WO2021056671A1 - 一种大型无人机uav的强自耦pi协同控制方法 - Google Patents
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- G05D1/08—Control of attitude, i.e. control of roll, pitch, or yaw
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- G05D—SYSTEMS FOR CONTROLLING OR REGULATING NON-ELECTRIC VARIABLES
- G05D1/00—Control of position, course, altitude or attitude of land, water, air or space vehicles, e.g. using automatic pilots
- G05D1/10—Simultaneous control of position or course in three dimensions
- G05D1/101—Simultaneous control of position or course in three dimensions specially adapted for aircraft
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- the present invention relates to the technical field of the aircraft control field, and in particular to a strong auto-coupling PI (Enhanced Auto-Coupling Proportional-Integral, EAC-PI) collaborative control method for a large unmanned aerial vehicle (UAV).
- PI Enhanced Auto-Coupling Proportional-Integral, EAC-PI
- the controller gain also needs to change, and this is also a variety of improved PID Control methods such as the original motivation of adaptive PID, nonlinear PID, neuron PID, intelligent PID, fuzzy PID, expert system PID, etc.
- improved PIDs can improve the adaptive control ability of the system by optimizing and tuning the controller gain parameters online, the existing various PID controls are still powerless for the control problems of non-affine nonlinear uncertain systems, especially The anti-disturbance robustness is poor.
- the large unmanned aerial vehicle is a typical multi-input multi-output and input limited non-affine nonlinear strong coupling uncertain system
- the traditional PID and its various The improved PID control methods seem helpless, and the existing control methods mainly include: second-order non-singular dynamic terminal sliding mode control method, second-order non-singular terminal sliding mode control method based on the cerebellar model (CMAC) interference observer, and A second-order non-singular terminal sliding mode control method based on wavelet cerebellar model (WCMAC) interference observer.
- CMAC cerebellar model
- WCMAC wavelet cerebellar model
- the second-order non-singular dynamic terminal sliding mode control method is out of control; the second-order non-singular terminal sliding mode control method based on CMAC and the second-order non-singular terminal sliding mode control based on WCMAC
- CMAC Cost-to-envelope-to-envelope-to-envelope-to-envelope-to-envelope-to-envelope-to-envelope-to-envelope
- WCMAC the second-order non-singular terminal sliding mode control based on WCMAC
- the purpose of the present invention is to address the defects in the background technology and propose a strong autocoupling PI collaborative control method for large UAV UAVs, through a model structure that is simple, easy to set parameters, good dynamic quality, high control accuracy, and anti-disturbance
- a powerful control method can effectively improve the dynamic quality and steady-state performance of the UAV control system, reduce the amount of calculation, improve real-time performance, and enhance the stability of the control system.
- the present invention adopts the following technical solutions:
- Step A Measure and obtain the expected trajectory y dj and differential signal of the UAV UAV And the actual output y j of the UAV, and establish its tracking error e j and the integral e j0 of the tracking error;
- e j represents the tracking error
- e j0 represents the integral of the tracking error
- step B Obtain the tracking error e j of the UAV UAV according to step A, according to the tracking error e j , the integral of the tracking error e j0 and the derivative signal of the desired trajectory
- the creation of the EAC-PI cooperative control law u j specifically includes the use of the following formula to obtain the EAC-PI cooperative control law:
- z j represents the speed factor of the EAC-PI controller on the jth channel of the UAV, and z j >0;
- ⁇ j represents the dimensionless enhancement factor of the EAC-PI controller of the j- th UAV channel, ⁇ j >0;
- u j represents the output coordinated control power of the j-th channel EAC-PI coordinated controller.
- step C according to the EAC-PI cooperative control law model of the jth channel of UAV established in step B, and through the integrated control force of the jth channel And the coordinated control force u j are respectively limited in amplitude processing to avoid integral saturation in the dynamic process and meet the requirements of the input limited system;
- u jm represents the maximum amplitude of the coordinated control input of the j-th channel, and u jm >0.
- a strong auto-coupling proportional-integral (EAC-PI) control method of the present invention concentrates the respective advantages of the three mainstream controllers and eliminates their respective limitations, namely: It has the advantages of simple PID structure, good robust stability of SMC, and strong anti-disturbance ability of ADRC; it not only effectively avoids the difficulty of PID gain tuning, but also effectively solves the high frequency chattering and chattering of SMC. The problem of irreconcilability between anti-disturbance capabilities also effectively avoids the problems of too many ADRC gain parameters and too much calculation.
- the invention of the EAC-PI control method has enriched the control theory system for more than half a century, and has provided an effective technical guarantee for the technical upgrade of various PID controllers in operation.
