CN104142627A

CN104142627A - Networked brushless direct current motor time-delay compensation and control method using active-disturbance-rejection control technology

Info

Publication number: CN104142627A
Application number: CN201410314689.5A
Authority: CN
Inventors: 张文安; 刘凯; 俞立
Original assignee: Zhejiang University of Technology ZJUT
Current assignee: Zhejiang University of Technology ZJUT
Priority date: 2014-07-03
Filing date: 2014-07-03
Publication date: 2014-11-12
Anticipated expiration: 2034-07-03
Also published as: CN104142627B

Abstract

The invention discloses a networked brushless direct current motor time-delay compensation and control method using the active-disturbance-rejection control technology. The method comprises the steps of (1) establishing a brushless direct current motor control system model containing time-varying network-induced delay, wherein the brushless direct current motor control system is described as a discrete time linear time-varying system containing single-step input time lag, and then the uncertain dynamic state, caused by time-varying delay, of the system is partially described as the additive noise of the system; (2) designing an extended state observer which is used for estimating the uncertain dynamic state caused by time-varying delay as a part of total disturbance; (3) conducting compensation on the time-varying delay item in the brushless direct current motor control system. The method can be used for effectively conducting real-time estimation and compensation on the uncertain dynamic state caused by time-varying network-induced delay by means of the extended state observer, and can well restrain the uncertainty caused by time delay, internal and external disturbance of the system and model uncertainty.

Description

A networked brushless DC motor delay compensation and control method using active disturbance rejection control technology

技术领域 technical field

本发明应用于网络化运动控制领域，涉及到基于工业网络的无刷直流电机控制问题，尤其是如何消除网络诱导时延对无刷直流电机控制系统性能的影响，实现一种有效的实时控制方法。 The present invention is applied in the field of networked motion control, and relates to the problem of brushless DC motor control based on industrial networks, especially how to eliminate the influence of network-induced time delay on the performance of brushless DC motor control system, and realize an effective real-time control method . the

背景技术 Background technique

随着电力电子技术和微电子技术的发展，促生了一种新型调速电动机，即无刷直流电机。由于其低噪声、高效率、结构简单、使用寿命长、响应快速、较大的起动转矩等优点，目前已被广泛应用到数控机床、机械臂以及家用电器等领域。随着工业生产规模的不断扩大，对生产过程的安全要求的不断提高，传统的电机控制系统越来越无法满足实际需求。现代网络控制技术的发展，使得网络化控制代替传统控制方式成为可能。 With the development of power electronics technology and microelectronics technology, a new type of speed-regulating motor, namely brushless DC motor, has been promoted. Due to its low noise, high efficiency, simple structure, long service life, fast response, and large starting torque, it has been widely used in CNC machine tools, robotic arms, and household appliances. With the continuous expansion of industrial production scale and the continuous improvement of the safety requirements of the production process, the traditional motor control system is increasingly unable to meet the actual needs. The development of modern network control technology makes it possible for network control to replace traditional control methods. the

网络化控制系统是指用通讯网络连接传感器、控制器和执行器，代替传统的点对点的连接方式而构成的闭环控制系统。与传统的控制系统相比具有诸多优点，比如可远程操控、减少系统的连线、便于安装与维护以及系统信息集成和共享等。但是，在控制回路中引入通信网络也带来了一些新的问题，由于采用分时复用的信息传递方式，限于网络的承载能力和有限的带宽，必然会造成信息的冲撞、重传等情况的发生，从而导致了信息在控制系统的传输过程产生时延，而且时延随着网络负载的变化而变化，是时变、不确定的。 A networked control system refers to a closed-loop control system that uses a communication network to connect sensors, controllers, and actuators instead of the traditional point-to-point connection. Compared with traditional control systems, it has many advantages, such as remote control, reduced system connections, easy installation and maintenance, and system information integration and sharing. However, the introduction of the communication network into the control loop also brings some new problems. Due to the time-division multiplexing information transmission method, which is limited to the network's carrying capacity and limited bandwidth, it will inevitably cause information collisions, retransmissions, etc. Occurs, resulting in time delay in the transmission process of information in the control system, and the time delay changes with the change of network load, which is time-varying and uncertain. the

网络诱导时延通常分为长时延(大于一个系统采样周期)和短时延(小于一个系统采样周期)，其中长时延的情况在实际系统中出现的频率并不高，长时延对运动控制系统会有很大的影响，工程上一般通过改善网络协议和结构将时延尽可能地减小，但是短时延的存在往往是不可避免的。 Network-induced delays are usually divided into long delays (greater than a system sampling period) and short delays (less than a system sampling period). The frequency of long delays in actual systems is not high. The motion control system will have a great impact. In engineering, the delay is generally reduced as much as possible by improving the network protocol and structure, but the existence of short delays is often unavoidable. the

本发明主要考虑如何降低甚至消除网络诱导时延对无刷直流电机控制系统性能的影响，目前，常用的处理方法包括鲁棒控制方法、Smith预估器补偿方法以及基于时间驱动人为延长时延的方法等。其中，鲁棒控制方法不需要精确知道网络时延的大小，且鲁棒控制器具有较好的抗干扰能力，但保守性较大。Smith预估器方法则是用一个预估模型对时延进行补偿，但是它对电机模型的精确性要求较高，这在实际中往往难以实现。基于时间驱动执行器的人为延长时延的方法能够将时变时延转化为定常时延，便利了控制器的设计，但是会导致系统控制输入不能及时更新，降低了系统的控制性能。 The present invention mainly considers how to reduce or even eliminate the impact of network-induced delay on the performance of the brushless DC motor control system. At present, commonly used processing methods include robust control methods, Smith predictor compensation methods, and time-driven artificially extended delays. method etc. Among them, the robust control method does not need to accurately know the size of the network delay, and the robust controller has better anti-interference ability, but it is relatively conservative. The Smith predictor method uses a predictive model to compensate for the time delay, but it requires high accuracy of the motor model, which is often difficult to achieve in practice. The method of artificially extending the delay based on the time-driven actuator can convert the time-varying delay into a constant delay, which facilitates the design of the controller, but it will cause the system control input to not be updated in time and reduce the control performance of the system. the

发明内容 Contents of the invention

为了克服上述提到的现有控制方法的无法解决时变时延引起的不确定动态进行准确估计、抗干扰能力较弱的不足，本发明采用自抗扰技术设计网络化无刷直流电机控制系统的时延补偿和控制策略，可以有效地将时变网络诱导时延引起的不确定动态用扩张状态观测器实时估计并补偿，此方法对时延引起的不确定性和系统内外扰动以及模型不确定性均具有很强的抑制能力。 In order to overcome the shortcomings of the above-mentioned existing control methods that cannot solve the uncertain dynamics caused by time-varying time delays for accurate estimation and weak anti-interference ability, the present invention adopts ADRC technology to design a networked brushless DC motor control system The time-delay compensation and control strategy of the time-varying network can effectively estimate and compensate the uncertain dynamics caused by the time-varying network-induced delay in real time with the extended state observer. Certainty has a strong inhibitory ability. the

本发明解决其技术问题所采用的技术方案： The technical solution adopted by the present invention to solve its technical problems:

一种采用自抗扰控制技术的网络化无刷直流电机时延补偿和控制方法，所述方法包括以下步骤： A networked brushless DC motor time delay compensation and control method using active disturbance rejection control technology, said method comprising the following steps:

步骤1)建立含有时变网络诱导时延的无刷直流电机控制系统模型。 Step 1) Establish a BLDC motor control system model with time-varying network-induced delay. the

考虑网络诱导时延小于一个采样周期的情况，将网络化无刷直流电机控制系统描述为一个具有一步输入时滞的离散时间线性时变系统，进而将时变时延引起的系统不确定动态部分描述为系统的加性噪声，具体过程包括： Considering that the network-induced delay is less than one sampling period, the networked brushless DC motor control system is described as a discrete-time linear time-varying system with one-step input delay, and then the uncertain dynamic part of the system caused by the time-varying delay Described as additive noise of the system, the specific process includes:

1.1)建立无刷直流电机控制系统的线性化传递函数模型 1.1) Establish the linearized transfer function model of the brushless DC motor control system

无刷直流电机控制系统由电流环和转速环构成，且电流环和转速环均可由一个一阶线性模型描述，经过两者的串联得到无刷直流电机控制系统的二阶系统模型，其传递函数为： The brushless DC motor control system consists of a current loop and a speed loop, and both the current loop and the speed loop can be described by a first-order linear model. After the two are connected in series, the second-order system model of the brushless DC motor control system is obtained. The transfer function for:

$\frac{N N ((s the s))}{U u ((s the s))} = = \frac{b b}{{s the s}^{22} + + as as + + c c} - - - - - - ((11))$

其中， $a = \frac{r}{L - M}, b = \frac{π K_{e}}{30 J (L - M)}, c = \frac{2 K_{e}^{2}}{J (L - M)},$ r是定子相绕组的电阻，L是绕组的自感，M是两相绕组间的互感，K_e是电动势系数，J为电机转动惯量，N(s)是电机转速的拉普拉斯变换，U(s)为导通两相的支路电压的拉普拉斯变换。为便于控制器的设计，将式(1)所示的传递函数模型转化为如下的状态空间模型： in, $a = \frac{r}{L - m}, b = \frac{π K_{e}}{30 J (L - m)}, c = \frac{2 K_{e}^{2}}{J (L - m)},$ r is the resistance of the stator phase winding, L is the self-inductance of the winding, M is the mutual inductance between the two-phase windings, K _e is the electromotive force coefficient, J is the moment of inertia of the motor, N(s) is the Laplace transform of the motor speed, U(s) is the Laplace transform of the branch circuit voltage that conducts the two phases. In order to facilitate the design of the controller, the transfer function model shown in formula (1) is transformed into the following state space model:

其中，x₁为直流电机的转速，x₂为直流电机的加速度，u为控制量，即导通两相的支路电压。 Among them, x ₁ is the rotational speed of the DC motor, x ₂ is the acceleration of the DC motor, and u is the control quantity, that is, the branch circuit voltage that conducts the two phases.

1.2)获得时变网络诱导时延影响下的电机控制系统模型 1.2) Obtain the motor control system model under the influence of time-varying network-induced delay

数据包在网络中传输时，存在从传感器到控制器和控制器到执行器之间的时延，用和分别表示测量信号从传感器传输到控制器所经历的时延和控制量从控制器传输到执行器的时延，那么控制回路总的网络诱导时延是由于时延小于一个采样周期，直流电机在一个周期内的控制输入电压u(t)由两部分构成，一部分是由上一周期计算得到的控制输入电压u(k-1)，另一部分是当前周期计算得到的控制输入电压u(k)，且具有以下形式： When data packets are transmitted in the network, there is a delay between the sensor to the controller and the controller to the actuator. and Represent the time delay experienced by the measurement signal from the sensor to the controller and the time delay of the control quantity from the controller to the actuator, then the total network-induced delay of the control loop is Since the time delay is less than one sampling cycle, the control input voltage u(t) of the DC motor in one cycle consists of two parts, one part is the control input voltage u(k-1) calculated in the previous cycle, and the other part is the current The control input voltage u(k) calculated periodically has the following form:

$u u ((t t)) = = \{\begin{matrix} u u ((k k - - 11)),, & {t t}_{k k} \leq \leq t t < < {t t}_{k k} + + {τ τ}_{k k} \\ u u ((k k)),, & {t t}_{k k} + + {τ τ}_{k k} \leq \leq t t < < {t t}_{k k} + + T T \end{matrix} - - - - - - ((33))$

其中，T是采样周期，t_k表示第k个采样时刻。因此，根据式(2)和(3)，离散化后的含有时变网络诱导时延的无刷直流电机控制系统模型为： Among them, T is the sampling period, and t _k represents the kth sampling moment. Therefore, according to formulas (2) and (3), the discretized BLDC motor control system model with time-varying network-induced delay is:

$\{\begin{matrix} {x x}_{11} ((k k + + 11)) = = {x x}_{11} ((k k)) + + T T {x x}_{22} ((k k)) \\ {x x}_{22} ((k k + + 11)) = = {e e}^{- - aT aT} {x x}_{22} ((k k)) - - \frac{11}{a a} (({e e}^{- - a a ((T T - - {τ τ}_{k k}))} - - 11)) ((bu bu ((k k)) - - c c {x x}_{11} ((k k)))) \\ - - \frac{11}{a a} (({e e}^{- - aT aT} - - {e e}^{- - a a ((T T - - {τ τ}_{k k}))})) ((bu bu ((k k - - 11)) - - c c {x x}_{11} ((k k - - 11)))) \end{matrix} - - - - - - ((44))$

将e^-aT用1-aT近似后，可将式(4)化为： After approximating e ^-aT with 1-aT, formula (4) can be transformed into:

$\{\begin{matrix} {x x}_{11} ((k k + + 11)) = = {x x}_{11} ((k k)) + + T T {x x}_{22} ((k k)) \\ {x x}_{22} ((k k + + 11)) = = {x x}_{22} ((k k)) + + T T ((- - a a {x x}_{22} ((k k)) - - \frac{11}{aT aT} (({e e}^{- - a a ((T T - - {τ τ}_{k k}))} - - 11)) ((bu bu ((k k)) - - c c {x x}_{11} ((k k)))) \\ - - \frac{11}{aT aT} (({e e}^{- - aT aT} - - {e e}^{- - a a ((T T - - {τ τ}_{k k}))})) ((bu bu ((k k - - 11)) - - c c {x x}_{11} ((k k - - 11)))) \end{matrix} - - - - - - ((55))$

将式(5)中由时变时延τ_k引起的时变动态用一个新的状态变量x₃(k)表示，即 $x_{3} (k) = - {ax}_{2} (k) - \frac{b}{aT} e^{- a ({T - τ}_{k})} u (k) + \frac{1}{aT} (e^{- a (T - τ_{k})} - 1) {cx}_{1} (k) - \frac{1}{aT} (e^{- aT} - e^{- a (T - τ_{k})}) (bu (k - 1) - {cx}_{1} (k - 1)),$ 并令由此可将由式(5)表示的网络化无刷直流电机控制系统模型扩张成如下的三阶系统模型： The time-varying dynamics caused by the time-varying time delay τ _k in equation (5) is represented by a new state variable x ₃ (k), namely $x_{3} (k) = - {ax}_{2} (k) - \frac{b}{aT} e^{- a ({T - τ}_{k})} u (k) + \frac{1}{aT} (e^{- a (T - τ_{k})} - 1) {cx}_{1} (k) - \frac{1}{aT} (e^{- aT} - e^{- a (T - τ_{k})}) (bu (k - 1) - {cx}_{1} (k - 1)),$ and order Therefore, the networked brushless DC motor control system model represented by equation (5) can be expanded into the following three-order system model:

$\{\begin{matrix} {x x}_{11} ((k k + + 11)) = = {x x}_{11} ((k k)) + + {Tx Tx}_{22} ((k k)) \\ {x x}_{22} ((k k + + 11)) = = {x x}_{22} ((k k)) + + T T (({x x}_{33} ((k k)) + + \frac{b b}{aT aT} u u ((k k)))) \\ {x x}_{33} ((k k + + 11)) = = {x x}_{33} ((k k)) + + Tw Tw ((k k)) \end{matrix} - - - - - - ((66))$

其中，x₁(k+1)、x₂(k+1)、x₃(k+1)分别为电机转速x₁(k)、电机加速度x₂(k)、新扩张状态量x₃(k)的下一采样时刻的值； Among them, x ₁ (k+1), x ₂ (k+1), and x ₃ (k+1) are motor speed x ₁ (k), motor acceleration x ₂ (k), new expansion state quantity x ₃ ( The value of the next sampling moment of k);

步骤2)设计扩张状态观测器，用于估计无刷直流电机控制系统中由网络诱导时延引起的不确定性； Step 2) Design an extended state observer for estimating the uncertainty caused by the network-induced time delay in the BLDC motor control system;

步骤3)设计带有扩张状态观测器的网络化无刷直流电机自抗扰控制器，实现时变网络诱导时延的实时补偿和电机转速实时控制。 Step 3) Design a networked BLDC motor ADRC controller with an extended state observer to realize real-time compensation of time-varying network-induced delay and real-time control of motor speed. the

进一步，所述步骤2)中，扩张状态观测器设计过程包括： Further, in the step 2), the extended state observer design process includes:

2.1)设计扩张状态观测器 2.1) Design the extended state observer

用于估计系统(6)中三个状态变量的扩张状态观测器具有如下形式： The extended state observer used to estimate the three state variables in system (6) has the following form:

$\{\begin{matrix} e e ((k k)) = = {z z}_{11} ((k k)) - - {x x}_{11} ((k k)),, \\ fe fe = = fal false ((e e ((k k)),, 0.5 0.5,, δ δ)),, \\ fe fe 11 = = fal false ((e e ((k k)),, 0.25 0.25,, δ δ)),, \\ {z z}_{11} ((k k + + 11)) = = {z z}_{11} ((k k)) + + h h (({z z}_{22} ((k k)) - - {β β}_{0101} e e ((k k)))) \\ {z z}_{22} ((k k + + 11)) = = {z z}_{22} ((k k)) + + h h (({z z}_{33} ((k k)) - - {β β}_{0202} fe fe + + \frac{b b}{aT aT} u u ((k k)))) \\ {z z}_{33} ((k k + + 11)) = = {z z}_{33} ((k k)) + + h h (({- - β β}_{0303} fe fe 11)) \end{matrix} - - - - - - ((77))$

其中，e(k)为电机转速参考值与实际转速的估计值之差，即电机转速的误差量，z₁(k)是对电机转速x₁(k)的估计，z₂(k)是对电机加速度x₂(k)的估计，z₃(k)是对新扩张状态量x₃(k)的估计，h是积分步长。fal(e(k),0.25,δ)为非线性函数，具体如式(8)所示。δ、β₀₁、β₀₂、β₀₃为一组待整定的参数，为保证一定的估计精度，根据高增益状态观测器设计原则，β₀₁、β₀₂、β₀₃可取得大一些，一般要大于噪声或扰动的上界。 Among them, e(k) is the difference between the reference value of the motor speed and the estimated value of the actual speed, that is, the error amount of the motor speed, z ₁ (k) is the estimation of the motor speed x ₁ (k), z ₂ (k) is The estimation of motor acceleration x ₂ (k), z ₃ (k) is the estimation of the new expansion state quantity x ₃ (k), and h is the integration step size. fal(e(k),0.25,δ) is a nonlinear function, as shown in formula (8). δ, β ₀₁ , β ₀₂ , and β ₀₃ are a group of parameters to be tuned. In order to ensure a certain estimation accuracy, according to the design principles of high-gain state observers, β ₀₁ , β ₀₂ , and β ₀₃ can be made larger, generally greater than An upper bound on the noise or perturbation.

$fal false ((e e ((k k)),, a a,, δ δ)) = = \{\begin{matrix} \frac{e e ((k k))}{{δ δ}^{11 - - a a}} & | | e e ((k k)) | | \leq \leq δ δ \\ {| | e e ((k k)) | |}^{a a} sign sign ((e e ((k k)))) & | | e e ((k k)) | | > > δ δ \end{matrix} - - - - - - ((88))$

其中，a为幂指数，δ为线性段的区间长度，sign()为符号函数，具体表达式如式(9)所示。 Among them, a is the power exponent, δ is the interval length of the linear segment, sign() is the sign function, and the specific expression is shown in formula (9). the

$sign sign ((x x)) = = \{\begin{matrix} 11 & x x > > 00 \\ 00 & x x = = 00 \\ - - 11 & x x < < 00 \end{matrix} - - - - - - ((99))$

2.2)对时变网络诱导时延引起的不确定性的估计 2.2) Estimation of uncertainty caused by time-varying network-induced delay

所设计的扩张状态观测器可对无刷直流电机的转速、电机的加速度以及新扩张的由网络诱导时延引起的不确定量进行估计，从式(7)可以看出，所设计的扩张状态观测器可将系统中含有时变时延的不确定动态作为总和扰动一并估计出来。对网络诱导时延进行补偿的关键和难点就在于对时变时延引起的不确定动态进行准确的估计，目前尚未有针对该问题的有效结果，本发明采用扩张状态观测器可将时变时延引起的不确定动态作为总和扰动的一部分进行估计。 The designed extended state observer can estimate the speed of the brushless DC motor, the acceleration of the motor, and the newly expanded uncertainty caused by the network-induced delay. It can be seen from equation (7) that the designed extended state The observer can estimate the uncertain dynamics of the system with time-varying delay as a sum of disturbances. The key and difficulty in compensating the network-induced delay is to accurately estimate the uncertain dynamics caused by the time-varying delay. At present, there is no effective result for this problem. The present invention adopts the extended state observer to make the time-varying time Uncertain dynamics due to delays are estimated as part of the sum disturbance. the

再进一步，所述步骤3)中，对网络化无刷直流电机控制系统中时变时延项的补偿过程： Further, in the step 3), to the compensation process of the time-varying delay item in the networked brushless DC motor control system:

3.1)安排过渡过程。此过程是将电机参考转速v，经过跟踪微分器获得转速v的近似转速的微分信号v₂，同时还可以获得转速v的过渡信号v₁，将跳变的转速信号平滑化，防止产生超调，式(10)给出跟踪微分器的具体形式。 3.1) Arrange the transition process. This process is to use the reference speed v of the motor to obtain the differential signal v ₂ of the approximate speed of the speed v through the tracking differentiator, and at the same time obtain the transition signal v ₁ of the speed v, and smooth the jumping speed signal to prevent overshoot , Equation (10) gives the specific form of the tracking differentiator.

