Mismatching disturbance observation method and device

Abstract

The invention discloses a mismatching disturbance observation method and device, and is applied to the technical field of control, and the method comprises the steps: building a motion equation of a controlled system and an auxiliary system corresponding to the controlled system; based on the motion equation of the controlled system and the auxiliary system, establishing an error auxiliary system; designing a sliding mode variable and a control law of the auxiliary system according to the state of the error auxiliary system; based on the control law, the error auxiliary system converges to a sliding mode surface with the sliding mode variable being zero in the approaching process; and designing an observation value of mismatching disturbance through the motion equation of the controlled system and the sliding mode variable.

Description

Technical Field

[0001] The present invention relates to the field of control technology, and in particular to a mismatch disturbance observation method and device. Background Art

[0002] In recent years, the continuous advancement of the upgrading of my country's manufacturing industry has provided a huge market for the development of my country's servo industry. With the continued good development of industries such as CNC machine tools, packaging machinery, and electronic special equipment, and the increasing maturity of AC servo technology, the application of servo technology in emerging industries such as the wind power industry in the new energy industry has enabled my country's servo market to develop rapidly. However, the controlled system is always affected by unknown disturbances, which affect the dynamic and steady-state performance of the system. Therefore, the observation of disturbances is an important part of servo control. By observing the disturbances through the observer and introducing the observation results into the controller, the performance loss of the controlled object under unknown disturbances can be reduced. This not only improves the performance and reliability of the system, but also provides conditions for the realization of precise control of the controlled object. Therefore, the observation and suppression of disturbances are the key to achieving high-quality operation of the servo system.

[0003] In high-order servo control systems, disturbances are mainly caused by mismatches in the internal parameters of the control system and real-time changes in external disturbances. Disturbances can be divided into matched disturbances and unmatched disturbances based on whether the matching conditions are met. When the channel through which the disturbance enters the system is the same as the channel through which the control action enters the system, the disturbance is called a matched disturbance. When the channel through which the disturbance enters the system is different from the channel through which the control action enters the system, the disturbance is called an unmatched disturbance. Compared with matched disturbances, which can be equivalent to direct compensation by control action, the emergence of unmatched disturbances significantly increases the difficulty of system control.

[0004] In the prior art, the mismatched disturbance is observed by designing a sliding mode control law to make the error system converge in the approach process and the sliding process. The mismatched disturbance observation method based on the sliding mode observer has the characteristics of simple structure, fast response speed and good robustness. Therefore, it has unparalleled advantages in the anti-disturbance observation of servo control systems that other strategies cannot match, and has been widely studied in the field of disturbance observation. However, the traditional mismatched disturbance observation method based on the sliding mode observer requires that both the approach process and the sliding process converge at the same time to realize the observation of the mismatched disturbance, which reduces the rapidity and flexibility of the mismatched disturbance observation.

[0005] In order to overcome these defects, the present application proposes a mismatch disturbance observation method and device. Summary of the invention

[0006] The purpose of this application is to provide a mismatch disturbance observation method and device, aiming to solve the problems existing in the above-mentioned background technology.

[0007] To achieve the above objectives, this application provides the following technical solutions:

[0008] The present application provides a mismatch disturbance observation method, comprising:

[0009] Establishing the motion equation of the controlled system and the auxiliary system corresponding to the controlled system;

[0010] Based on the motion equation of the controlled system and the auxiliary system, establishing an error auxiliary system;

[0011] Designing a sliding mode variable and a control law of the auxiliary system according to a state of the error auxiliary system;

[0012] Based on the control law, the error auxiliary system converges to a sliding mode surface where the sliding mode variable is zero during the approach process;

[0013] The observed value of the mismatched disturbance is designed through the motion equation of the controlled system and the sliding mode variable.

[0014] Furthermore, the step of establishing the motion equation of the controlled system and the auxiliary system corresponding to the controlled system specifically includes the following steps:

[0015] Assume that the motion equation of the controlled system is:

[0016]

[0017] in is a constant; is the state of the controlled system; and are x1 and x2 with respect to time The derivative of is the control input of the controlled system; a(·) is a function of states x1 and x2; b(·) is a function of states x1, x2 and u; is the mismatch disturbance;

[0018] The auxiliary systems are:

[0019]

[0020] Where z1 and z2 are the states of the auxiliary system; u2 is the control input of the auxiliary system; and are the derivatives of z1 and z2 with respect to time t respectively.