- the invention has broad application prospects in the field of non-affine nonlinear uncertain control systems and aircraft control.
- Figure 1 is a framework diagram of the UAV UAV control system based on the EAC-PI controller of the present invention
- Fig. 2 is an airspeed tracking trajectory diagram in the tracking control result of the nominal UAV system of the present invention
- Fig. 3 is a track diagram of the track tilt angle in the tracking control result of the nominal UAV system of the present invention
- Fig. 4 is a track diagram of track and azimuth tracking in the tracking control result of the nominal UAV system of the present invention
- Figure 5 is a UAV system thrust control input diagram in the nominal UAV system tracking control result of the present invention.
- Figure 6 is a UAV system overload coefficient control input diagram in the nominal UAV system tracking control result of the present invention.
- Figure 7 is a UAV system roll angle control input diagram in the nominal UAV system tracking control result of the present invention.
- Fig. 8 is an airspeed tracking trajectory diagram in the tracking control result of the disturbed UAV system of the present invention.
- FIG. 9 is a track diagram of track tilt angle tracking in the tracking control result of the disturbed UAV system of the present invention.
- Fig. 10 is a track diagram of the track and azimuth angle in the tracking control result of the disturbed UAV system of the present invention.
- Figure 12 is a UAV system overload coefficient control input diagram in the tracking control result of the disturbed UAV system of the present invention.
- Fig. 13 is a UAV system roll angle control input diagram in the tracking control result of the disturbed UAV system of the present invention.
- V, ⁇ and ⁇ are the UAV's airspeed, track inclination angle and track azimuth angle respectively; T, n, ⁇ are engine thrust, overload coefficient and roll angle respectively; g is the acceleration due to gravity; M is the mass of the UAV ; D is resistance and is expressed as:
- the actual flight safety requirements of UAV should also be considered, that is, the roll angle ⁇ should meet:
- UAV is a three-input three-output non-affine nonlinear strong coupling system.
- the present invention first defines the non-affine nonlinear uncertain dynamics of each channel separately Is the sum of three disturbances, namely:
- the system (4) is a three-input three-output linear uncertain system which is completely equivalent to the UAV system (3), and the control of the system (4) is equivalent to the control of the UAV system (3).
- MIMO non-affine nonlinear uncertain systems can be expressed as MIMO linear uncertain systems (4), Has universal significance. Not only that, through the definition of total disturbance, all known or unknown uncertain factors are represented by total disturbance, and the idea of converting a non-affine nonlinear uncertain system into a linear uncertain system completely dilutes linearity and nonlinearity.
- b 1 g/M
- the error dynamic system of the j-th channel can be established as follows:
- the error system (8) is a second-order error dynamics system (EDS).
- EDS error dynamics system
- z j >0 and ⁇ j >0 are the speed factor and dimensionless enhancement factor of the EAC-PI controller of the jth channel of the UAV system
- b j is the control gain of the jth channel of the UAV
- b 1 g/M
- u j is not only the cooperative control force output of the j-th channel EAC-PI cooperative controller, but also the cooperative control force input of the j-th channel controlled object.
- the speed factor is not only an important link factor between the two gains k p and k i in the EAC-PI controller, but also an equivalent conversion factor of k p and k i.
- the main function of the enhancement factor is to adjust the control force of the proportional link. When 0 ⁇ j ⁇ 1, the control force of the proportional link is reduced, otherwise, the control force of the proportional link is enhanced.
- Theorem 1 Assuming that the comprehensive disturbance is bounded:
- ⁇ (j 1, 2, 3), then if and only when z j >0 and ⁇ j >0, the EAC-PI controller (9)
- the composed closed-loop control system is globally robust and stable, and the EAC-PI controller has good anti-disturbance robustness.
- the error system (11) is a dynamic system under the excitation of bounded disturbance
- the initial state Take the unilateral Laplace transform for the error dynamic system (11), then:
- the organized closed-loop control system is:
- the first term of the closed-loop control system (13) is a zero-input response
- the second term is a zero-state response.
- the system transfer function is:
- k 1 0.5( ⁇ j - ⁇ j )/ ⁇ j
- k 2 -0.5( ⁇ j + ⁇ j )/ ⁇ j .
- Theorem 1 shows that when z j >0 and ⁇ j >0, the gain tuning rule of formula (10) can ensure the global stability of the closed-loop control system composed of EAC-PI controller (9). Therefore, z j has Large setting margin.
