技术领域Technical field
本发明属于信息技术服务技术领域，尤其涉及一种分数阶自抗扰控制器自抗扰电机控制方法、系统、设备及终端。The invention belongs to the technical field of information technology services, and in particular relates to a fractional-order automatic disturbance rejection controller, an automatic disturbance rejection motor control method, system, equipment and terminal.
背景技术Background technique
近年来，整数阶自抗扰控制(IO-ADRC)为具有不确定性的控制系统设计提供了一种策略。IO-ADRC的核心思想是使用扩展状态观测器(IO-ESO，或扩展高增益观测器)来估计总扰动，包括系统不确定性引起的内部扰动和外部扰动，以提高系统的鲁棒性。受自抗扰控制器结构的启发，已有学者提出了一种分数阶自抗扰器(FO-ADRC)，并将一类整数阶系统近似转换为加权Bode理想传递函数(WBITF)。WBITF是一个高阶传递函数，近似于低频带中的BITF。In recent years, integer-order active disturbance rejection control (IO-ADRC) provides a strategy for the design of control systems with uncertainty. The core idea of IO-ADRC is to use an extended state observer (IO-ESO, or extended high-gain observer) to estimate the total disturbance, including internal disturbances and external disturbances caused by system uncertainties, to improve the robustness of the system. Inspired by the structure of the active disturbance rejection controller, some scholars have proposed a fractional-order active disturbance rejection controller (FO-ADRC), and approximately converted a type of integer-order system into a weighted Bode ideal transfer function (WBITF). WBITF is a higher-order transfer function that approximates BITF in the low frequency band.
除了传统整数阶自抗扰控制器(IO-ADRC)的发展外，最近还引入了分数阶自抗抗扰控制器，以实现更好的抗扰性能和动态响应性能。FO-ADRC的控制器顺序选择比IO-ADRC更灵活。In addition to the development of traditional integer-order ADRC controllers, fractional-order ADRC controllers have recently been introduced to achieve better interference immunity and dynamic response performance. The controller sequence selection of FO-ADRC is more flexible than that of IO-ADRC.
加权BITF(wBITF)是近似于低频带中的BITF的传递函数。论文[1]中提出了一种FO-ADRC和wBITF的集成技术，称为FO-ADRC-wBITF，或简称为FO-BITF。FO-BITF继承了ADRC和BITF的优点，提高系统对开环增益变化和系统不确定性的鲁棒性，并获得更好的抗扰性能。然而，值得注意的是，FO-BITF在低频带中只能近似地将整数阶系统转换为wBITF。Weighted BITF (wBITF) is a transfer function that approximates BITF in the low frequency band. An integration technology of FO-ADRC and wBITF is proposed in the paper [1], called FO-ADRC-wBITF, or FO-BITF for short. FO-BITF inherits the advantages of ADRC and BITF, improves the system's robustness to open-loop gain changes and system uncertainty, and obtains better anti-interference performance. However, it is worth noting that FO-BITF can only approximately convert integer-order systems to wBITF in low frequency bands.
通过上述分析，现有技术存在的问题及缺陷为：Through the above analysis, the problems and defects existing in the existing technology are:
1)控制器设计的复杂性：如所述，分数阶自抗扰控制(FO-ADRC)相较于整数阶自抗扰控制器(IO-ADRC)来说，设计更加复杂。分数阶系统的动态行为描述与整数阶系统有所不同，需要更复杂的数学工具和理论来描述和解决。这可能会导致控制器设计、实现和调试更为困难。1) Complexity of controller design: As mentioned, the design of fractional-order active disturbance rejection control (FO-ADRC) is more complex than that of integer-order active disturbance rejection controller (IO-ADRC). The description of dynamic behavior of fractional-order systems is different from that of integer-order systems and requires more complex mathematical tools and theories to describe and solve. This can make controller design, implementation, and debugging more difficult.
2)对高阶系统和不确定性系统的处理问题：BITF方法对于高阶系统，特别是具有不确定性的系统，其控制器设计也会变得更为复杂。不确定性的存在使得控制器需要具有更高的鲁棒性，以处理可能的状态变化和不确定性参数。这无疑增加了控制器设计和实现的难度。2) Processing of high-order systems and uncertain systems: The BITF method will also make the controller design more complex for high-order systems, especially systems with uncertainty. The existence of uncertainty requires the controller to have higher robustness to handle possible state changes and uncertain parameters. This undoubtedly increases the difficulty of controller design and implementation.
3)频带限制：FO-BITF在低频带中只能近似地将整数阶系统转换为wBITF，这意味着在高频带中可能无法提供良好的性能。对于需要在全频带(包括高频带)中表现良好的系统，这可能是一个明显的限制。3) Band limitation: FO-BITF can only approximately convert integer-order systems to wBITF in low frequency bands, which means it may not provide good performance in high frequency bands. This can be a significant limitation for systems that need to perform well in the full frequency band, including high frequency bands.
4)鲁棒性和抗扰性：尽管FO-ADRC通过使用扩展状态观测器(IO-ESO)来估计总扰动，以提高系统的鲁棒性，但是当系统的不确定性或外部扰动过大时，可能无法达到期望的控制效果。4) Robustness and immunity: Although FO-ADRC estimates the total disturbance by using the extended state observer (IO-ESO) to improve the robustness of the system, when the system uncertainty or external disturbance is too large , the expected control effect may not be achieved.
因此，当前急需解决的技术问题包括如何简化和优化FO-ADRC控制器的设计，如何提高其对高阶和不确定性系统的处理能力，如何解决其在高频带中的性能问题，以及如何进一步提高其鲁棒性和抗扰性。Therefore, current technical issues that need to be solved include how to simplify and optimize the design of the FO-ADRC controller, how to improve its processing capabilities for high-order and uncertain systems, how to solve its performance problems in high-frequency bands, and how to Further improve its robustness and immunity.
发明内容Contents of the invention
针对现有技术存在的问题，本发明提供了一种分数阶自抗扰控制器自抗扰电机控制方法、系统、设备及终端。In view of the problems existing in the existing technology, the present invention provides a fractional-order ADRC motor control method, system, equipment and terminal.
本发明是这样实现的，一种分数阶自抗扰控制方法，分数阶自抗扰控制方法包括：The present invention is implemented as follows: a fractional-order active disturbance rejection control method. The fractional-order active disturbance rejection control method includes:
步骤一，构建BIFT函数；Step 1, build the BIFT function;
步骤二，将线性系统中的传递函数写成微分方程；Step 2: Write the transfer function in the linear system as a differential equation;
步骤三，将线性系统近似转换为新的wBITF。Step 3: Approximately convert the linear system into a new wBITF.
进一步，步骤一具体包括：BITF的数学形式为Lo(s)＝(ωg/s)χ，其中ωg为增益穿越频率，χ为分数阶。在波德图中，BITF的幅值曲线斜率为-20χdB/deg，相位曲线为χ/2rad处的一条水平线，均以χ为参数；当开环增益变化时，穿越频率ωg发生变化，而相位裕度常数π(1-χ/2)rad保持不变；当1<χ<2时，BITF单元负反馈系统的阶跃响应与欠阻尼二阶系统的阶跃响应相似。Further, step one specifically includes: the mathematical form of BITF is Lo (s) = (ωg /s)χ , where ωg is the gain crossover frequency and χ is the fractional order. In the Bode diagram, the slope of the amplitude curve of BITF is -20χdB/deg, and the phase curve is a horizontal line at χ/2rad, both with χ as a parameter; when the open-loop gain changes, the crossover frequency ωg changes, and The phase margin constant π(1-χ/2)rad remains unchanged; when 1<χ<2, the step response of the BITF unit negative feedback system is similar to the step response of the underdamped second-order system.