[0021] Furthermore, the step of establishing the error auxiliary system based on the motion equation of the controlled system and the auxiliary system specifically includes the following steps:

[0022] Subtract the motion equation of the controlled system from the auxiliary system to obtain the error auxiliary system:

[0023]

[0024] Where e1 and e2 are the states of the error auxiliary system, and are the derivatives of e1 and e2 with respect to time t, satisfying e1: = x1-z1, e2: = x2-z2, e a :=a(x1,x2)-a(z1,z2),e b :=b(x1,x2,u)-b(z1,z2,u).

[0025] Furthermore, the step of designing the sliding mode variable and the control law of the auxiliary system according to the state of the error auxiliary system specifically includes the following steps:

[0026] The sliding mode variables are:

[0027] σ=e2+c2e1

[0028] Where σ is the sliding mode variable, and σ=0 is defined as the sliding mode surface; c2 is a constant coefficient, and c2>0; e1 and e2 are the states of the error auxiliary system;

[0029] The auxiliary system control law is:

[0030]

[0031] Where u2 is the control input of the auxiliary system; k1, k2, k3, k4, c2, ρ, t1, N are constant coefficients, and k3, k4, c2, ρ, t1, N>0, k3 is a parameter for adjusting the convergence dynamics, ρ is a parameter for adjusting the convergence accuracy, and t1 is a parameter for presetting the convergence time of the sliding mode variable; is the observed value of the mismatched disturbance; Θ(t1, t, ρ, k3) is a function of time t.

[0032] Furthermore, the step of designing the observation value of the mismatched disturbance through the motion equation of the controlled system and the sliding mode variable specifically includes the following steps:

[0033] Assume that the observation error of the sliding mode observer is:

[0034]

[0035] Where d is the mismatch disturbance; is the observed value of the mismatched disturbance; k2 is the constant of the controlled system; σ(t) is the value of the sliding mode variable σ at time t;

[0036] Based on the observation error, the observation value of the designed mismatch disturbance is:

[0037]

[0038] Among them, e1=x1-z1, c2>0 is a constant coefficient, are the parameters of the sliding mode observer, k1 and k2 are constants, and s is the Laplace operator;

[0039] According to the observed values ​​of the mismatched disturbance, we get:

[0040] When the parameter hour,

[0041] in for The approximate value of and are the derivatives of the states e1 and e2 of the error auxiliary system with respect to time t, respectively;

[0042] Then the observation error satisfies:

[0043]

[0044] When the sliding mode variable converges to zero in the approaching process, the observation error tends to zero, and the mismatch disturbance of the controlled system is observed.

[0045] Furthermore, the parameters of the sliding mode observer include:

[0046] According to the bandwidth f of the sliding mode observer s , design parameters

[0047]

[0048] Where π is the ratio of a circle to a circle;

[0049] After the approach process is completed, the parameters Configure the bandwidth f of the sliding mode observer s ;

[0050] According to the sliding mode observer phase lag Design parameters

[0051]

[0052] Where w is the angular frequency of the input signal; tan(·) is the tangent function;

[0053] After the approach process is completed, the parameters Configuring the Phase Lag of the Sliding Mode Observer

[0054] The present application provides a mismatch disturbance observation device, comprising:

[0055] Establishing module: establishing the motion equation of the controlled system and the auxiliary system corresponding to the controlled system; establishing the error auxiliary system based on the motion equation of the controlled system and the auxiliary system;

[0056] Design module: designs sliding mode variables and control laws of the auxiliary system according to the state of the error auxiliary system;

[0057] Observation module: Based on the control law, the error auxiliary system converges to the sliding surface where the sliding mode variable is zero during the approach process; through the motion equation of the controlled system and the sliding mode variable, the observation value of the mismatched disturbance is designed.

[0058] The present application provides a device, which includes a processor and a memory coupled to the processor, wherein the memory stores program instructions for implementing a mismatched disturbance observation method; the processor is used to execute the program instructions stored in the memory to implement a mismatched disturbance observation.

[0059] The present application provides a storage medium storing program instructions executable by a processor, wherein the program instructions are used to execute a mismatched disturbance observation method.