$\{\begin{matrix} e e ((k k)) = = {v v}_{11} ((k k)) - - v v ((k k)) \\ fh fh = = fhan fhan ((e e ((k k)),, {v v}_{22} ((k k)),, r r,, {h h}_{00})) \\ {v v}_{11} ((k k)) = = {v v}_{11} ((k k)) + + {hv hv}_{22} ((k k)) \\ {v v}_{22} ((k k)) = = {v v}_{22} ((k k)) + + hfh hfh \end{matrix} - - - - - - ((1010))$

其中，r为快速跟踪因子，h为积分步长，h₀为滤波因子，fhan(e(k),v₂(k),r,h₀)为最速控制综合函数，fhan(x₁,x₂,r,h)具体表达式如下： Among them, r is the fast tracking factor, h is the integral step size, h ₀ is the filter factor, fhan(e(k),v ₂ (k),r,h ₀ ) is the comprehensive function of the fastest control, fhan(x ₁ ,x ₂ , r, h) The specific expression is as follows:

$\{\begin{matrix} d d = = rh rh \\ {d d}_{00} = = hd hd \\ y the y = = {x x}_{11} + + {hx hx}_{22} \\ {a a}_{00} = = \sqrt{{d d}^{22} + + 88 r r | | y the y | |} \\ a a = = \{\begin{matrix} {x x}_{22} + + \frac{(({a a}_{00} - - d d))}{22} sign sign ((y the y)),, & | | y the y | | > > {d d}_{00} \\ {x x}_{22} + + \frac{y the y}{h h},, & | | y the y | | \leq \leq {d d}_{00} \end{matrix} \\ fhan fhan = = - - \{\begin{matrix} rsign rsign ((a a)),, & | | a a | | > > d d \\ r r \frac{a a}{d d},, & | | a a | | \leq \leq d d \end{matrix} \end{matrix} - - - - - - ((1111))$

3.2)用扩张状态观测器估计网络诱导时延引起的不确定性。通过扩张状态观测器获得对新扩张状态量x₃(k)的估计z₃(k)，新扩张的量x₃(k)中既含有时变时延引起的不确定动态又含有内外扰动，扩张状态观测器一并将其作为总和扰动予以估计。 3.2) Estimate the uncertainty caused by the network-induced delay with the extended state observer. Obtain the estimate z ₃ (k) of the new expanded state quantity x ₃ (k) through the expanded state observer, the newly expanded quantity x ₃ (k) contains both the uncertain dynamics caused by the time-varying delay and the internal and external disturbances, The extended state observer is estimated together as a sum disturbance.

3.3)时延引起的控制系统不确定性补偿和控制律设计。此过程得到两个误差量，即e₁(k)＝v₁(k)-z₁(k)和e₂(k)＝v₂(k)-z₂(k)。经过非线性组合模块可计算出控制量u₀(k)，计算过程如式(12)所示。 3.3) Uncertainty compensation and control law design of control system caused by time delay. This process yields two error quantities, e ₁ (k)=v ₁ (k)-z ₁ (k) and e ₂ (k)=v ₂ (k)-z ₂ (k). The control quantity u ₀ (k) can be calculated through the nonlinear combination module, and the calculation process is shown in formula (12).

$\{\begin{matrix} {e e}_{11} ((k k)) = = {v v}_{11} ((k k)) - - {z z}_{11} ((k k)),, {e e}_{22} ((k k)) = = {v v}_{22} ((k k)) - - {z z}_{22} ((k k)) \\ {u u}_{00} ((k k)) = = - - fhan fhan (({e e}_{11} ((k k)),, {e e}_{22} ((k k)),, r r,, h h)) \\ u u ((k k)) = = aT aT (({u u}_{00} ((k k)) - - {z z}_{33} ((k k)))) / / b b \end{matrix} - - - - - - ((1212))$

为了补偿系统中由时变时延引起的不确定性和内外扰动，在得到的控制量u₀(k)中减去z₃(k)得到新的控制量，即补偿过程可抵消系统中所有含有时变时延的总和扰动项，从而使系统转化成了纯积分的线性系统，同时也消除了时变时延对系统性能的影响。 In order to compensate the uncertainty and internal and external disturbances caused by the time-varying delay in the system, the new control quantity is obtained by subtracting z ₃ (k) from the obtained control quantity u ₀ (k), namely The compensation process can cancel all the sum disturbance items with time-varying delay in the system, so that the system can be transformed into a purely integral linear system, and the influence of time-varying delay on system performance can also be eliminated.

与现有技术相比，本发明的优点在于： Compared with prior art, the advantage of the present invention is:

1、可对由网络诱导时延引起的系统不确定动态进行较准确的估计 1. It can estimate the uncertain dynamics of the system caused by the network-induced delay more accurately

本发明设计的扩张状态观测器，可对无刷直流电机控制系统的状态量进行实时估计，即系统中z₁(k)对电机转速x₁(k)的估计，z₂(k)对电机加速度x₂(k)的估计，z₃(k)对新扩张的含有不确定性的状态量x₃(k)的估计。因此，所设计的扩张状态观测器可以将系统中由时变网络诱导时延引起的不确定动态作为总和扰动一并估计出来,有效解决了对时变时延引起的不确定动态进行准确估计这一难题。 The extended state observer designed in the present invention can estimate the state quantities of the brushless DC motor control system in real time, that is, z ₁ (k) in the system can estimate the motor speed x ₁ (k), and z ₂ (k) can estimate the motor speed x 1 (k) The estimation of acceleration x ₂ (k), z ₃ (k) is the estimation of the newly expanded state quantity x ₃ (k) containing uncertainty. Therefore, the designed extended state observer can estimate the uncertain dynamics caused by the time-varying network-induced delay in the system as a sum disturbance, which effectively solves the problem of accurately estimating the uncertain dynamics caused by the time-varying delay. a problem.

2、对时变网络诱导时延引起的不确定动态的补偿 2. Compensation for uncertain dynamics caused by time-varying network-induced delay

利用扩张状态观测器获得的扰动总和估计z₃(k)可重新构造如式(12)所示的控制律，利用该控制律可抵消系统中所有含有时变网络诱导时延动态的总和扰动，从而使系统转化成了纯积分的线性系统，消除了时变网络诱导时延对系统性能的影响。 The control law shown in Equation (12) can be reconstructed by using the disturbance sum estimation z ₃ (k) obtained by the extended state observer, which can cancel all the sum disturbances in the system with time-varying network-induced delay dynamics, Therefore, the system is transformed into a purely integral linear system, and the influence of time-varying network-induced delay on system performance is eliminated.

3、具有很强的抗干扰能力 3. Strong anti-interference ability

z₃(k)作为新扩张出的系统状态量，既含有时变时延引起的不确定动态又含有内外扰动，扩张状态观测器一并将其作为总和扰动予以估计，从而在补偿过程中，在补偿由时变网络诱导时延引起的不确定动态的同时也补偿了内外扰动，消除了内外扰动对系统性能的影响。 z ₃ (k), as a newly expanded system state quantity, contains both uncertain dynamics caused by time-varying time delay and internal and external disturbances. The expanded state observer estimates it as a total disturbance, so that in the compensation process, While compensating the uncertain dynamics caused by time-varying network-induced delay, internal and external disturbances are also compensated, eliminating the influence of internal and external disturbances on system performance.