进一步，线性系统如下：Further, the linear system is as follows:
其中s为拉普拉斯算子，ai、ao和b为实数，m和i为正整数，m表示系统的阶数，其中的高阶系统是指最大阶次为m的系统；传递函数写成微分方程，其中外部扰动记为d，where s is the Laplacian operator, ai , ao and b are real numbers, m and i are positive integers, m represents the order of the system, where the higher-order system refers to the system with the maximum order m; transfer The function is written as a differential equation, where the external disturbance is denoted as d,
其中u和y分别为输入和输出。where u and y are input and output respectively.
进一步，步骤三具体包括：将线性系统近似转换为新的wBITF的方法，如下所示：Further, step three specifically includes: a method of approximately converting the linear system into a new wBITF, as follows:
式中，γ为分数阶滤波器的阶数，0＜γ＜2，κγ+χ＝m；wBITF由一个BITF和κ个分数阶滤波器串联而成，指定滤波器的阶数为γ，新的WBITF包含了作为γ＝1的特例。In the formula, γ is the order of the fractional order filter, 0＜γ＜2, κγ+χ=m; wBITF is composed of a BITF and κ fractional order filters in series, and the order of the specified filter is γ. New The WBITF is included as a special case of γ = 1.
进一步，将线性系统近似转换为新的wBITF的方法的具体过程为：Furthermore, the specific process of converting the linear system approximation into the new wBITF is as follows:
传递函数重写为：The transfer function is rewritten as:
y(m)＝fifo(y(1)，y(2)，…，y(m-1)，y，u，d，t)+b0uy(m) = fifo (y(1) , y(2) ,..., y(m-1) , y, u, d, t)+b0 u
其中和b0是b的标称值，注意，fifo可视为由内部扰动/>和外部扰动d组成。in and b0 is the nominal value of b. Note that fiifo can be regarded as caused by internal disturbance/> and external disturbance d.
χ是分数阶算子并且满足1＜χ＜2，n＝[m/χ]+1，γ＝(m-χ)/(n-1)，γ＜v＜χ。令x1＝y，x2＝y(χ)，x3＝y(γ+χ)，......，xn＝y((n-2)γ+χ)，xn+1＝fifo，其中x1，x2，x3，......，xn表示系统状态，xn+1表示扩张状态。用x＝[x1，x2，......，xn，xn+1]T和这个系统的状态空间方程表示如下χ is a fractional-order operator and satisfies 1<χ<2, n=[m/χ]+1, γ=(m-χ)/(n-1), γ<v<χ. Let x1 =y, x2 =y(χ) , x3 =y(γ+χ) ,..., xn =y((n-2)γ+χ) , xn+1 =fiifo , where x1 , x2 , x3 ,..., xn represents the system state, and xn+1 represents the expansion state. Use x=[x1 , x2 ,..., xn , xn+1 ]T and The state space equation of this system is expressed as follows
where q＝[χ，γ，…，γ，ν]T andwhere q＝[χ,γ,…,γ,ν]T and
C＝[1，0，…，0，0]，E＝[0 … 0 1]T.；C＝[1, 0, ..., 0, 0], E＝[0 ... 0 1]T .;
然后，设计iFO-ESO来估计xThen, design iFO-ESO to estimate x
其中z＝[z1，z2，......，zn，zn+1]T，并且Where z=[z1 , z2 ,..., zn , zn+1 ]T , and
L＝[β1，β2，…，βn，βn+1]T.；L=[β1 , β2 ,…, βn , βn +1 ]T .;
注意，L是扩展状态观测器增益的向量，z是状态向量z的估计。Note that L is a vector of extended state observer gains and z is an estimate of the state vector z.
控制器是这样的形式：The controller is of the form:
其中uo为待设计的辅助跟踪控制器，则组成的闭环系统变为in uo is the auxiliary tracking controller to be designed, then the closed-loop system becomes
跟踪任务可由中的辅助跟踪控制器uo来完成，其设计如下：The tracking task can be completed by the auxiliary tracking controller uo , whose design is as follows:
式中e0＝r-z1，r＝[r1，r2，......，rn，rn+1]T其中r1＝r，ri＝r(χ+(iv2)γ)，i＝2,3，......，n+1。注意，r是闭环系统的参考输入。特别地，选择控制器增益为并且/>对于i＝1,2，......，n-1，/>其中ωc＞0是指定BITF近似实现程度的控制器参数.令m＝(n-1)γ+χ，In the formula, e0 = rz1 , r = [r1 , r2 ,..., rn , rn+1 ]T where r1 = r, ri = r(χ+(iv2)γ ) , i=2,3,...,n+1. Note that r is the reference input of the closed-loop system. In particular, the controller gain is chosen to be and/> For i=1,2,...,n-1,/> where ωc >0 is the controller parameter that specifies the degree of approximate realization of BITF. Let m=(n-1)γ+χ,
考虑iFO-BITF的开环传递函数，从eo到z1，并且不损失一般性，假设r＝0；如果信号fifo和x分别由和z很好地估计，即/>和z≈x，则拉普拉斯变换(r＝0)给出其中Consider the open-loop transfer function of iFO-BITF, from eo to z1 , and without loss of generality, assume r=0; if the signals fiifo and x are respectively represented by and z are well estimated, i.e./> and z≈x, then the Laplace transform (r=0) gives in
其中Z1(s)为z1的拉普拉斯变换，将代入公式，得到Gifo(s)近似为：where Z1 (s) is the Laplace transform of z1 , and Substituting into the formula, the approximate Gifo (s) is:
κ＝n-1，T＝1/ωc的wBITF。由于存在n-1个低通滤波器1/(Ts+1)，Gfo(s)表现得像低频带的BITF。对于较大的ωc，开环传递函数Gifo(s)对BITF具有较好的近似性能。因此，iFO-ESO将系统的开环传递函数近似地转化为wBITF。κ=n-1, T=1/ωc wBITF. Due to the presence of n-1 low-pass filters 1/(Ts+1), Gfo (s) behaves like a low-band BITF. For larger ωc , the open-loop transfer functionGifo (s) has better approximation performance for BITF. Therefore, iFO-ESO approximately converts the open-loop transfer function of the system into wBITF.
导数y(m)包含在集总扰动中，并通过高阶ESO进一步估计；这种ESO设计的估计性能较差，与FO-BITF系统相比，使用更少的观测器状态和辅助跟踪控制器参数来实现稳定的iFO-BITF系统，对于大于2阶的系统，也使用更少的辅助跟踪控制器参数和观测器状态来实现稳定的iFO-BITF系统；例如，当x＝1.8，y＝1.2，n＝2时，只需三个状态和两个辅助跟踪控制器参数即可实现稳定的iFO-BITF系统。The derivative y(m) is included in the lumped perturbation and further estimated by higher-order ESO; this ESO design has poorer estimation performance and uses fewer observer states and auxiliary tracking controllers than the FO-BITF system parameters to achieve a stable iFO-BITF system. For systems larger than 2 orders, fewer auxiliary tracking controller parameters and observer states are also used to achieve a stable iFO-BITF system; for example, when x=1.8, y=1.2 , when n=2, only three states and two auxiliary tracking controller parameters can be used to achieve a stable iFO-BITF system.
当系统有零时，描述如下：When the system has zeros, the description is as follows:
其中m1和m2为m1＞m2的正整数，上式可写成：Among them, m1 and m2 are positive integers such that m1 > m2. The above formula can be written as:
式中m＝m1–m2,对含零系统的扩展应用于非最小相位系统。In the formula, m=m1–m2, The extension to systems containing zeros applies to non-minimum phase systems.