[0060] The present application provides a mismatch disturbance observation method and device, which has the following beneficial effects:

[0061] (1) The present application configures the observation error into an expression related to the sliding mode variable, ensuring that when the approach process converges, the sliding mode variable converges to zero, and the observation error also converges to zero, so that the value of the mismatched disturbance can be effectively observed, and the effect of mismatched disturbance observation can be achieved by only requiring the approach process to converge, without requiring the sliding process to converge in the observation process;

[0062] (2) By designing the control law, the convergence time of the approach process can be preset without predicting the initial state of the system; the convergence accuracy of the approach process can also be preset, thereby achieving the adjustment of the observer accuracy; at the same time, the control law is used to ensure the convergence of the approach process, thereby solving the problem that the convergence of the traditional observer requires the prediction of the upper bound of the differential of the disturbance;

[0063] (3) According to the frequency information of the mismatched disturbance in actual applications, the parameters of the sliding mode observer are calculated, and the bandwidth and phase lag of the sliding mode observer can be preset. BRIEF DESCRIPTION OF THE DRAWINGS

[0064] Figure 1 A schematic diagram of a flow chart of a mismatched disturbance observation method according to Embodiment 1 of the present application;

[0065] Figure 2 The Bode diagram of the actual mismatched disturbance system of Example 1 of the present application;

[0066] Figure 3 Schematic diagram of sliding mode variables and observation errors in Example 1 of the present application;

[0067] Figure 4 This is a schematic diagram of the effect of observation mismatch disturbance in Example 1 of the present application;

[0068] Figure 5 This is a block diagram of an implementation method of a mismatched disturbance observation method according to Embodiment 1 of the present application;

[0069] Figure 6 A schematic diagram showing the difference between a mismatched disturbance observation method in Example 1 of the present application and a traditional mismatched disturbance observation method;

[0070] Figure 7 This is a structural schematic diagram of a mismatched disturbance observation device according to Embodiment 2 of the present application;

[0071] Figure 8 This is a schematic diagram of the device structure of Example 3 of the present application;

[0072] Fig. 9 This is a schematic diagram of the storage medium structure of Example 4 of the present application. DETAILED DESCRIPTION

[0073] It should be understood that the specific embodiments described herein are only used to explain the present application and are not used to limit the present application.

[0074] The following will be combined with the drawings in the embodiments of the present application to clearly and completely describe the technical solutions in the embodiments of the present application. Obviously, the described embodiments are only part of the embodiments of the present application, not all of the embodiments. Based on the embodiments in the present application, all other embodiments obtained by ordinary technicians in this field without making creative work are within the scope of protection of this application.

[0075] Example 1

[0076] See also Figure 1 , is a flow chart of a mismatched disturbance observation method according to Embodiment 1 of the present application; the steps include:

[0077] S1: Establishing the motion equation of the controlled system and the auxiliary system corresponding to the controlled system.

[0078] In this embodiment, the motion equation of the controlled system is assumed to be:

[0079]

[0080] in is a constant; is the state of the controlled system; and are x1 and x2 with respect to time The derivative of is the control input of the controlled system; a(·) is a function of states x1 and x2; b(·) is a function of states x1, x2 and u, that is, The matching condition is not met, so it is called mismatch disturbance.

[0081] The auxiliary system replaces the state of the controlled system, ignores the disturbance term, adds the auxiliary system control term u2, and assumes that the auxiliary system is:

[0082]

[0083] Where z1 and z2 are the states of the auxiliary system; u2 is the control input of the auxiliary system; and are the derivatives of z1 and z2 with respect to time t respectively.

[0084] S2: Based on the motion equation of the controlled system and the auxiliary system, an error auxiliary system is established.

[0085] In this embodiment, the motion equation of the controlled system is subtracted from the auxiliary system to obtain the error auxiliary system:

[0086]

[0087] Where e1 and e2 are the states of the error auxiliary system, and are the derivatives of e1 and e2 with respect to time t, satisfying e1: = x1-z1, e2: = x2-z2, e a :=a(x1,x2)a(z1,z2),e b :=b(x1,x2,u)-b(z1,z2,u).

[0088] S3: Designing a sliding mode variable and a control law of the auxiliary system according to the state of the error auxiliary system.