附图说明 Description of drawings

图1是具有时延的网络化直流电机控制系统结构图。 Figure 1 is a structural diagram of a networked DC motor control system with time delay. the

图2是具有时变短时延的网络化控制系统的信号时序图。 Fig. 2 is a signal sequence diagram of a networked control system with time-varying short delay. the

图3是自抗扰控制器的结构框图。 Figure 3 is a block diagram of the ADRC controller. the

图4是具有时延补偿的电机转速跟踪曲线图。 Figure 4 is a motor speed tracking curve with time delay compensation. the

图5是加入外部扰动时电机转速跟踪曲线图。 Figure 5 is a motor speed tracking curve when external disturbance is added. the

具体实施方式 Detailed ways

为了使本发明的技术方案、设计思路能更加清晰，下面结合附图再进行详尽的描述。 In order to make the technical scheme and design idea of the present invention clearer, a detailed description will be given below in conjunction with the accompanying drawings. the

参照图1～图5，一种采用自抗扰控制技术的网络化无刷直流电机时延补偿和控制方法，所述方法包括以下步骤： Referring to Figures 1 to 5, a networked brushless DC motor time delay compensation and control method using ADRC technology, the method includes the following steps:

$\frac{N N ((s the s))}{U u ((s the s))} = = \frac{b b}{{s the s}^{22} + + as as + + c c} - - - - - - ((1313))$

$u u ((t t)) = = \{\begin{matrix} u u ((k k - - 11)),, & {t t}_{k k} \leq \leq t t < < {t t}_{k k} + + {τ τ}_{k k} \\ u u ((k k)),, & {t t}_{k k} + + {τ τ}_{k k} \leq \leq t t < < {t t}_{k k} + + T T \end{matrix} - - - - - - ((1515))$

$\{\begin{matrix} {x x}_{11} ((k k + + 11)) = = {x x}_{11} ((k k)) + + T T {x x}_{22} ((k k)) \\ {x x}_{22} ((k k + + 11)) = = {e e}^{- - aT aT} {x x}_{22} ((k k)) - - \frac{11}{a a} (({e e}^{- - a a ((T T - - {τ τ}_{k k}))} - - 11)) ((bu bu ((k k)) - - {cx cx}_{11} ((k k)))) \\ - - \frac{11}{a a} (({e e}^{- - aT aT} - - {e e}^{- - a a ((T T - - {τ τ}_{k k}))})) ((bu bu ((k k - - 11)) - - {cx cx}_{11} ((k k - - 11)))) \end{matrix} - - - - - - ((1616))$

$\{\begin{matrix} {x x}_{11} ((k k + + 11)) = = {x x}_{11} ((k k)) + + T T {x x}_{22} ((k k)) \\ {x x}_{22} ((k k + + 11)) = = {x x}_{22} ((k k)) + + T T ((- - {ax ax}_{22} ((k k)) - - \frac{11}{aT aT} (({e e}^{- - a a ((T T - - {τ τ}_{k k}))} - - 11)) ((bu bu ((k k)) - - {cx cx}_{11} ((k k)))) \\ - - \frac{11}{aT aT} (({e e}^{- - aT aT} - - {e e}^{- - a a ((T T - - {τ τ}_{k k}))})) ((bu bu ((k k - - 11)) - - {cx cx}_{11} ((k k - - 11)))) \end{matrix} - - - - - - ((1717))$

将式(5)中由时变时延τ_k引起的时变动态用一个新的状态变量x₃(k)表示，即 $x_{3} (k) = - {ax}_{2} (k) - \frac{b}{aT} e^{- a (T - τ_{k})} u (k) + \frac{1}{aT} (e^{- a (T - τ_{k})} - 1) {cx}_{1} (k) - \frac{1}{aT} (e^{- aT} - e^{- a (T - τ_{k})}) (bu (k - 1) - {cx}_{1} (k - 1)),$ 并令由此可将由式(5)表示的网络化无刷直流电机控制系统模型扩张成如下的三阶系统模型： The time-varying dynamics caused by the time-varying delay τ _k in equation (5) is represented by a new state variable x ₃ (k), namely $x_{3} (k) = - {ax}_{2} (k) - \frac{b}{aT} e^{- a (T - τ_{k})} u (k) + \frac{1}{aT} (e^{- a (T - τ_{k})} - 1) {cx}_{1} (k) - \frac{1}{aT} (e^{- aT} - e^{- a (T - τ_{k})}) (bu (k - 1) - {cx}_{1} (k - 1)),$ and order Therefore, the networked brushless DC motor control system model represented by equation (5) can be expanded into the following three-order system model:

$\{\begin{matrix} {x x}_{11} ((k k + + 11)) = = {x x}_{11} ((k k)) + + T T {x x}_{22} ((k k)) \\ {x x}_{22} ((k k + + 11)) = = {x x}_{22} ((k k)) + + T T (({x x}_{33} ((k k)) + + \frac{b b}{aT aT} u u ((k k)))) \\ {x x}_{33} ((k k + + 11)) = = {x x}_{33} ((k k)) + + Tw Tw ((k k)) \end{matrix} - - - - - - ((1818))$

2.1)设计扩张状态观测器 2.1) Design the extended state observer

$\{\begin{matrix} e e ((k k)) = = {z z}_{11} ((k k)) - - {x x}_{11} ((k k)),, \\ fe fe = = fal false ((e e ((k k)),, 0.5 0.5,, δ δ)),, \\ fe fe 11 = = fal false ((e e ((k k)),, 0.25 0.25,, δ δ)),, \\ {z z}_{11} ((k k + + 11)) = = {z z}_{11} ((k k)) + + h h (({z z}_{22} ((k k)) - - {β β}_{0101} e e ((k k)))) \\ {z z}_{22} ((k k + + 11)) = = {z z}_{22} ((k k)) + + h h (({z z}_{33} ((k k)) - - {β β}_{0202} fe fe + + \frac{b b}{aT aT} u u ((k k)))) \\ {z z}_{33} ((k k + + 11)) = = {z z}_{33} ((k k)) + + h h ((- - {β β}_{0303} fe fe 11)) \end{matrix} - - - - - - ((1919))$

$fal false ((e e ((k k)),, a a,, δ δ)) = = \{\begin{matrix} \frac{e e ((k k))}{{δ δ}^{11 - - a a}} & | | e e ((k k)) | | \leq \leq δ δ \\ {| | e e ((k k)) | |}^{a a} sign sign ((e e ((k k)))) & | | e e ((k k)) | | > > δ δ \end{matrix} - - - - - - ((2020))$

$sign sign ((x x)) = = \{\begin{matrix} 11 & x x > > 00 \\ 00 & x x = = 00 \\ - - 11 & x x < < 00 \end{matrix} - - - - - - ((21 twenty one))$

所设计的扩张状态观测器可对无刷直流电机的转速、电机的加速度以及新扩张的由网络诱导时延引起的不确定量进行估计，从式(7)可以看出，所设计的扩张状态观测器可将系统中含有时变时延的不确定动态作为总和扰动一并估计出来。对网络诱导时延进行补偿的关键和难点就在于对时变时延引起的不确定动态进行准确的估计，目前尚未有针对该问题的有效结果，本发明采用扩张状态观测器可将时变时延引起的不确定动态作为总和扰动的一部分进行估计。 The designed extended state observer can estimate the speed of the BLDC motor, the acceleration of the motor, and the newly expanded uncertainty caused by the network-induced delay. It can be seen from equation (7) that the designed extended state The observer can estimate the uncertain dynamics of the system with time-varying delay as a sum of disturbances. The key and difficulty in compensating the network-induced delay is to accurately estimate the uncertain dynamics caused by the time-varying delay. At present, there is no effective result for this problem. The present invention uses the extended state observer to convert the time-varying time Uncertain dynamics due to delays are estimated as part of the sum disturbance. the