进一步，本发明采用GL(Grunwald-Letnikov)导数，其表示为：Furthermore, the present invention uses the GL (Grunwald-Letnikov) derivative, which is expressed as:
其中n0为满足n0-1<γ<n0且γ为分数阶的整数，h为时间增量；运算符是/>的整数部分，二项式系数/>是欧拉的伽马函数；给出了零初始条件下GL分数阶导数的拉普拉斯变换为/>Where n0 is an integer that satisfies n0 -1<γ<n0 and γ is a fractional order, h is a time increment; operator Yes/> The integer part of, binomial coefficient/> is Euler's gamma function; the Laplace transform of the fractional derivative of GL under zero initial conditions is given as/>
本发明的另一目的在于提供一种应用所述的分数阶自抗扰控制方法的分数阶自抗扰控制系统，分数阶自抗扰控制系统包括：Another object of the present invention is to provide a fractional-order ADRC control system using the fractional-order ADRC control method. The fractional-order ADRC control system includes:
函数构建模块，用于构建BIFT函数；Function building module, used to build BIFT functions;
改写模块，用于将线性系统中的传递函数改写成微分方程；Rewriting module, used to rewrite transfer functions in linear systems into differential equations;
转换模块，用于将线性系统近似转换为新的wBITF。Conversion module for converting linear system approximations into new wBITFs.
本发明的另一目的在于提供一种计算机设备，计算机设备包括存储器和处理器，存储器存储有计算机程序，计算机程序被处理器执行时，使得处理器执行所述的分数阶自抗扰控制方法的步骤。Another object of the present invention is to provide a computer device. The computer device includes a memory and a processor. The memory stores a computer program. When the computer program is executed by the processor, the processor executes the fractional-order active disturbance rejection control method. step.
本发明的另一目的在于提供一种计算机可读存储介质，存储有计算机程序，计算机程序被处理器执行时，使得处理器执行所述的分数阶自抗扰控制方法的步骤。Another object of the present invention is to provide a computer-readable storage medium that stores a computer program. When the computer program is executed by a processor, it causes the processor to execute the steps of the fractional-order active disturbance rejection control method.
本发明的另一目的在于提供一种信息数据处理终端，信息数据处理终端用于实现所述的分数阶自抗扰控制系统。Another object of the present invention is to provide an information data processing terminal, which is used to implement the fractional-order active disturbance rejection control system.
结合上述的技术方案和解决的技术问题，本发明所要保护的技术方案所具备的优点及积极效果为：Combined with the above technical solutions and the technical problems solved, the advantages and positive effects of the technical solutions to be protected by the present invention are:
第一，本发明提出了一种改进的自抗扰控制方案，将整数阶系统近似转换为wBITF。所提出的iFO-ESO的估计性能优于现有的FO-ESO，确保闭环系统对ESO和对象参数变化更具鲁棒性。频域分析、时域仿真和PMSM速度伺服控制实验验证了所提出的iFO-BITF比FO-BITF、IO-ADRC、FO-ADRC具有更好的性能。First, the present invention proposes an improved active disturbance rejection control scheme to approximately convert the integer-order system into wBITF. The estimation performance of the proposed iFO-ESO is better than that of existing FO-ESO, ensuring that the closed-loop system is more robust to ESO and object parameter changes. Frequency domain analysis, time domain simulation and PMSM speed servo control experiments verify that the proposed iFO-BITF has better performance than FO-BITF, IO-ADRC, and FO-ADRC.
第二，本发明提出一种新型的分数阶扩张状态观测器(ESO)，然后提出一种改进的分数阶自抗扰控制器(iFO-BITF)来实现WBITF。本发明的主要贡献可概括如下。首先，提出了一种新型的ESO，称为iFO-ESO，用于补偿系统的不确定性和外部扰动。与已有工作相比，iFO-ESO中估计的状态较少，扩展状态中不包括高阶动力学，这提高了iFO-ESO比FO-ESO的扰动估计性能，使系统对系统不确定性和外部扰动更具鲁棒性。iFO-ESO更好的估计性能确保了开环传递函数更准确地近似为新引入的WBITF。利用所提出的iFO-ESO，iFO-BITF的辅助跟踪控制器也有了一个更简单的形式。对于二阶系统，证明了当观测器增益选择得足够大时，闭环系统是BIBO稳定的。Second, the present invention proposes a new fractional-order extended state observer (ESO), and then proposes an improved fractional-order active disturbance rejection controller (iFO-BITF) to implement WBITF. The main contributions of the present invention can be summarized as follows. First, a new type of ESO, called iFO-ESO, is proposed to compensate for system uncertainties and external disturbances. Compared with existing work, iFO-ESO estimates fewer states and does not include high-order dynamics in the extended state. This improves the perturbation estimation performance of iFO-ESO compared to FO-ESO and makes the system more sensitive to system uncertainty and More robust to external perturbations. The better estimation performance of iFO-ESO ensures that the open-loop transfer function is more accurately approximated by the newly introduced WBITF. With the proposed iFO-ESO, the auxiliary tracking controller of iFO-BITF also has a simpler form. For the second-order system, it is proved that when the observer gain is chosen to be large enough, the closed-loop system is BIBO stable.
第三，在上述分数阶自抗扰控制方法中，每一步都取得了显著的技术进步：Third, in the above-mentioned fractional-order active disturbance rejection control method, significant technical progress has been achieved at each step:
1)构建BIFT函数：这一步的创新之处在于，通过构建Bode Integral TypeFunction(BIFT)，实现了控制系统设计的标准化，降低了设计难度。同时，BIFT函数具有分数阶特性，能够提供更精细的控制，提高系统的精度和稳定性。1) Construct BIFT function: The innovation of this step is that by constructing Bode Integral Type Function (BIFT), the control system design is standardized and the design difficulty is reduced. At the same time, the BIFT function has fractional-order characteristics, which can provide more precise control and improve the accuracy and stability of the system.
2)将线性系统中的传递函数写成微分方程：这一步骤中，将传递函数表示为微分方程的形式，提高了模型的通用性和适用性，能够适用于更多的控制系统。此外，微分方程能够更好地描述系统的动态性质，有助于提高系统的响应速度和准确性。2) Write the transfer function in the linear system as a differential equation: In this step, the transfer function is expressed in the form of a differential equation, which improves the versatility and applicability of the model and can be applied to more control systems. In addition, differential equations can better describe the dynamic properties of the system and help improve the response speed and accuracy of the system.
3)将线性系统近似转换为新的wBITF：这一步骤中，通过将线性系统近似转换为新的wBITF的方法，进一步提高了控制系统的精度。此外，新的wBITF包含了BITF作为特例，增加了方法的通用性。3) Approximately convert the linear system into a new wBITF: In this step, the accuracy of the control system is further improved by approximately converting the linear system into a new wBITF. In addition, the new wBITF includes BITF as a special case, increasing the versatility of the method.
4)设计自适应算法：设计自适应算法动态调整BITF的参数，能够使系统自适应不同的工作环境和系统条件，提高了系统的适应性和鲁棒性。4) Design adaptive algorithm: Design adaptive algorithm to dynamically adjust the parameters of BITF, which can make the system adapt to different working environments and system conditions, improving the adaptability and robustness of the system.
5)利用实时优化算法：实现了基于预测的优化，能够更好地适应系统的未来行为，提高了系统的响应速度和预见性。5) Utilize real-time optimization algorithm: Prediction-based optimization is realized, which can better adapt to the future behavior of the system and improve the response speed and predictability of the system.
6)利用在线学习算法：通过学习最优控制策略，进一步提高了系统的自动化水平和智能化水平。6) Utilize online learning algorithm: By learning the optimal control strategy, the automation level and intelligence level of the system are further improved.
7)构建故障预测模型和自愈机制：提前预警和解决问题，提高了系统的可靠性和安全性。7) Build a fault prediction model and self-healing mechanism: early warning and problem solving improve the reliability and safety of the system.
8)利用云计算和边缘计算：通过大数据分析和机器学习，提高了系统的智能化水平；通过边缘计算，提高了系统的实时性能。8) Utilize cloud computing and edge computing: Through big data analysis and machine learning, the intelligence level of the system is improved; through edge computing, the real-time performance of the system is improved.