[0089] In this embodiment, only the approaching phase is needed, and the performance of the sliding phase does not need to be considered, so the sliding mode variable is:

[0090] σ=e2+c2e1 (4)

[0091] Where σ is the sliding mode variable, and σ=0 is defined as the sliding mode surface; c2 is a constant coefficient, and c2>0; e1 and e2 are the states of the error auxiliary system;

[0092] In order to ensure that the trajectory of the error auxiliary system can converge to the sliding surface in the approach process, the control law in the auxiliary system that can make the approach process preset convergence time and preset convergence accuracy is designed as follows:

[0093]

[0094] Where u2 is the control input of the auxiliary system; k1, k2, k3, k4, c2, ρ, t1, N are constant coefficients, and k3, k4, c2, ρ, t1, N>0, k3 is a parameter for adjusting the convergence dynamics, ρ is a parameter for adjusting the convergence accuracy, and t1 is a parameter for presetting the convergence time of the sliding mode variable; is the observed value of the mismatched disturbance; Θ(t1, t, ρ, k3) is a function of time t.

[0095] where Θ(t1, t, ρ, k3) satisfies:

[0096]

[0097] In the formula,

[0098]

[0099] Where k3, ρ, N, t1, t are constant coefficients, satisfying k3, ρ, N, t1, t>0; n1→N means n1 approaches N, z→x + Indicates that the variable z approaches x from the positive direction; lim(·) is the limit symbol; sign(·) is the sign function:

[0100]

[0101] Then the control law (5) can ensure the stability of the approach process, and within the preset time t1, the amplitude of the sliding mode variable |σ(t)| can converge to ρ|σ(t)|, that is, Among them, σ(t) is defined as the value of the sliding mode variable σ at time t, and |·| is the absolute value function. By presetting parameters ρ and t1, the steady-state accuracy ρ|σ(0)| and the convergence time t1 can be adjusted.

[0102] S4: Based on the control law, the error auxiliary system converges to the sliding mode surface where the sliding mode variable is zero during the approach process.

[0103] In this embodiment, based on the control law, the state trajectory of the error auxiliary system converges to a neighborhood of a preset accuracy of the sliding mode surface where the sliding mode variable is zero within a finite time during the approach process.

[0104] Furthermore, in order to achieve flexible configuration of the observer, the sliding mode observer parameters are calculated according to the frequency information of the mismatched disturbance in actual applications. To achieve the required observer bandwidth f s or phase lag

[0105] According to the bandwidth f of the sliding mode observer s , design parameters

[0106]

[0107] Where π is the ratio of a circle to a circle;

[0108] Therefore, after the approach process is completed, the parameter Configure the bandwidth f of the sliding mode observer s .

[0109] According to the sliding mode observer phase lag Design parameters

[0110]

[0111] Where w is the angular frequency of the input signal; tan(·) is the tangent function;

[0112] Therefore, after the approach process is completed, the parameter Configuring the Phase Lag of the Sliding Mode Observer

[0113] See also Figure 2 , is the system Bode diagram of the actual mismatch disturbance of Example 1 of the present application. When the design bandwidth is fs=100 Hz, the observed mismatch disturbance is used as input and the actual mismatch disturbance is used as output.

[0114] S5: Designing observation values ​​of mismatched disturbances through the motion equation of the controlled system and the sliding mode variables.

[0115] In this embodiment, when the observation error is approximately equal to the sliding mode variable, the observation error will approach zero together with the sliding mode variable, and the purpose of observing the mismatched disturbance only needs the approaching stage without the sliding stage to converge can be achieved. Therefore, according to the required observer bandwidth and phase lag, the observation value expression of the mismatched disturbance is designed so that the observation error converges together with the approaching process.

[0116] Assume that the observation error of the sliding mode observer is:

[0117]

[0118] Where d is the mismatch disturbance; is the observed value of the mismatched disturbance; k2 is the constant of the controlled system; σ(t) is the value of the sliding mode variable σ at time t.

[0119] In order to satisfy the condition of formula (11), the observation value of the mismatched disturbance is designed as:

[0120]

[0121] Among them, e1=x1-z1, c2>0 is a constant coefficient, are the parameters of the sliding mode observer, k1 and k2 are constants, and s is the Laplace operator.

[0122] According to formula (12), we get: hour:

[0123]

[0124] in for The approximate value of; c2 is the parameter of the sliding mode variable (4); and are the derivatives of states e1 and e2 of the error auxiliary system (3) with respect to time t.

[0125] Then the observation error satisfies:

[0126]

[0127] When the mismatched disturbance observation value is designed as in formula (12), it can be seen from formula (14) that as the sliding mode variable converges to zero in the approach process, the observation error tends to zero, and the mismatched disturbance of the controlled system is observed.