$\{\begin{matrix} e e ((k k)) = = {v v}_{11} ((k k)) - - v v ((k k)) \\ fh fh = = fhan fhan ((e e ((k k)),, {v v}_{22} ((k k)),, r r,, {h h}_{00})) \\ {v v}_{11} ((k k + + 11)) = = {v v}_{11} ((k k)) + + h h {v v}_{22} ((k k)) \\ {v v}_{22} ((k k + + 11)) = = {v v}_{22} ((k k)) + + hfh hfh \end{matrix} - - - - - - ((22 twenty two))$

$\{\begin{matrix} d d = = rh rh \\ {d d}_{00} = = hd hd \\ y the y = = {x x}_{11} + + h h {x x}_{22} \\ {a a}_{00} = = \sqrt{{d d}^{22} + + 88 r r | | y the y | |} \\ a a = = \{\begin{matrix} {x x}_{22} + + \frac{(({a a}_{00} - - d d))}{22} sign sign ((y the y)),, & | | y the y | | > > {d d}_{00} \\ {x x}_{22} + + \frac{y the y}{h h},, & | | y the y | | \leq \leq {d d}_{00} \end{matrix} \\ fhan fhan = = - - \{\begin{matrix} rsign rsign ((a a)),, & | | a a | | > > d d \\ r r \frac{a a}{d d},, & | | a a | | \leq \leq d d \end{matrix} \end{matrix} - - - - - - ((23 twenty three))$

$\{\begin{matrix} {e e}_{11} ((k k)) = = {v v}_{11} ((k k)) - - {z z}_{11} ((k k)),, {e e}_{22} ((k k)) = = {v v}_{22} ((k k)) - - {z z}_{22} ((k k)) \\ {u u}_{00} ((k k)) = = - - fhan fhan (({e e}_{11} ((k k)),, {e e}_{22} ((k k)),, r r,, h h)) \\ u u ((k k)) = = aT aT (({u u}_{00} ((k k)) - - {z z}_{33} ((k k)))) / / b b \end{matrix} - - - - - - ((24 twenty four))$

为了补偿系统中由时变时延引起的不确定性和内外扰动，在得到的控制量 u₀(k)中减去z₃(k)得到新的控制量，即补偿过程可抵消系统中所有含有时变时延的总和扰动项，从而使系统转化成了纯积分的线性系统，同时也消除了时变时延对系统性能的影响。 In order to compensate the uncertainty and internal and external disturbances caused by the time-varying delay in the system, the new control quantity is obtained by subtracting z ₃ (k) from the obtained control quantity u ₀ (k), namely The compensation process can cancel all the sum disturbance items with time-varying delay in the system, so that the system can be transformed into a purely integral linear system, and the influence of time-varying delay on system performance can also be eliminated.

如图1所示，由于网络的引入，数据在传输过程存在时延，主要包括从传感器到控制器之间的时延和控制器到执行器之间的时延控制回路总的时延传感器节点采用时间驱动，以固定的采样周期T对直流电机输出转速进行采样。控制器节点和执行器(无刷直流电机)节点均为事件驱动，当数据到达控制器时计算控制量并传输到无刷直流电机系统。 As shown in Figure 1, due to the introduction of the network, there is a delay in the data transmission process, mainly including the delay between the sensor and the controller and the delay between the controller and the actuator The total delay of the control loop The sensor nodes are driven by time and sample the output speed of the DC motor with a fixed sampling period T. Both the controller node and the actuator (brushless DC motor) node are event-driven, and when the data reaches the controller, the control quantity is calculated and transmitted to the BLDC motor system.

如图2所示，数据在通过无线网络传输时，存在从传感器到控制器和控制器到执行器之间的时延，当无刷直流电机输出数据时，由于传感器采用的是时间驱动，无刷直流电机转速经过传感器以周期T进行采样，得到离散的转速值序列。当采样得到的转速数据到达控制器时，这之间会有一定的时延存在，而这个时延是时变的、不确定的，但是其大小是限定在一个采样周期以内；当控制器计算出控制量，再将控制量数据传输到无刷直流电机时，这之间依然存在时延，而且这个时延是时变的、不确定的；当数据到达无刷直流电机时数据的时延大小是前面所述的两时延之和，而且时延之和也是限定在一个采样周期以内，所以作用到对象的控制量实际上是由两部分构成，一部分是由上一周期计算得到的控制量，另一部分是当前周期计算得到的控制量。 As shown in Figure 2, when the data is transmitted through the wireless network, there is a time delay between the sensor and the controller and between the controller and the actuator. When the brushless DC motor outputs data, since the sensor is driven by time, no The rotational speed of the brushed DC motor is sampled by the sensor at a period T to obtain a discrete rotational speed value sequence. When the sampled speed data reaches the controller, there will be a certain time delay between them, and this time delay is time-varying and uncertain, but its size is limited within one sampling period; when the controller calculates When the control quantity is output, and then the control quantity data is transmitted to the brushless DC motor, there is still a delay between them, and this delay is time-varying and uncertain; when the data reaches the brushless DC motor, the data delay The size is the sum of the two delays mentioned above, and the sum of the delays is also limited within one sampling period, so the control amount applied to the object is actually composed of two parts, one part is the control calculated in the previous cycle The other part is the control quantity calculated in the current cycle. the

如图3所示，本专利研究的对象是无刷直流电机，在测试自抗扰方法的有效性时，可以给定电机转速的参考值，通过安排的过渡过程后会得到两个量，一个是电机转速参考值的过渡信号v₁(k)，另一个是电机转速参考值的微分信号v₂(k)。电机输出的转速值以及控制量作为扩张状态观测器的输入，使得扩张状态观测器能分别对电机转速x₁(k)、电机加速度x₂(k)和扰动总和x₃(k)三个状态量进行估计，其对应的三个估计值分别是z₁(k)、z₂(k)、z₃(k)。据此可计算出电机转速的误差以及误差的微分，即e₁(k)＝v₁(k)-z₁(k)和e₂(k)＝v₂(k)-z₂(k)。得到的两个误差信号经过如式(12)所示的非线性组合可计算出控制量u₀(k)，为了消除系统中含有的由时变时延引起的不确定动态，在得到的控制量u₀(k)中减去z₃(k)得到新的控制量电压当此控制量作用到对象时，可以抵消系统中所有由时变时延引起的不确定动态，使系统转化成了纯积分的线性系统。 As shown in Figure 3, the research object of this patent is a brushless DC motor. When testing the effectiveness of the ADRR method, the reference value of the motor speed can be given, and two quantities will be obtained after the transition process arranged, one is the transition signal v ₁ (k) of the motor speed reference value, and the other is the differential signal v ₂ (k) of the motor speed reference value. The rotational speed value output by the motor and the control quantity are used as the input of the extended state observer, so that the extended state observer can separately analyze the three states of the motor speed x ₁ (k), the motor acceleration x ₂ (k) and the disturbance sum x ₃ (k) The corresponding three estimated values are z ₁ (k), z ₂ (k), and z ₃ (k). Based on this, the error of the motor speed and the differential of the error can be calculated, namely e ₁ (k)=v ₁ (k)-z ₁ (k) and e ₂ (k)=v ₂ (k)-z ₂ (k) . The control variable u ₀ (k) can be calculated through the nonlinear combination of the two error signals obtained as shown in formula (12). In order to eliminate the uncertain dynamics caused by the time-varying delay in the system, the obtained control Subtract z ₃ (k) from u ₀ (k) to get the new control voltage When this control quantity acts on the object, it can offset all uncertain dynamics caused by time-varying delay in the system, and transform the system into a purely integral linear system.