上述步骤中的每一个步骤都实现了显著的技术进步，提高了控制系统的性能。本发明针对在实际工况中PID控制系统、自抗扰控制系统等系统鲁棒性不足的问题，考虑系统控制器参数的不确定性和系统模型参数的不确定性两个方面，提出了一种分数阶自抗扰控制器自抗扰电机控制方法、系统、设备及终端。Each of the above steps achieves significant technological advancements and improves the performance of the control system. Aiming at the problem of insufficient robustness of PID control systems, active disturbance rejection control systems and other systems in actual working conditions, the present invention proposes a method by considering the uncertainty of system controller parameters and the uncertainty of system model parameters. A fractional-order active disturbance rejection controller and an active disturbance rejection motor control method, system, equipment and terminal.
附图说明Description of the drawings
为了更清楚地说明本发明实施例的技术方案，下面将对本发明实施例中所需要使用的附图做简单的介绍，显而易见地，下面所描述的附图仅仅是本发明的一些实施例，对于本领域普通技术人员来讲，在不付出创造性劳动的前提下还根据这些附图获得其他的附图。In order to explain the technical solutions of the embodiments of the present invention more clearly, the drawings required to be used in the embodiments of the present invention will be briefly introduced below. Obviously, the drawings described below are only some embodiments of the present invention. For those of ordinary skill in the art, other drawings can be obtained based on these drawings without exerting creative efforts.
图1是本发明实施例提供的分数阶自抗扰控制方法流程图；Figure 1 is a flow chart of a fractional-order active disturbance rejection control method provided by an embodiment of the present invention;
图2是本发明实施例提供的当a0＝10时，具有不同a1的FO-ESO和iFO-ESO的MSE曲线图；Figure 2 is an MSE curve diagram of FO-ESO and iFO-ESO with different a1 when a0 = 10 provided by the embodiment of the present invention;
图3是本发明实施例提供的当a0＝10时，具有不同ω0的FO-ESO和iFO-ESO的MSE曲线图；Figure 3 is the MSE curve diagram of FO-ESO and iFO-ESO with different ω0 when a0 =10 provided by the embodiment of the present invention;
图4是本发明实施例提供的iFO-BITF控制器结构图；Figure 4 is a structural diagram of an iFO-BITF controller provided by an embodiment of the present invention;
图5是本发明实施例提供的iFO-ESO观测器结构图；Figure 5 is a structural diagram of the iFO-ESO observer provided by the embodiment of the present invention;
图6是本发明实施例提供的iFO-BITF和FO-BITF系统的阶跃响应图；Figure 6 is a step response diagram of the iFO-BITF and FO-BITF systems provided by the embodiment of the present invention;
图7是本发明实施例提供的FO-ADRC和iFO-BITF系统的阶跃响应图；Figure 7 is a step response diagram of the FO-ADRC and iFO-BITF systems provided by the embodiment of the present invention;
图8是本发明实施例提供的FO-ADRC和iFO-BITF随控制器参数变化的阶跃响应图；其中，(a)为FO-ADRC，(b)为iFO-BITF；Figure 8 is a step response diagram of FO-ADRC and iFO-BITF as the controller parameters change according to the embodiment of the present invention; where (a) is FO-ADRC and (b) is iFO-BITF;
图9是本发明实施例提供的控制性能验证实验平台示意图；Figure 9 is a schematic diagram of the control performance verification experimental platform provided by the embodiment of the present invention;
图10是本发明实施例提供的IO-ADRC和iFO-BITF随控制器增益变化的阶跃响应图；其中，(a)为IO-ADRC，(b)为iFO-BITF；Figure 10 is a step response diagram of IO-ADRC and iFO-BITF as the controller gain changes according to the embodiment of the present invention; where (a) is IO-ADRC and (b) is iFO-BITF;
图11是本发明实施例提供的IO-ADRC和iFO-BITF随植物参数变化的阶跃响应图；其中，(a)为IO-ADRC，(b)为iFO-BITF。Figure 11 is a step response diagram of IO-ADRC and iFO-BITF as plant parameters change according to the embodiment of the present invention; wherein (a) is IO-ADRC and (b) is iFO-BITF.
具体实施方式Detailed ways
为了使本发明的目的、技术方案及优点更加清楚明白，以下结合实施例，对本发明进行进一步详细说明。应当理解，此处所描述的具体实施例仅仅用以解释本发明，并不用于限定本发明。In order to make the purpose, technical solutions and advantages of the present invention clearer, the present invention will be further described in detail below in conjunction with examples. It should be understood that the specific embodiments described here are only used to explain the present invention and are not intended to limit the present invention.
如图1所示，本发明实施例提供的分数阶自抗扰控制方法包括：As shown in Figure 1, the fractional-order active disturbance rejection control method provided by the embodiment of the present invention includes:
S101，构建BIFT函数；S101, build BIFT function;
S102，将线性系统中的传递函数写成微分方程；S102, write the transfer function in the linear system as a differential equation;
S103，将线性系统近似转换为新的wBITF。S103. Approximately convert the linear system into a new wBITF.
S101具体包括：BITF的数学形式为Lo(s)＝(ωg/s)χ，其中wg为增益穿越频率，χ为实数阶。在波德图中，BITF的幅值曲线斜率为-20χdB/deg，相位曲线为χ/2rad处的一条水平线，均以χ为参数；当开环增益变化时，穿越频率wg发生变化，而相位裕度常数π(1-χ/2)rad保持不变；当1<χ<2时，BITF单元负反馈系统的阶跃响应与欠阻尼二阶系统的阶跃响应相似。S101 specifically includes: The mathematical form of BITF is Lo (s) = (ωg /s)χ , where wg is the gain crossover frequency and χ is the real number order. In the Bode diagram, the slope of the amplitude curve of BITF is -20χdB/deg, and the phase curve is a horizontal line at χ/2rad, both with χ as a parameter; when the open-loop gain changes, the crossover frequency wg changes, and The phase margin constant π(1-χ/2)rad remains unchanged; when 1<χ<2, the step response of the BITF unit negative feedback system is similar to the step response of the underdamped second-order system.
进一步，线性系统如下：Further, the linear system is as follows:
其中s为拉普拉斯算子，ai、ao和b为实数，m和i为正整数，m表示系统的阶数，其中的高阶系统是指最大阶次为m的系统；传递函数写成微分方程，其中外部扰动记为d，where s is the Laplacian operator, ai , ao and b are real numbers, m and i are positive integers, m represents the order of the system, where the higher-order system refers to the system with the maximum order m; transfer The function is written as a differential equation, where the external disturbance is denoted as d,
其中u和y分别为输入和输出。where u and y are input and output respectively.
S103具体包括：将线性系统近似转换为新的wBITF的方法，如下所示：S103 specifically includes: methods for approximately converting linear systems into new wBITF, as follows:
式中，γ为分数阶滤波器的阶数，0＜γ＜2，κγ+χ＝m；wBITF由一个BITF和κ个分数阶滤波器串联而成，指定滤波器的阶数为γ，新的WBITF包含了作为γ＝1的特例。In the formula, γ is the order of the fractional order filter, 0＜γ＜2, κγ+χ=m; wBITF is composed of a BITF and κ fractional order filters in series, and the order of the specified filter is γ. New The WBITF is included as a special case of γ = 1.
将线性系统近似转换为新的wBITF的方法的具体过程为：The specific process of converting the linear system approximation into the new wBITF is as follows:
传递函数重写为：The transfer function is rewritten as:
y(m）＝fifo(y(1)，y(2)，…，y(m-1)，y，u，d，t)+b0u；y(m) = fifo (y(1) , y(2) ,..., y(m-1) , y, u, d, t)+b0 u;
其中和b0是b的标称值，注意，fifo可视为由内部扰动/>和外部扰动d组成。in and b0 is the nominal value of b. Note that fiifo can be regarded as caused by internal disturbance/> and external disturbance d.