[0128] Under the control law (5), after the approach process is completed, the mismatched disturbance observation error It can approximately converge to -ρσ(t). Mismatched perturbation estimation error e d The magnitude of (t) |e d (t)|converges to The maximum time required is approximately t1+t2.

[0129] Therefore, the sliding mode observer for mismatched disturbance proposed in this application is:

[0130]

[0131] To prove the above conclusions:

[0132] Proof 1: Under the control law (5), the trajectory of the error-assisted system can asymptotically converge to the sliding surface σ(t) = 0, that is, σ(t) → 0, t → ∞.

[0133] Design a scalar function V(σ, t) with continuous partial derivatives as a Lyapunov candidate function, satisfying:

[0134]

[0135] Get the derivative of the Lyapunov candidate function V with respect to time t:

[0136]

[0137] When N approaches positive infinity, that is, N→+∞, according to Then the function w1(x):

[0138]

[0139] Function w2(x):

[0140]

[0141] From formula (18), we can see that the function w1(x)=0, w2(x)=0 if and only if x≤0.

[0142] Therefore, for t1≠0, Right now:

[0143]

[0144] For the function Ω1(t, t1):

[0145]

[0146] So for k1>0, the function Θ(t1,t,ρ,k3,N):

[0147]

[0148] remember represents the maximum amplitude of the observation error, then for From equations (5) and (22), we can get:

[0149]

[0150] in is the derivative of the sliding mode variable σ with respect to time t, c2, k1, k2, N, t1, K1, K2>0 are constants, e d is the final observation error.

[0151] Under the control law (5), it can be seen from formula (23) that: The error-assisted system trajectory can converge to the sliding surface σ(t) = 0. That is, σ(t)→0, t→∞.

[0152] Proof 2: Under the control law (5), the amplitude of the sliding mode variable σ(t) converges to |ρσ(0)| within the preset time t1, that is,

[0153] remember is the derivative of the sliding mode variable σ with respect to time t. Assuming that the sliding mode variable σ>0, let k1>0. According to formula (23), the differential of the sliding mode variable is scaled:

[0154]

[0155] It is easy to prove that ω1(x) is second-order differentiable over all real numbers, that is And from equations (18) and (19), we can know that:

[0156]

[0157] Assuming that σ>0, we can simplify equation (24) by equation (25) and equation (7):

[0158]

[0159] Integrate and scale inequality (26):

[0160]

[0161] Where ρ is a constant and 0<ρ<1; σ(0) and ω1(0) are the values ​​of the function ω1(x) of the sliding mode variables and at time t=0 respectively.

[0162] The inequality can be simplified by equation (26) and equation (27):

[0163]

[0164] When the initial t = 0, the value of the sliding mode variable σ(t) is σ(0):

[0165]

[0166] When the time reaches the preset value t1, hour:

[0167]

[0168] At time t, the value of the sliding mode variable is σ(t).

[0169] According to the assumption that σ(t)>0, we can obtain from (30):

[0170]

[0171] If we assume that σ(t)<0, we can prove

[0172]

[0173] Where σ(0) represents the value of the sliding mode variable σ(t) at time t=0; |·| represents the absolute value.

[0174] In summary:

[0175]

[0176] Therefore, under the control law (5), the amplitude of the sliding mode variable σ(t) converges to |ρσ(0)| within the preset time t1, that is, The steady-state accuracy ρσ(0) and the convergence time t1 can be adjusted by presetting the parameters t1 and ρ∈(0,1).

[0177] Proof 3: This application only requires the convergence of the approach process, not the convergence of the sliding process, to effectively observe the mismatch disturbance When the parameter When the mismatch perturbation observation error It can converge approximately to -k2σ(t). After the approximation process is completed, the mismatched perturbation observation error e d can converge approximately to 0.

[0178] when When , according to formula (12), the mismatch disturbance estimate is It can be approximated as:

[0179]

[0180] From the formula (3), the error auxiliary system Mismatched perturbation observation error e d It can be approximated as:

[0181]

[0182] It can be seen from formula (35) that the observation error of the mismatched disturbance is only related to whether the approach process converges. There is no need for a sliding process to allow the error auxiliary system (3) to converge to the equilibrium point.

[0183] From Proof 1, we can see that Therefore, the error-assisted system trajectory will converge to the sliding surface, and the sliding variable σ(t) will converge to 0. From Proof 2, we can see that the convergence time and steady-state error of the sliding variable σ(t) can be adjusted by parameters t1 and ρ.

