKP kernel, ρ1 and ρ2 are thresholds, and the butterfly hysteresis phenomenon is observed. The butterfly hysteresis loop is composed of two loops on the left and right sides. The ridge function on the left is defined as: The ridge function on the right is defined as: Where a is the slope, and a>0, k L and k R Represents design parameters.

8. The method for controlling output constraints of a flexible intelligent material actuator considering butterfly hysteresis input according to claim 7, characterized in that: The step of determining the actual control signal according to the temporary control signal and the butterfly hysteresis model based on the butterfly pseudo-inverse algorithm includes: Determine the approximately optimal signal u based on the butterfly pseudo-inverse algorithm * (t), so that the following equation holds true The actual input range of the butterfly hysteresis is defined as [u -max ,u +max ]; According to the BKP kernel, w(t) is determined in [u min ,u +max ] is monotonically increasing, and in [u -max ,u min ] is monotonically decreasing; For u(t)∈[u -max ,u max ],definition: And make in, is the upper bound of μ(t,ρ1,ρ2); According to the BKP core and Under the premise of boundedness, compare the peak values ​​of the left and right double rings, that is, N -max and N +max The size of Define a new variable w l (t), the corresponding input is u l (t), where l∈[u -max -u min ,u +max -u min ]; let u0(t)=u min u l (t)=u0(t)+l If N +max ≥N -max , then execute event 1 to determine the actual control signal u(t), otherwise execute event 2 to determine the actual control signal u(t).

9. The method for controlling output constraints of a flexible intelligent material actuator considering butterfly hysteresis input according to claim 8, characterized in that: The event 1 includes: If w min (t)>w(t), then u * (t) = u min ; If w +max (t)<w(t), then u * (t) = u +max ; If w min (t)≤w(t)≤w +max (t),u * (t) is calculated using the following steps: Step (1): Assume that the input range is divided into n equal parts, define Corresponding for Step (2): Calculation and Step (3): When Then lock the interval, Step (4): Let l increase from zero to Step (5): Calculate w l (t), if w(t)>w l (t), then keep increasing l and repeat step (5) until w(t)≤w l (t), then execute step (6); Step (6): Stop increasing l and set l at this moment to l x , then solve for The actual control signal u(t) is solved using the butterfly pseudo-inverse algorithm as shown below: u(t)=u * (t) The event 2 includes: If w min (t)>w(t), then u * (t) = u min ; If w -max (t)<w(t), then u * (t) = u -max ; If w -max (t)≤w(t)≤w min (t), divide the input range into n equal parts, and solve The actual control signal u(t) is solved using the butterfly pseudo-inverse algorithm as shown below: u(t)=u * (t)。

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