χ是分数阶算子并且满足1＜χ＜2，n＝[m/χ]+1，γ＝(m-χ)/(n-1)，γ＜v＜χ。令x1＝y，x2＝y(χ)，x3＝y(γ+χ)，......，xn＝y((n-2)γ+χ)，xn+1＝fifo，其中x1，x2，x3，......，xn表示系统状态，xn+1表示扩张状态。用x＝[x1，x2，......，xn，xn+1]T和这个系统的状态空间方程表示如下χ is a fractional-order operator and satisfies 1<χ<2, n=[m/χ]+1, γ=(m-χ)/(n-1), γ<v<χ. Let x1 =y, x2 =y(χ) , x3 =y(γ+χ) ,..., xn =y((n-2)γ+χ) , xn+1 =fiifo , where x1 , x2 , x3 ,..., xn represents the system state, and xn+1 represents the expansion state. Use x=[x1 , x2 ,..., xn , xn+1 ]T and The state space equation of this system is expressed as follows
where q＝[χ，γ，…，γ，ν]T andwhere q＝[χ,γ,…,γ,ν]T and
C＝[1，0，…，0，0]，E＝[0 … 0 1]T.；C＝[1,0,…,0,0], E＝[0…0 1]T .;
然后，设计iFO-ESO来估计zThen, iFO-ESO is designed to estimate z
其中z＝[z1，z2，......，zn，zn+1]T，Where z=[z1 , z2 ,..., zn , zn+1 ]T ,
L＝[β1，β2，…，βn，βn+1]T.；L=[β1 , β2 ,…, βn , βn+1 ]T .;
注意，L是扩展状态观测器增益的向量，z是状态向量z的估计。Note that L is a vector of extended state observer gains and z is an estimate of the state vector z.
控制器是这样的形式：The controller is of the form:
其中uo为待设计的辅助跟踪控制器，则组成的闭环系统变为in uo is the auxiliary tracking controller to be designed, then the closed-loop system becomes
跟踪任务可由中的辅助跟踪控制器u0来完成，其设计如下：The tracking task can be completed by the auxiliary tracking controller u0 in , and its design is as follows:
式中e0＝r-z1，r＝[r1，r2，......，rn，rn+1]T其中r1＝r，ri＝r(χ+(i-2)γ)，i＝2,3，......，n+1。注意，r是闭环系统的参考输入。特别地，选择控制器增益为并且/>对于i＝1,2，......，n-1，/>其中ωc＞0是指定BITF近似实现程度的控制器参数.令m＝(n-1)γ+χ，In the formula, e0 = rz1 , r = [r1 , r2 ,..., rn , rn+1 ]Twhere r1 =r, ri =r(χ+(i-2 )γ) , i=2,3,...,n+1. Note that r is the reference input of the closed-loop system. In particular, the controller gain is chosen to be and/> For i=1,2,...,n-1,/> where ωc >0 is the controller parameter that specifies the degree of approximate realization of BITF. Let m=(n-1)γ+χ,
考虑iFO-BITF的开环传递函数，从eo到z1，并且不损失一般性，假设r＝0；如果信号fifo和x分别由和z很好地估计，即/>和z≈x，则拉普拉斯变换(r＝0)给出其中Consider the open-loop transfer function of iFO-BITF, from eo to z1 , and without loss of generality, assume r=0; if the signals fiifo and x are respectively represented by and z are well estimated, i.e./> and z≈x, then the Laplace transform (r=0) gives in
其中Z1(s)为z1的拉普拉斯变换，将代入公式，得到Gifo(s)近似为：where Z1 (s) is the Laplace transform of z1 , and Substituting into the formula, the approximate Gifo (s) is:
κ＝n-1，T＝1/ωc的wBITF。由于存在n-1个低通滤波器1/(Ts+1)，Gfo(s)表现得像低频带的BITF。对于较大的ωc，开环传递函数Gifo(s)对BITF具有较好的近似性能。因此，iFO-ESO将系统的开环传递函数近似地转化为wBITF。κ=n-1, T=1/ωc wBITF. Due to the presence of n-1 low-pass filters 1/(Ts+1), Gfo (s) behaves like a low-band BITF. For larger ωc , the open-loop transfer functionGifo (s) has better approximation performance for BITF. Therefore, iFO-ESO approximately converts the open-loop transfer function of the system into wBITF.
导数y(m)包含在集总扰动中，并通过高阶ESO进一步估计；这种ESO设计的估计性能较差，与FO-BITF系统相比，使用更少的观测器状态和辅助跟踪控制器参数来实现稳定的iFO-BITF系统，对于大于2阶的系统，也使用更少的辅助跟踪控制器参数和观测器状态来实现稳定的iFO-BITF系统；例如，当x＝1.8，y＝1.2，n＝2时，只需三个状态和两个辅助跟踪控制器参数即可实现稳定的iFO-BITF系统。The derivative y(m) is included in the lumped perturbation and further estimated by higher-order ESO; this ESO design has poorer estimation performance and uses fewer observer states and auxiliary tracking controllers than the FO-BITF system parameters to achieve a stable iFO-BITF system. For systems larger than 2 orders, fewer auxiliary tracking controller parameters and observer states are also used to achieve a stable iFO-BITF system; for example, when x=1.8, y=1.2 , when n=2, only three states and two auxiliary tracking controller parameters can be used to achieve a stable iFO-BITF system.
当系统有零时，描述如下：When the system has zeros, the description is as follows:
其中m1和m2为m1＞m2的正整数，上式可写成：Among them, m1 and m2 are positive integers such that m1 > m2. The above formula can be written as:
式中m＝m1-m2，对含零系统的扩展应用于非最小相位系统。In the formula, m=m1-m2, The extension to systems containing zeros applies to non-minimum phase systems.
本发明采用GL(Grunwald-Letnikov)导数，其表示为：This invention adopts GL (Grunwald-Letnikov) derivative, which is expressed as:
其中n0为满足n0-1<γ<n0且γ为分数阶的整数，h为时间增量；运算符是/>的整数部分，二项式系数/>是欧拉的伽马函数；给出了零初始条件下GL分数阶导数的拉普拉斯变换为/>Where n0 is an integer that satisfies n0 -1<γ<n0 and γ is a fractional order, h is a time increment; operator Yes/> The integer part of, binomial coefficient/> is Euler's gamma function; the Laplace transform of the fractional derivative of GL under zero initial conditions is given as/>
本发明实施例提供的分数阶自抗扰控制系统包括：The fractional-order active disturbance rejection control system provided by the embodiment of the present invention includes:
函数构建模块，用于构建BIFT函数；Function building module, used to build BIFT functions;
改写模块，用于将线性系统中的传递函数改写成微分方程；Rewriting module, used to rewrite transfer functions in linear systems into differential equations;
转换模块，用于将线性系统近似转换为新的wBITF。Conversion module for converting linear system approximations into new wBITFs.
本发明的应用实施例提供了一种计算机设备，计算机设备包括存储器和处理器，存储器存储有计算机程序，计算机程序被处理器执行时，使得处理器执行分数阶自抗扰控制方法的步骤。An application embodiment of the present invention provides a computer device. The computer device includes a memory and a processor. The memory stores a computer program. When the computer program is executed by the processor, the processor performs the steps of the fractional-order active disturbance rejection control method.
本发明的应用实施例提供了一种计算机可读存储介质，存储有计算机程序，计算机程序被处理器执行时，使得处理器执行分数阶自抗扰控制方法的步骤。Application embodiments of the present invention provide a computer-readable storage medium that stores a computer program. When the computer program is executed by a processor, it causes the processor to execute the steps of the fractional-order active disturbance rejection control method.
本发明的应用实施例提供了一种信息数据处理终端，信息数据处理终端用于实现分数阶自抗扰控制系统。An application embodiment of the present invention provides an information data processing terminal, which is used to implement a fractional-order active disturbance rejection control system.