- EAC-PI cooperative controller In order to make the EAC-PI cooperative controller have a fast response speed and strong anti-disturbance ability, it is required that the larger z j is, the better. However, if z j is too large, it may cause overshoot and oscillation due to integral saturation. Therefore, it is required to set the speed factor z j of EAC-PI reasonably.
- the specific method is as follows:
- k p> 0 is a non-independent property proportional gain
- T i is the integral time constant independent PI controllers.
- z j is the reciprocal of T i, i.e., z j dimension is / sec, so called speed factor.
- T i the time scale of the controlled object
- the speed factor z j of the EAC-PI controller is required to be larger, otherwise the opposite is true.
- the speed factor z j is not only the internal core coupling factor of the EAC-PI controller (9) and the equivalent conversion factor of the EAC-PI controller gain tuning rule (10), but also the scale ⁇ reflecting the speed of the controlled object.
- a definite external connection (21) is established. Therefore, the value range of the speed factor z j can be set according to the speed characteristics of the controlled object.
- u jm > 0 is the maximum amplitude of the control input of the j-th channel.
- Integral link control force limit
- the influence of factors such as the flight environment may cause problems such as uncertain aerodynamic parameters and failure of the actuator.
- problems such as uncertain aerodynamic parameters and failure of the actuator.
- n a (1-k n ) n between the expected overload coefficient n and the actual overload coefficient n a
- FIG. 8-13 show that when the UAV has uncertain parameters and actuator failures, the EAC-PI control method of the present invention not only still has fast response speed and high control accuracy, but also has good robustness and stability. It further shows that the strong autocoupling PI control method for large and small UAVs of the present invention is a globally stable and strong anti-disturbance control method.
- PID controllers, SMC and ADRC based on cybernetic strategies are currently the three mainstream controllers widely used in the field of control engineering, the limitations of traditional PID controllers are also very obvious.
- various improved PID controllers such as adaptive PID controller, nonlinear PID controller, parameter self-learning nonlinear PID controller, fuzzy PID controller, optimal PID controller, neuron PID controller, expert PID controllers have overcome the parameter tuning problems of traditional PID controllers to a large extent, and have certain non-linear control capabilities.
- the existing improved PID controllers have a large amount of calculation, and have poor real-time performance and resistance.
- the calculation amount of gain parameters and related nonlinear functions is too large, the control system structure is more complicated, and the stability of the control system cannot be analyzed theoretically.