[0184] Therefore, the present invention only requires the convergence of the approaching process, but not the convergence of the sliding process, to effectively observe the mismatch disturbance. When the parameter When the mismatch perturbation observation error It can converge approximately to -k2σ(t). After the approximation process is completed, the mismatched perturbation observation error e d can converge approximately to 0.

[0185] Proof 4: When the mismatched disturbance is a step signal, the mismatched disturbance estimation error e d (t) converges to The maximum time required is t1+t2.

[0186] Since equation (35) uses approximate processing, the influence of the first-order inertia link is ignored, and the time lag caused by the first-order inertia link is ignored.

[0187] Let the mismatch disturbance estimate after approximation by equation (34) be The unapproximated mismatch perturbation estimate is denoted by The approximate error caused by the approximate processing of formula (34) is recorded as From formula (3), we can know You can get:

[0188]

[0189] Where s is the Laplace operator, is a constant, d is the mismatch disturbance, is the approximate error. Then for equation (36), with the mismatched disturbance d as the step response as input, the approximate error As output. Approximation error The time domain step response expression of is:

[0190]

[0191] The approximate error Less than or equal to At least time t2 is required, that is

[0192] According to equations (35) and (37), the observer error e d :

[0193]

[0194] From Proof 1, we can see that σ(t) converges asymptotically to σ(t)=0, that is, σ(t)→0, t→∞.

[0195] From Proof 2, we can see that |σ(t)| will converge to ρ|k2σ(0)| at least within time t1, that is,

[0196] Therefore, when the mismatch disturbance is a step signal, the mismatch disturbance estimation error e d (t) converges to The maximum time required is t1+t2.

[0197] Proof 5: After the approach process is completed, the parameters The bandwidth f of the mismatched disturbance sliding mode observer is configured by choosing s and phase lag

[0198] According to equations (4) and (12), the mismatch disturbance d and mismatch disturbance estimation in the amplitude-frequency domain are The relationship is:

[0199]

[0200] Where s is the Laplace transform operator; as a parameter.

[0201] Mismatched perturbation d to mismatched perturbation observations The transfer function G is:

[0202]

[0203] Where s is the Laplace transform operator; as a parameter.

[0204] Therefore, the observation bandwidth f of the mismatched disturbance s :

[0205]

[0206] Where π is the ratio of the circumference of a circle, because The unit is rad / s, so it is necessary to convert the unit to Hz through pi.

[0207] Let the Laplace transform operator s = jw, where w is the angular frequency of the input signal and j is the imaginary unit. From equation (40), we can get:

[0208]

[0209] The observed phase lag of the mismatched perturbation for:

[0210]

[0211] Therefore, you can use the parameter The bandwidth f of the sliding mode observer for mismatched disturbances is configured after the approach process is completed. s or phase lag

[0212] See also Figure 3 , which is a schematic diagram of the sliding mode variables and observation errors of Example 1 of the present application.

[0213] Take system (43) as an example:

[0214]

[0215] in is the system status; and are x1 and x2 with respect to time The derivative of is the control input of the system.

[0216] Take d(t) = sin(2πt) as the disturbance input, set the convergence time of the approach process to t1 = 10, and the constant ρ = 0.001 / 11 = 9.09091×10 -5 To adjust the convergence accuracy. Set the bandwidth f s =100Hz, according to formula (9) we can get According to formula (10), the phase lag at this time is

[0217] See also Figure 4 , is a schematic diagram of the effect of the observation mismatch disturbance of Example 1 of the present application. Wherein, d is the ratio matching disturbance, is the mismatch disturbance observed by the observer. The observation error converges within the preset time t1=10, and the observation error e in steady state d ≤10 -3 , it can be seen that the method proposed in this application can effectively observe mismatch disturbances.

[0218] In summary, Example 1 of the present application aims at a controlled system affected by a mismatched disturbance, establishes an auxiliary system and an error auxiliary system, and designs sliding mode variables and control laws according to the state of the error auxiliary system to ensure the convergence of the approach process of the sliding mode control. When the trajectory of the error auxiliary system converges to the sliding mode surface in the approach process, the mismatched disturbance of the controlled system can be observed. In a traditional sliding mode observer, both the approach process and the sliding process need to converge to achieve effective observation of the target. The mismatched disturbance method based on the sliding mode observer proposed in the present application can achieve the desired observation capability only with the convergence of the approach process. At the same time, the convergence time, convergence accuracy, sliding mode observer bandwidth and phase lag of the approach process can be preset, thereby improving the mismatched disturbance observation capability and the flexibility of the sliding mode observer configuration.