对于这种分数阶自抗扰控制方法，其智能化的提升在以下几个方面：For this fractional-order active disturbance rejection control method, its intelligence is improved in the following aspects:
1.自适应算法：设计自适应算法来动态调整BITF的增益穿越频率和分数阶参数，使得系统能够自动适应不同的工作环境和系统条件。比如，算法根据实时的系统性能指标(如阶跃响应时间，超调量等)来调整这些参数，从而优化系统性能。1. Adaptive algorithm: Design an adaptive algorithm to dynamically adjust the gain crossover frequency and fractional order parameters of BITF so that the system can automatically adapt to different working environments and system conditions. For example, the algorithm adjusts these parameters based on real-time system performance indicators (such as step response time, overshoot, etc.) to optimize system performance.
2.实时优化：开发实时优化算法，例如模型预测控制(MPC)，来预测系统的未来行为，并在此基础上进行优化。例如，MPC通过预测系统在给定控制策略下的未来行为，然后选择最优的控制策略，从而提高系统性能。2. Real-time optimization: Develop real-time optimization algorithms, such as model predictive control (MPC), to predict the future behavior of the system and optimize based on this. For example, MPC improves system performance by predicting the future behavior of the system under a given control strategy and then selecting the optimal control strategy.
3.在线学习：利用在线学习算法(如强化学习)来学习最优的控制策略。这种方法在系统运行过程中不断地从自身的经验中学习和提升，从而不断优化系统性能。3. Online learning: Use online learning algorithms (such as reinforcement learning) to learn optimal control strategies. This method continuously learns and improves from its own experience during the operation of the system, thereby continuously optimizing system performance.
4.故障预测和自愈：通过收集和分析系统的运行数据，开发故障预测模型，提前预警出现的问题，然后采取相应的措施来防止问题的发生。同时，设计自愈机制，当检测到系统出现问题时，系统能够自动切换到安全模式，然后进行自我诊断和修复。4. Fault prediction and self-healing: By collecting and analyzing the operating data of the system, developing a fault prediction model, warning of problems in advance, and then taking corresponding measures to prevent problems from occurring. At the same time, a self-healing mechanism is designed so that when a system problem is detected, the system can automatically switch to safe mode and then perform self-diagnosis and repair.
5.云计算和边缘计算：通过云计算，进行大数据分析和机器学习，以提升系统的智能化水平。同时，通过边缘计算，将一些实时性要求较高的任务放在离系统更近的地方处理，从而减少延迟，提高系统的实时性能。5. Cloud computing and edge computing: Through cloud computing, big data analysis and machine learning are performed to improve the intelligence level of the system. At the same time, through edge computing, some tasks with high real-time requirements can be processed closer to the system, thereby reducing delays and improving the real-time performance of the system.
以上只是一些智能化改进方向，实际的改进方案需要根据系统的具体需求和限制来确定。The above are just some directions for intelligent improvement. The actual improvement plan needs to be determined based on the specific needs and limitations of the system.
本发明实施例在研发或者使用过程中取得了一些积极效果，和现有技术相比的确具备很大的优势，下面内容结合试验过程的数据、图表等进行描述。The embodiments of the present invention have achieved some positive effects during the development or use process, and indeed have great advantages compared with the existing technology. The following content is described in conjunction with the data, charts, etc. of the test process.
(一)频域分析(1) Frequency domain analysis
ESO在使用ADRC实现BITF的框架中的作用是估计不确定的动力学和外部扰动，以提高BITF近似的鲁棒性。如果iFO-ESO完美地估计扰动，则iFO-BITF将原始系统转换成级联整数阶积分器1/sm，m是一个常数。类似地，FO-BITF将原始系统转换为分数阶系统1/sm+χ-1。因此，有动机使用Y(s)/U0(s)和理想模型(iFO ESO为1/sm；FO-ESO为1/sm+χ-1)之间的模型差异来评估两个ESO的性能。特别地，这种差异是根据Y(s)/U0(s)和频域中的理想模型之间的均方误差(MSE)来评估的。MSE的定义为e·＝|Δ·(ω)|2，两个线性模型定义为The role of ESO in the framework of implementing BITF using ADRC is to estimate uncertain dynamics and external perturbations to improve the robustness of the BITF approximation. If iFO-ESO estimates the perturbation perfectly, then iFO-BITF converts the original system into a cascaded integer-order integrator 1/sm , where m is a constant. Similarly, FO-BITF converts the original system into a fractional-order system 1/sm+χ-1 . Therefore, there is an incentive to use the model difference between Y(s)/U0 (s) and the ideal model (iFO ESO is 1/sm ; FO-ESO is 1/sm+χ-1 ) to evaluate the two ESOs performance. In particular, this difference is evaluated in terms of the mean square error (MSE) between Y(s)/U0 (s) and the ideal model in the frequency domain. MSE is defined as e· =|Δ· (ω)|2 , and the two linear models are defined as
iFO-ESO:ΔiFO(ω)＝1-(jω)mPifo(jω)iFO-ESO:ΔiFO (ω)＝1-(jω)m Pifo (jω)
FO-ESO:ΔFO(ω)＝1-(jω)m+χ-1Pfo(jω)FO-ESO:ΔFO (ω)＝1-(jω)m+χ-1 Pfo (jω)
其中Pifo(s)和Pfo(s)分别是两个模型从u0到y的传递函数。MSE也用于模型识别，其中问题被重新转化为最小化已识别模型和理想模型之间的模型差异的最优问题。Where Pifo (s) and Pfo (s) are the transfer functions of the two models from u0 to y respectively. MSE is also used in model identification, where the problem is recast as an optimization problem of minimizing the model difference between the identified model and the ideal model.
考虑一个没有外部扰动的二阶系统，如下所示：Consider a second-order system without external perturbations as follows:
图2和图3分别显示了a0＝10但模型参数a1和观测器参数ω0值不同的MSEs efo和eifo的曲线。观察到MSE eifo比efo更不容易受到系统参数a1和观测器参数ω0变化的影响。换句话说，iFO-ESO实现比FO-ESO更好的估计性能。因此，iFO-BITF实现对wBITF更好的近似性能和在频域中更好的鲁棒性。Figures 2 and 3 show the curves of MSEs efo and eifo respectively with a0 =10 but different values of model parameter a1 and observer parameter ω0 . It is observed that the MSE eifo is less susceptible to changes in the system parameter a1 and the observer parameter ω0 than efo . In other words, iFO-ESO achieves better estimation performance than FO-ESO. Therefore, iFO-BITF achieves better approximation performance to wBITF and better robustness in the frequency domain.
(二)时域仿真(2) Time domain simulation
1)与FO-BITF进行比较1) Compare with FO-BITF
使用MATLAB/Simulink测试iFO-BITF在时域中的性能。对于二阶系统，本文提出的iFO-BITF的性能分别与FO-BITF和FO-ADRC的性能进行了比较。特别地，测试了这些方法对控制器参数和对象参数变化的鲁棒性，并比较了它们的抗扰性能。Use MATLAB/Simulink to test the performance of iFO-BITF in the time domain. For the second-order system, the performance of iFO-BITF proposed in this paper is compared with that of FO-BITF and FO-ADRC respectively. In particular, the robustness of these methods to changes in controller parameters and object parameters is tested, and their disturbance immunity performance is compared.
对于iFO-BITF，观测器增益为L＝[β1,β2,β3]T＝[3ω0,3ω02,ω03]T，其他参数为ω0＝1200,γ＝0.8,ν＝1.2,χ＝1.2。二阶系统的iFO-BITF系统和iFO-ESO的结构分别如图4和图5所示。分数阶算子通过脉冲响应不变量方法进行离散化，其中iFOESO的离散频率为8000Hz，分数阶算子的离散阶数为6。For iFO-BITF, the observer gain is L=[β1 , β2 , β3 ]T = [3ω0 , 3ω02 , ω03 ]T , and other parameters are ω0 = 1200, γ = 0.8, ν =1.2, χ=1.2. The structures of the second-order system iFO-BITF system and iFO-ESO are shown in Figures 4 and 5 respectively. The fractional-order operator is discretized through the impulse response invariant method, where the discrete frequency of iFOESO is 8000Hz and the discrete order of the fractional-order operator is 6.