如图4所示，从图中可以看出，应用自抗扰控制方法，即使存在时变网络诱导时延，无刷直流电机控制系统的输出转速仍然具有很快的响应时间，而且跟踪曲线稳定、没有超调和稳态误差，说明由网络诱导时延产生不确定动态被有效的补偿，电机控制系统基本不受时变时延对其性能的影响。 As shown in Figure 4, it can be seen from the figure that the output speed of the brushless DC motor control system still has a fast response time and the tracking curve is stable even if there is a time-varying network-induced delay when the ADRC method is applied. , There is no overshoot and steady-state error, indicating that the uncertain dynamics caused by the network-induced delay are effectively compensated, and the motor control system is basically not affected by the time-varying delay on its performance. the

如图5所示，从图可以看出，即使在有外部扰动的情况下，电机转速仍能很快地跟踪上给定的参考值，达到参考值后没有出现明显抖动，在有外部扰动时仍然能有效补偿时变网络诱导时延引起的不确定动态，由此可见，所设计的自抗扰控制算法不仅对网络诱导时延具有很好的补偿效果，对外部噪声也有很好的抑制能力。 As shown in Figure 5, it can be seen from the figure that even in the case of external disturbances, the motor speed can still quickly track the given reference value, and there is no obvious jitter after reaching the reference value. It can still effectively compensate the uncertain dynamics caused by the time-varying network-induced delay. It can be seen that the designed ADRC algorithm not only has a good compensation effect on the network-induced delay, but also has a good ability to suppress external noise. . the

Claims

1. A networked brushless DC motor time delay compensation and control method that adopts active disturbance rejection control technology, is characterized in that: the method comprises the following steps:

Step 1) Establish a BLDC motor control system model with time-varying network-induced delay, describe the networked BLDC motor control system as a discrete-time linear time-varying system with one-step input delay, and then describe the time-varying time The uncertain dynamic part of the system caused by the delay is described as the additive noise of the system, including the following process:

1.1) Establish the linearized transfer function model of the brushless DC motor control system

The transfer function of the second-order system model of the BLDC motor control system is:

\frac{N N ((s the s))}{U u ((s the s))} = = \frac{b b}{{s the s}^{22} + + as as + + c c} - - - - - - ((11))

in,

a = \frac{r}{L - m}, b = \frac{π K_{e}}{30 J (L - m)}, c = \frac{2 K_{e}^{2}}{J (L - m)},

r is the resistance of the stator phase winding, L is the self-inductance of the winding, M is the mutual inductance between the two-phase windings, K _e is the electromotive force coefficient, J is the moment of inertia of the motor, N(s) is the Laplace transform of the motor speed, U(s) is the Laplace transform of the branch circuit voltage that conducts two phases; the transfer function model shown in formula (1) is transformed into the following state space model:

Among them, x ₁ is the speed of the DC motor, x ₂ is the acceleration of the DC motor, and u is the control value, that is, the branch voltage of the two phases;

1.2) Obtain the motor control system model under the influence of time-varying network-induced delay

When data packets are transmitted in the network, there is a delay between the sensor to the controller and the controller to the actuator. and Represent the time delay experienced by the measurement signal from the sensor to the controller and the time delay of the control quantity from the controller to the actuator, then the total network-induced delay of the control loop is Since the time delay is less than one sampling cycle, the control input voltage u(t) of the DC motor in one cycle consists of two parts, one part is the control input voltage u(k-1) calculated in the previous cycle, and the other part is the current The control input voltage u(k) calculated periodically has the following form:

u u ((t t)) = = \{\begin{matrix} u u ((k k - - 11)),, & {t t}_{k k} \leq \leq 11 < < {t t}_{k k} + + {τ τ}_{k k} \\ u u ((k k)),, & {t t}_{k k} + + {τ τ}_{k k} \leq \leq t t < < {t t}_{k k} + + T T \end{matrix} - - - - - - ((33))

Among them, T is the sampling period, and t _k represents the k-th sampling moment; therefore, according to equations (2) and (3), the discretized BLDC motor control system model with time-varying network-induced delay is:

\{\begin{matrix} {x x}_{11} ((k k + + 11)) = = {x x}_{11} ((k k)) + + T T {x x}_{22} ((k k)) \\ {x x}_{22} ((k k + + 11)) = = {e e}^{- - aT aT} {x x}_{22} ((k k)) - - \frac{11}{a a} (({e e}^{- - a a ((T T - - {τ τ}_{k k}))} - - 11)) ((bu bu ((k k)) - - {cx cx}_{11} ((k k)))) \\ - - \frac{11}{a a} (({e e}^{- - aT aT} - - {e e}^{- - a a ((T T - - {τ τ}_{k k}))})) ((bu bu ((k k - - 11)) - - {cx cx}_{11} ((k k - - 11)))) \end{matrix} - - - - - - ((44))

After approximating e ^-aT with 1-aT, formula (4) can be transformed into:

\{\begin{matrix} {x x}_{11} ((k k + + 11)) = = {x x}_{11} ((k k)) + + T T {x x}_{22} ((k k)) \\ {x x}_{22} ((k k + + 11)) = = {x x}_{22} ((k k)) + + T T ((- - {ax ax}_{22} ((k k)) - - \frac{11}{aT aT} (({e e}^{- - a a ((T T - - {τ τ}_{k k}))} - - 11)) ((bu bu ((k k)) - - {cx cx}_{11} ((k k)))) \\ - - \frac{11}{a a} (({e e}^{- - aT aT} - - {e e}^{- - a a ((T T - - {τ τ}_{k k}))})) ((bu bu ((k k - - 11)) - - {cx cx}_{11} ((k k - - 11)))) \end{matrix} - - - - - - ((55))

The time-varying dynamics caused by the time-varying time delay τ _k in equation (5) is represented by a new state variable x ₃ (k), namely

x_{3} (k) = - {ax}_{2} (k) - \frac{b}{aT} e^{- a (T - τ_{k})} u (k) + \frac{1}{aT} (e^{- a (T - τ_{k})} - 1) {cx}_{1} (k) - \frac{1}{aT} (e^{- aT} - e^{- a (T - τ_{k})}) (bu (k - 1) - {cx}_{1} (k - 1))

, and make Therefore, the networked brushless DC motor control system model represented by equation (5) is expanded into the following three-order system model:

\{\begin{matrix} {x x}_{11} ((k k + + 11)) = = {x x}_{11} ((k k)) + + {Tx Tx}_{22} ((k k)) \\ {x x}_{22} ((k k + + 11)) = = {x x}_{22} ((k k)) + + T T (({x x}_{33} ((k k)) + + \frac{b b}{aT aT} u u ((k k)))) \\ {x x}_{33} ((k k + + 11)) = = {x x}_{33} ((k k)) + + Tw Tw ((k k)) \end{matrix} - - - - - - ((66))

Among them, x ₁ (k+1), x ₂ (k+1), and x ₃ (k+1) are motor speed x ₁ (k), motor acceleration x ₂ (k), new expansion state quantity x ₃ ( The value of the next sampling moment of k);

Step 2) Design an extended state observer for estimating the uncertainty caused by the network-induced time delay in the BLDC motor control system;

Step 3) Design a networked BLDC motor ADRC controller with an extended state observer to realize real-time compensation of time-varying network-induced delay and real-time control of motor speed.