[0219] Example 2

[0220] See also Figure 7, is a structural diagram of a mismatched disturbance observation device according to Embodiment 2 of the present application; the specific contents include:

[0221] Establishing module: establishing the motion equation of the controlled system and the auxiliary system corresponding to the controlled system; establishing the error auxiliary system based on the motion equation of the controlled system and the auxiliary system;

[0222] Design module: designs sliding mode variables and control laws of the auxiliary system according to the state of the error auxiliary system;

[0223] Observation module: Based on the control law, the error auxiliary system converges to the sliding surface where the sliding mode variable is zero during the approach process; through the motion equation of the controlled system and the sliding mode variable, the observation value of the mismatched disturbance is designed.

[0224] Example 3

[0225] See also Figure 8 , is a schematic diagram of the device structure of Embodiment 3 of the present application. The device 50 includes a processor 51 and a memory 52 coupled to the processor 51 .

[0226] The memory 52 stores program instructions for implementing the above-mentioned mismatched disturbance observation method.

[0227] The processor 51 is used to execute program instructions stored in the memory 52 to implement a mismatch disturbance observation.

[0228] The processor 51 may also be referred to as a CPU (Central Processing Unit).

[0229] The processor 51 may be an integrated circuit chip with signal processing capabilities. The processor 51 may also be a general-purpose processor, a digital signal processor (DSP), an application-specific integrated circuit (ASIC), a field-programmable gate array (FPGA) or other programmable logic devices, discrete gate or transistor logic devices, discrete hardware components. The general-purpose processor may be a microprocessor or the processor may also be any conventional processor, etc.

[0230] Example 4

[0231] See also Fig. 9, which is a schematic diagram of the structure of the storage medium of Example 4 of the present application. The storage medium of the embodiment of the present application stores a program file 61 that can implement all the above methods, wherein the program file 61 can be stored in the above storage medium in the form of a software product, including a number of instructions to enable a computer device (which can be a personal computer, server, or network device, etc.) or a processor (processor) to perform all or part of the steps of the methods of each embodiment of the present invention. The aforementioned storage medium includes: various media that can store program codes, such as a USB flash drive, a mobile hard disk, a read-only memory (ROM), a random access memory (RAM), a magnetic disk or an optical disk, or a computer, a server, a mobile phone, a tablet, and other devices.

[0232] It should be noted that, in this article, the terms "include", "comprises" or any other variations thereof are intended to cover non-exclusive inclusion, so that a process, device, article or method including a series of elements includes not only those elements, but also includes other elements not explicitly listed, or also includes elements inherent to such process, device, article or method. In the absence of further restrictions, an element defined by the sentence "includes a ..." does not exclude the presence of other identical elements in the process, device, article or method including the element.

[0233] The above description is only a preferred embodiment of the present application, and does not limit the patent scope of the present application. Any equivalent structure or equivalent process transformation made using the contents of the present application specification and drawings, or directly or indirectly used in other related technical fields, are also included in the patent protection scope of the present application.

[0234] Although the embodiments of the present application have been shown and described, it will be appreciated by those skilled in the art that various changes, modifications, substitutions and variations may be made to the embodiments without departing from the principles and spirit of the present application, and that the scope of the present application is defined by the appended claims and their equivalents.

[0235] Of course, the present invention may have many other implementations. Based on this implementation, other implementations obtained by ordinary technicians in this field without any creative work are all within the scope of protection of the present invention.

Claims

1. A mismatched disturbance observation method, characterized in that: include: Establishing the motion equation of the controlled system and the auxiliary system corresponding to the controlled system; Based on the motion equation of the controlled system and the auxiliary system, establishing an error auxiliary system; Designing a sliding mode variable and a control law of the auxiliary system according to a state of the error auxiliary system; Based on the control law, the error auxiliary system converges to a sliding mode surface where the sliding mode variable is zero during the approach process; The observed value of the mismatched disturbance is designed through the motion equation of the controlled system and the sliding mode variable.