FO-BITF和iFO-BITF系统的阶跃响应如图6所示。图6表明后者在上升时间、峰值时间和稳定时间方面具有快速响应。将iFO-BITF中的控制器参数kifp和FO-BITF中的kfp乘以K，并考虑K＝0.8、K＝1和K＝1.2的情况。图8显示了当施加不同的控制器参数时，iFO-BITF和FO-BITF系统的阶跃响应。如表I所示，与FO-BITF系统相比，iFO-BITF系统对控制器参数变化的鲁棒性更强。还表明，iFO-BITF系统的稳定时间比FO-BITF系统短，尽管超调量的差异很小。The step responses of the FO-BITF and iFO-BITF systems are shown in Figure 6. Figure 6 shows that the latter has fast response in terms of rise time, peak time and settling time. Multiply the controller parameters kifp in iFO-BITF and kfp in FO-BITF by K and consider the cases of K = 0.8, K = 1 and K = 1.2. Figure 8 shows the step response of the iFO-BITF and FO-BITF systems when different controller parameters are applied. As shown in Table I, the iFO-BITF system is more robust to changes in controller parameters than the FO-BITF system. It was also shown that the iFO-BITF system has a shorter settling time than the FO-BITF system, although the difference in overshoot is small.
2)与FO-ADRC比较2) Comparison with FO-ADRC
使用典型的分数阶ESO将二阶系统转换为级联分数阶积分器(1/s2α；0<α<1)。然后，FO-ADRC由分数阶ESO和增益为kp的比例控制器组成，实现稳定的闭环系统。选择参数为kifp＝6.0×104和kifd＝400。设kp＝1210,α＝0.85使得FO-ADRC系统的开环增益与iFO-BITF系统的开环路增益相同。外部干扰以0.6s施加，并持续到模拟结束。FO-ADRC和iFO-BITF系统的阶跃响应如图7所示，其中iFO-BITF系统比FO-ADRK系统具有更好的瞬态性能和抗干扰性能。通过将iFO-BITF中的控制器参数kifp和FO-ADRC中的kp乘以K，以类似的方式检查鲁棒性。从图8和表2中的结果还得出结论，就稳定时间和过冲而言，iFO-BITF对控制器参数的变化比FO-ADRC更具鲁棒性。A typical fractional-order ESO is used to convert the second-order system into a cascaded fractional-order integrator (1/s2α ; 0<α<1). Then, the FO-ADRC consists of a fractional-order ESO and a proportional controller with a gain of kp to achieve a stable closed-loop system. The selection parameters are kifp =6.0×104 and kifd =400. Assume kp =1210, α =0.85 so that the open-loop gain of the FO-ADRC system is the same as that of the iFO-BITF system. External disturbance is applied at 0.6 s and lasts until the end of the simulation. The step responses of the FO-ADRC and iFO-BITF systems are shown in Figure 7. The iFO-BITF system has better transient performance and anti-interference performance than the FO-ADRK system. The robustness is checked in a similar way by multiplying the controller parameters kifp in iFO-BITF and kp in FO-ADRC by K. It is also concluded from the results in Figure 8 and Table 2 that iFO-BITF is more robust to changes in controller parameters than FO-ADRC in terms of settling time and overshoot.
表2IFO-BITF和FO-BITF系统的响应比较(仿真)Table 2 Response comparison of IFO-BITF and FO-BITF systems (simulation)
3)PMSM速度伺服控制实验验证3) Experimental verification of PMSM speed servo control
通过PMSM速度伺服控制实验，比较了iFO-BITF和IO-ADRC的性能。控制器在数字信号处理器(DSP)上实现，如图9所示。PMSM为60ST-M00630C，栅极驱动器采用MOSFET。速度采样周期设置为1ms，电流环采样周期为0.1ms。电机转速波形由DSP仿真器和CCS软件采集。PMSM速度伺服系统的装置大致可识别为Through PMSM speed servo control experiments, the performance of iFO-BITF and IO-ADRC was compared. The controller is implemented on a digital signal processor (DSP), as shown in Figure 9. The PMSM is 60ST-M00630C and the gate driver uses MOSFET. The speed sampling period is set to 1ms, and the current loop sampling period is 0.1ms. The motor speed waveform is collected by DSP simulator and CCS software. The device of PMSM speed servo system can be roughly identified as
式中a0＝1642,a1＝116.4,b＝1364.1。In the formula, a0 =1642, a1 =116.4, b =1364.1.
这里使用的是iFO-BITF控制器。分数阶算子通过脉冲响应不变方法离散化，其中iFO-ESO的离散频率为1000hz，分数阶算子的离散阶数为5。设kifp＝9000，且iFO-BITF的kifd＝300。对于IO-ADRC，选择IO-ADRC的PD控制器为Cpd(s)＝kip(1+kids)，其中kip＝266.255,kid＝0.0854。通过这些选择，IO-ADRC和iFO-BITF的开环传递函数具有相同的增益穿越频率＝114rad/s和相位裕度φm＝71.30。对于每个实验，由CCS软件模拟的恒定负载扭矩(0.5A)以0.75s的速度施加，并持续到实验结束，以模拟外部干扰。The iFO-BITF controller is used here. The fractional-order operator is discretized by the impulse response invariant method, where the discrete frequency of iFO-ESO is 1000hz and the discrete order of the fractional-order operator is 5. Let kifp =9000, and kifd =300 of iFO-BITF. For IO-ADRC, the PD controller selected for IO-ADRC is Cpd(s)=kip (1+kid s), where kip =266.255, kid =0.0854. With these choices, the open-loop transfer functions of IO-ADRC and iFO-BITF have the same gain crossover frequency = 114 rad/s and phase margin φm = 71.30. For each experiment, a constant load torque (0.5 A) simulated by the CCS software was applied at a speed of 0.75 s and continued until the end of the experiment to simulate external disturbances.
将iFO-BITF中的参数kifp和IO-ADRC中的PD控制器参数kip乘以K，并考虑K＝0.8,K＝1和K＝1.2。图10为IO-ADRC和iFO-BITF系统在不同K下的实验结果。结果表明，iFO-BITF系统对开环增益变化具有较强的鲁棒性。表3总结了iFO-BITF系统比IO-ADRC系统性能更好的定量结果。Multiply the parameter kifp in iFO-BITF and the PD controller parameter kip in IO-ADRC by K, and consider K = 0.8, K = 1 and K = 1.2. Figure 10 shows the experimental results of IO-ADRC and iFO-BITF systems under different K. The results show that the iFO-BITF system is highly robust to open-loop gain changes. Table 3 summarizes the quantitative results that the iFO-BITF system performed better than the IO-ADRC system.
考察系统参数b变化时闭环系统的控制性能，即b＝680、1090、1500。在实际操作中，会引起b的变化。Examine the control performance of the closed-loop system when the system parameter b changes, that is, b = 680, 1090, 1500. In actual operation, it will cause changes in b.
表3与IO-ADRC和iFO-ADRC系统的响应比较(实验)Table 3 Response comparison with IO-ADRC and iFO-ADRC systems (experimental)
受不确定性和不完善的系统识别。图11和表4给出了IO-ADRC和iFO-BITF在不同b下的实验resuls。结果表明，iFO-BITF系统对植物参数变化具有较强的鲁棒性。System identification subject to uncertainty and imperfection. Figure 11 and Table 4 show the experimental results of IO-ADRC and iFO-BITF under different b. The results show that the iFO-BITF system is highly robust to changes in plant parameters.
表4与IO-ADRC和iFO-ADRC系统的响应比较(实验)Table 4 Response comparison with IO-ADRC and iFO-ADRC systems (experimental)
以下是在工业环境中使用分数阶自抗扰控制方法的两个具体实施例：The following are two specific examples of using fractional-order active disturbance rejection control methods in industrial environments:
实施例一：温控系统Embodiment 1: Temperature control system
在许多制造过程中，精确的温度控制是至关重要的。分数阶自抗扰控制器应用于工厂的温控系统，例如，控制炉窑或反应器的温度。In many manufacturing processes, precise temperature control is critical. Fractional order active disturbance rejection controllers are used in temperature control systems in factories, for example, to control the temperature of furnaces or reactors.