2. the networked brushless DC motor time delay compensation and control method adopting active disturbance rejection control technology according to claim 1, is characterized in that, in described step 2), the extended state observer design process comprises:

2.1) Design the extended state observer

The extended state observer for estimating the three state variables in system (6) has the following form:

\{\begin{matrix} e e ((k k)) = = {z z}_{11} ((k k)) - - {x x}_{11} ((k k)),, \\ fe fe = = fal false ((e e ((k k)),, 0.5 0.5,, δ δ)),, \\ fe fe 11 = = fal false ((e e ((k k)),, 0.25 0.25,, δ δ)),, \\ {z z}_{11} ((k k + + 11)) = = {z z}_{11} ((k k)) + + h h (({z z}_{22} ((k k)) - - {β β}_{0101} e e ((k k)))) \\ {z z}_{22} ((k k + + 11)) = = {z z}_{22} ((k k)) + + h h (({z z}_{33} ((k k)) - - {β β}_{0202} fe fe + + \frac{b b}{aT aT} u u ((k k)))) \\ {z z}_{33} ((k k + + 11)) = = {z z}_{33} ((k k)) + + h h ((- - {β β}_{0303} fe fe 11)) \end{matrix} - - - - - - ((77))

Among them, e(k) is the difference between the reference value of the motor speed and the estimated value of the actual speed, that is, the error amount of the motor speed, z ₁ (k) is the estimation of the motor speed x ₁ (k), z ₂ (k) is the The estimation of the motor acceleration x ₂ (k), z ₃ (k) is the estimation of the new expansion state quantity x ₃ (k), h is the integration step size; fal(e(k),0.25,δ) is a nonlinear function , specifically as shown in formula (8), δ, β ₀₁ , β ₀₂ , β ₀₃ are a set of parameters to be tuned;

fal false ((e e ((k k)),, a a,, δ δ)) = = \{\begin{matrix} \frac{e e ((k k))}{{δ δ}^{11 - - a a}},, & | | e e ((k k)) | | \leq \leq δ δ \\ {| | e e ((k k)) | |}^{a a} sign sign ((e e ((k k)))),, & | | e e ((k k)) | | > > δ δ \end{matrix} - - - - - - ((88))

Among them, a is the power exponent, δ is the interval length of the linear segment, sign() is the sign function, and the specific expression is shown in formula (9):

sign sign ((x x)) = = \{\begin{matrix} 11 & x x > > 00 \\ 00 & x x = = 00 \\ - - 11 & x x < < 00 \end{matrix} - - - - - - ((99))

2.2) Estimation of uncertainty caused by time-varying network-induced delay

The designed extended state observer can estimate the speed and acceleration of the BLDC motor and the uncertainties caused by the newly expanded network-induced delay. It can be seen from equation (7) that the designed extended state observer The uncertain dynamics with time-varying delays in the system can be estimated together as a sum disturbance; the key and difficulty in compensating network-induced delays is to accurately estimate the uncertain dynamics caused by time-varying delays. Extended state observers estimate uncertain dynamics due to time-varying delays as part of the sum perturbation.

3. The networked brushless DC motor time delay compensation and control method adopting active disturbance rejection control technology according to claim 1 and 2, characterized in that, in the step 3), the networked brushless DC motor control The compensation process of the time-varying delay term in the system:

3.1) Arranging the transition process: this process is to use the reference speed v of the motor to obtain the differential signal v ₂ of the approximate speed of the speed v through the tracking differentiator, and at the same time obtain the transition signal v ₁ of the speed v, and smooth the jumping speed signal to prevent overshooting, formula (10) gives the specific form of the tracking differentiator:

\{\begin{matrix} e e ((k k)) = = {v v}_{11} ((k k)) - - v v ((k k)) \\ fh fh = = fhan fhan ((e e ((k k)),, {v v}_{22} ((k k)),, r r,, {h h}_{00})) \\ {v v}_{11} ((k k + + 11)) = = {v v}_{11} ((k k)) + + {hv hv}_{22} ((k k)) \\ {v v}_{22} ((k k + + 11)) = = {v v}_{22} ((k k)) + + hfh hfh \end{matrix} - - - - - - ((1010))

Among them, r is the fast tracking factor, h is the integral step size, h ₀ is the filter factor, fhan(e(k),v ₂ (k),r,h ₀ ) is the comprehensive function of the fastest control, fhan(x ₁ ,x ₂ , r, h) The specific expression is as follows:

\{\begin{matrix} d d = = rh rh \\ {d d}_{00} = = hd hd \\ y the y = = {x x}_{11} + + h h {x x}_{22} \\ {a a}_{00} = = \sqrt{{d d}^{22} + + 88 r r | | y the y | |} \\ a a = = \{\begin{matrix} {x x}_{22} + + \frac{(({a a}_{00} - - d d))}{22} sign sign ((y the y)),, & | | y the y | | > > {d d}_{00} \\ {x x}_{22} + + \frac{y the y}{h h},, & | | y the y | | \leq \leq {d d}_{00} \end{matrix} \\ fhan fhan = = - - \{\begin{matrix} rsign rsign ((a a)),, & | | a a | | > > d d \\ r r \frac{a a}{d d},, & | | a a | | \leq \leq d d \end{matrix} \end{matrix}- - - - - - - ((1111))

3.2) Use the extended state observer to estimate the uncertainty caused by the network-induced delay; obtain the estimate z ₃ (k) of the new extended state quantity x ₃ (k) through the extended state observer, x ₃ (k) contains both Uncertain dynamics caused by time-varying delays contain internal and external disturbances, which are estimated as sum disturbances by the extended state observer;

3.3) Uncertainty compensation of control system caused by time delay and control law design, this process obtains two error quantities, namely e ₁ (k)=v ₁ (k)-z ₁ (k) and e ₂ (k)= v ₂ (k)-z ₂ (k), the control variable u ₀ (k) can be calculated through nonlinear combination, and the calculation process is shown in formula (12):

\{\begin{matrix} {e e}_{11} ((k k)) = = {v v}_{11} ((k k)) - - {z z}_{11} ((k k)) {,, e e}_{22} ((k k)) = = {v v}_{22} ((k k)) - - {z z}_{22} ((k k)) \\ {u u}_{00} ((k k)) = = - - fhan fhan (({e e}_{11} ((k k)),, {e e}_{22} ((k k)),, r r,, h h)) \\ u u ((k k)) = = aT aT (({u u}_{00} ((k k)) - - {z z}_{33} ((k k)))) / / b b \end{matrix} - - - - - - ((1212))

Subtract z ₃ (k) from the obtained control quantity u ₀ (k) to obtain a new control quantity, namely The compensation process can cancel all the sum disturbance items with time-varying delay in the system, so that the system can be transformed into a purely integral linear system.