2. A mismatched disturbance observation method according to claim 1, characterized in that: The step of establishing the motion equation of the controlled system and the auxiliary system corresponding to the controlled system specifically includes the following steps: Assume that the motion equation of the controlled system is: in is a constant; is the state of the controlled system; and are x1 and x2 with respect to time The derivative of is the control input of the controlled system; a(·) is a function of states x1 and x2; b(·) is a function of states x1, x2 and u; is the mismatch disturbance; The auxiliary systems are: Where z1 and z2 are the states of the auxiliary system; u2 is the control input of the auxiliary system; and are the derivatives of z1 and z2 with respect to time t respectively.

3. The mismatched disturbance observation method according to claim 1, characterized in that: The step of establishing the error auxiliary system based on the motion equation of the controlled system and the auxiliary system specifically includes the following steps: Subtract the motion equation of the controlled system from the auxiliary system to obtain the error auxiliary system: Where e1 and e2 are the states of the error auxiliary system, and are the derivatives of e1 and e2 with respect to time t, satisfying e1: = x1-z1, e2: = x2-z2, e a :=a(x1,x2)-a(z1,z2),e b :=b(x1,x2,u)-b(z1,z2,u).

4. The mismatched disturbance observation method according to claim 1, characterized in that: The step of designing the sliding mode variable and the control law of the auxiliary system according to the state of the error auxiliary system specifically includes the following steps: The sliding mode variables are: σ=e2+c2e1 Where σ is the sliding mode variable, and σ=0 is defined as the sliding mode surface; c2 is a constant coefficient, and c2>0; e1 and e2 are the states of the error auxiliary system; The auxiliary system control law is: Where u2 is the control input of the auxiliary system; k1, k2, k3, k4, c2, ρ, t1, N are constant coefficients, and k3, k4, c2, ρ, t1, N>0, k3 is a parameter for adjusting the convergence dynamics, ρ is a parameter for adjusting the convergence accuracy, and t1 is a parameter for presetting the convergence time of the sliding mode variable; is the observed value of the mismatched disturbance; Θ(t1, t, ρ, k3) is a function of time t.

5. The mismatched disturbance observation method according to claim 1, characterized in that: The step of designing the observation value of the mismatched disturbance by using the motion equation of the controlled system and the sliding mode variable specifically includes the following steps: Assume that the observation error of the sliding mode observer is: Where d is the mismatch disturbance; is the observed value of the mismatched disturbance; k2 is the constant of the controlled system; σ(t) is the value of the sliding mode variable σ at time t; Based on the observation error, the observation value of the designed mismatch disturbance is: Where e1 = x1-z1, c2>0 is a constant coefficient, τ>0 is a parameter of the sliding mode observer, k1 and k2 are constants, and s is the Laplace operator; According to the observed values ​​of the mismatched disturbance, we get: When the parameter τ>>0, in for The approximate value of and are the derivatives of the states e1 and e2 of the error auxiliary system with respect to time t, respectively; Then the observation error satisfies: When the sliding mode variable converges to zero in the approaching process, the observation error tends to zero, and the mismatch disturbance of the controlled system is observed.

6. A mismatched disturbance observation method according to claim 5, characterized in that: The parameters τ of the sliding mode observer include: According to the bandwidth f of the sliding mode observer s , design parameter τ: τ=2πf s Where π is the ratio of a circle to a circle; After the approach process is completed, the bandwidth f of the sliding mode observer is configured by the parameter τ s ; According to the sliding mode observer phase lag Design parameter τ: Where w is the angular frequency of the input signal; tan(·) is the tangent function; After the approach process is completed, the phase lag of the sliding mode observer is configured by the parameter τ 7. A device for a mismatched disturbance observation method according to claim 1, characterized in that: include: Establishing module: establishing the motion equation of the controlled system and the auxiliary system corresponding to the controlled system; Based on the motion equation of the controlled system and the auxiliary system, establishing an error auxiliary system; Design module: designs sliding mode variables and control laws of the auxiliary system according to the state of the error auxiliary system; Observation module: Based on the control law, the error auxiliary system converges to the sliding surface where the sliding mode variable is zero during the approach process; through the motion equation of the controlled system and the sliding mode variable, the observation value of the mismatched disturbance is designed.

8. A device, characterized in that The device includes a processor and a memory coupled to the processor, wherein the memory stores program instructions for implementing a mismatched disturbance observation method as described in any one of claims 1-6; and the processor is used to execute the program instructions stored in the memory to implement a mismatched disturbance observation.

9. A storage medium, characterized in that: Program instructions executable by a processor are stored, and the program instructions are used to execute a mismatched disturbance observation method as described in any one of claims 1-6.

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