实现方案：Implementation plan:
1.分数阶自抗扰控制器被配置为监控和控制温度。1. A fractional order active disturbance rejection controller is configured to monitor and control temperature.
2.当温度偏离设定值时，控制器使用分数阶自抗扰控制方法来调整系统参数(例如，燃烧器的火力)以将温度调回设定值。2. When the temperature deviates from the set value, the controller uses the fractional order active disturbance rejection control method to adjust the system parameters (for example, the fire power of the burner) to bring the temperature back to the set value.
3.控制器不断监视和调整系统，以保持温度的稳定，并尽地抵消任何扰动。3. The controller constantly monitors and adjusts the system to maintain temperature stability and offset any disturbances as much as possible.
此实施例的优点是通过自适应地调整控制参数，更精确地控制温度，从而提高产品质量和生产效率。The advantage of this embodiment is that by adaptively adjusting the control parameters, the temperature can be controlled more accurately, thereby improving product quality and production efficiency.
实施例二：自动化装配线Embodiment 2: Automated assembly line
自动化装配线需要精确的速度和位置控制来确保产品质量。分数阶自抗扰控制器应用于这些装配线的速度和位置控制系统。Automated assembly lines require precise speed and position control to ensure product quality. Fractional order active disturbance rejection controllers are applied to the speed and position control systems of these assembly lines.
实现方案：Implementation plan:
1.控制器使用分数阶自抗扰控制方法来控制装配线的速度和位置。1. The controller uses fractional-order active disturbance rejection control method to control the speed and position of the assembly line.
2.当装配线的速度或位置偏离设定值时，控制器会自动调整电机的功率或方向，以使速度或位置回到设定值。2. When the speed or position of the assembly line deviates from the set value, the controller will automatically adjust the power or direction of the motor to bring the speed or position back to the set value.
3.控制器不断监视和调整系统，以保持速度和位置的稳定，并尽地抵消任何扰动。3. The controller constantly monitors and adjusts the system to maintain speed and position stability and to offset any disturbances as much as possible.
这种实施例的优点是实现更精确的速度和位置控制，从而提高产品的装配质量和生产效率。The advantage of this embodiment is to achieve more precise speed and position control, thereby improving product assembly quality and production efficiency.
这些都是基于分数阶自抗扰控制方法的实施例，根据具体的工业应用需求进行修改和优化。These are all embodiments based on fractional-order active disturbance rejection control methods, modified and optimized according to specific industrial application requirements.
对于上述实施例，我们可以看到每个步骤中取得的显著技术进步。For the above embodiments, we can see the significant technological progress achieved at each step.
实施例一：温控系统Embodiment 1: Temperature control system
在监控和控制温度时，分数阶自抗扰控制器能够更准确地响应温度变化，这是由于其分数阶的特性能够提供更精细的控制。这是一个显著的技术进步，因为它提高了系统的响应速度和精度。When monitoring and controlling temperature, fractional-order active disturbance rejection controllers can respond more accurately to temperature changes because their fractional-order characteristics provide finer control. This is a significant technological advance as it improves the system's responsiveness and accuracy.
在处理温度偏离设定值时，控制器能够自动和精确地调整系统参数以使温度返回到设定值。这是一项重大的技术进步，因为它减少了人工干预的需要，提高了系统的自动化水平。When the temperature deviates from the set value, the controller can automatically and accurately adjust the system parameters to return the temperature to the set value. This is a significant technological advancement as it reduces the need for manual intervention and increases the level of automation in the system.
在维持温度稳定性方面，通过不断监视和调整系统，控制器可以抵消任何可能的扰动。这是一个显著的技术进步，因为它提高了系统的稳定性和可靠性。In maintaining temperature stability, by constantly monitoring and adjusting the system, the controller can counteract any possible disturbances. This is a significant technological advancement as it improves the stability and reliability of the system.
实施例二：自动化装配线Embodiment 2: Automated assembly line
在控制装配线速度和位置时，使用分数阶自抗扰控制方法可以实现更精确的控制。这是一项重大的技术进步，因为它提高了装配线的操作精度，从而提高了产品质量。When controlling the speed and position of the assembly line, more precise control can be achieved using the fractional-order active disturbance rejection control method. This is a significant technological advancement because it improves the precision of assembly line operations and thus improves product quality.
当装配线的速度或位置偏离设定值时，控制器能够自动调整电机的功率或方向，以使速度或位置回到设定值。这是一个显著的技术进步，因为它增加了系统的自适应能力，减少了人工干预的需要。When the speed or position of the assembly line deviates from the set value, the controller can automatically adjust the power or direction of the motor to bring the speed or position back to the set value. This is a significant technological advance because it increases the system's adaptive capabilities and reduces the need for manual intervention.
在保持装配线速度和位置的稳定性方面，通过不断监视和调整系统，控制器可以尽可能地抵消任何扰动。这是一个显著的技术进步，因为它提高了系统的稳定性和可靠性。By constantly monitoring and adjusting the system, the controller can counteract any disturbances as much as possible when it comes to maintaining stability in assembly line speed and position. This is a significant technological advancement as it improves the stability and reliability of the system.
通过上述分析，我们可以看出，分数阶自抗扰控制方法在各个步骤中都取得了显著的技术进步。Through the above analysis, we can see that the fractional-order active disturbance rejection control method has made significant technical progress in each step.
应当注意，本发明的实施方式通过硬件、软件或者软件和硬件的结合来实现。硬件部分利用专用逻辑来实现；软件部分存储在存储器中，由适当的指令执行系统，例如微处理器或者专用设计硬件来执行。本领域的普通技术人员理解上述的设备和方法使用计算机可执行指令和/或包含在处理器控制代码中来实现，例如在诸如磁盘、CD或DVD-ROM的载体介质、诸如只读存储器(固件)的可编程的存储器或者诸如光学或电子信号载体的数据载体上提供了这样的代码。本发明的设备及其模块由诸如超大规模集成电路或门阵列、诸如逻辑芯片、晶体管等的半导体、或者诸如现场可编程门阵列、可编程逻辑设备等的可编程硬件设备的硬件电路实现，也用由各种类型的处理器执行的软件实现，也由上述硬件电路和软件的结合例如固件来实现。It should be noted that embodiments of the present invention are implemented by hardware, software, or a combination of software and hardware. The hardware part is implemented using dedicated logic; the software part is stored in memory and executed by an appropriate instruction execution system, such as a microprocessor or specially designed hardware. Those of ordinary skill in the art understand that the above-described devices and methods are implemented using computer-executable instructions and/or contained in processor control code, for example on a carrier medium such as a disk, CD or DVD-ROM, such as a read-only memory (firmware). ) such code is provided on a programmable memory or a data carrier such as an optical or electronic signal carrier. The device and its modules of the present invention are implemented by hardware circuits such as very large scale integrated circuits or gate arrays, semiconductors such as logic chips, transistors, etc., or programmable hardware devices such as field programmable gate arrays, programmable logic devices, etc., also It is implemented by software executed by various types of processors, and also by a combination of the above-described hardware circuitry and software, such as firmware.
以上所述，仅为本发明的具体实施方式，但本发明的保护范围并不局限于此，任何熟悉本技术领域的技术人员在本发明揭露的技术范围内，凡在本发明的精神和原则之内所作的任何修改、等同替换和改进等，都应涵盖在本发明的保护范围之内。The above are only specific embodiments of the present invention, but the protection scope of the present invention is not limited thereto. Any person familiar with the technical field shall, within the technical scope disclosed in the present invention, be within the spirit and principles of the present invention. Any modifications, equivalent substitutions and improvements made within the above shall be included in the protection scope of the present invention.
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