- a strong auto-coupling proportional-integral (EAC-PI) control method of the present invention concentrates the respective advantages of the three mainstream controllers and eliminates their respective limitations, namely: It has the advantages of simple PID structure, good robust stability of SMC, and strong anti-disturbance ability of ADRC; it not only effectively avoids the difficulty of PID gain tuning, but also effectively solves the high frequency chattering and chattering of SMC. The problem of irreconcilability between anti-disturbance capabilities also effectively avoids the problems of too many ADRC gain parameters and too much calculation.
- the invention of the EAC-PI control method has enriched the control theory system for more than half a century, and has provided an effective technical guarantee for the technical upgrade of various PID controllers in operation.
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Abstract
无人机UAV系统是一类输入受限的非仿射非线性强耦合多输入多输出(MIMO)复杂系统，为了解决该复杂系统的控制难题，本发明提出了一种大型无人机UAV的强自耦PI协同控制方法。本发明的控制方法将UAV动态和内外不确定性定义为总和扰动，从而将非仿射非线性强耦合的MIMO复杂系统变换为不确定的MIMO线性系统，进而构建了总和扰动激励下的误差动态系统，据此通过与被控对象模型无关的速度因子和增强因子为核心耦合因子设计了强自耦PI(EAC-PI)协同控制器模型，理论分析与仿真结果都表明了EAC-PI协同控制系统具有良好的全局鲁棒稳定性，有效解决了PID的整定难题，本发明在飞行器控制领域具有广泛的应用前景。
Description
本发明涉及飞行器控制领域技术领域，尤其涉及一种大型无人机(Unmanned Aerial Vehicle,UAV)的强自耦PI(Enhanced Auto-Coupling Proportional-Integral，EAC-PI)协同控制方法。
近半个多世纪以来，基于频域设计方法的经典控制(控制论)与基于时域设计方法的现代控制(模型论)独立发展，形成了各自的方法论体系。在实际控制工程中，控制目标与被控对象实际行为之间的误差是容易获取的，也是能够适当加以处理的，因而“基于误差来消除误差”的控制策略的原形，即PID(Proportional-Integral-Derivative，PID)控制器在工业控制领域获得了广泛应用。对于实际控制工程问题，由于通常很难给出其“内部机理的描述”，因而基于数学模型的现代控制理论给出的控制策略，在实际控制工程中很难得到有效应用。这就是控制工程实践与控制理论之间延续了半个多世纪而未能得到很好解决的脱节现象。经典控制理论的精髓是根据实际值与控制目标的偏差来产生控制策略，只要合理选择PID增益使闭环系统稳定就能达到控制目标，这是其被广泛采用的原因。然而，科学技术的发展对控制器的精度、速度和鲁棒性提出了更高的要求，PID控制的缺点逐渐显露出来：尽管PID控制能够保证系统稳定，但闭环系统动态品质对PID增益变化敏感。这个缺点导致了控制系统中“快速性”和“超调”之间不可调和的矛盾，因此，当系统运行工况改变时，控制器增益也需要随之变化，而这也是各种改进型PID控制方法如自适应PID、非线性PID、神经元PID、智能PID、模糊PID、专家系统PID等的原始动机。尽管各种改进型PID能够通过在线优化整定控制器增益参数来提高系统的自适应控制能力，然而，针对非仿射非线性不确定系统的控制问题，现有各类PID控制仍然无能为力，特别是抗扰动鲁棒性较差。
由于大型无人机(Unmanned Aerial Vehicle,UAV)是一类典型的多输入多输出且输入受限的非仿射非线性强耦合不确定系统,针对该类复杂系统的控制,传统PID及其各类改进型PID控制方法都显得无能为力,而现有的控制方法主要有：二阶非奇异动态terminal滑模控制方法，基于小脑模型(CMAC)干扰观测器的二阶非奇异terminal滑模控制方法以及基于小波小脑模型(WCMAC)干扰观测器的二阶非奇异terminal滑模控制方法。然而，当UAV存在参数摄动和执行器故障时，二阶非奇异动态terminal滑模控制方法失控；基于CMAC的二阶非奇异terminal滑模控制方法以及基于WCMAC的二阶非奇异terminal滑模控制方法都是利用CMAC或WCMAC对UAV的内外不确定性进行干扰估计，然而，这两种方法的计算量较大，实时性欠佳。
发明内容
本发明的目的在于针对背景技术中的缺陷，提出一种大型无人机UAV的强自耦PI协同控制方法，通过一种模型结构简单、参数整定容易、动态品质好、控制精度高、抗扰动能力强的控制方法，有效改善UAV控制系统的动态品质与稳态性能、减小计算量、提高实时性、增强控制系统的稳定性。
为达此目的，本发明采用以下技术方案：
一种大型无人机UAV的强自耦PI协同控制方法，具体步骤如下：
步骤A：测量获取无人机UAV的期望轨迹y
dj、微分信号
和UAV的实际输出y
j，并以此建立其跟踪误差e
j和跟踪误差的积分e
j0；
包括使用如下计算公式分别建立跟踪误差和跟踪误差的积分：
其中，e
j表示跟踪误差；e
j0表示跟踪误差的积分，j＝1,2,3是UAV的通道序号。
优选的，步骤B：根据步骤A获得无人机UAV的跟踪误差e
j，根据跟踪误差e
j、跟踪误差的积分e
j0和期望轨迹的微分信号
创建EAC-PI协同控制律u
j，具体包括使用如下公式获取EAC-PI的协同控制律：
其中，z
j表示UAV第j通道EAC-PI控制器的速度因子，z
j＞0；
λ
j表示UAV第j通道EAC-PI控制器的无量纲的增强因子，λ
j＞0；
b
j表示第j通道的控制增益，且b
1＝g/M,b
2＝1,b
3＝1；
u
j表示第j通道EAC-PI协同控制器的输出协同控制力。
优选的，步骤C：根据步骤B建立的UAV第j通道EAC-PI协同控制律模型，并通过对第j通道的积分控制力
和协同控制力u
j分别进行限幅处理，避免动态过程中的积分饱和现象，并满足输入受限系统的要求；
根据EAC-PI控制器模型控制无人机，具体包括使用如下公式进行限幅处理：
|u
jI|≤0.5u
jm，|u
j|≤u
jm
其中，u
jm表示第j通道协同控制输入的最大幅值，u
jm＞0。
与现有三大主流控制器相比，本发明的一种强自耦比例-积分(EAC-PI)控制方法集中了三大主流控制器的各自优势并消除了其各自的局限性，即：既具备PID结构简单的优势，又具备SMC良好的鲁棒稳定性优势，还具备ADRC抗扰动能力强的优势；既有效避免了PID增益整定困难的问题，又有效解决了SMC在高频抖振与抗扰动能力之间不可调和的难题，还有效避免了ADRC增益参数过多、计算量过大的难题。EAC-PI控制方法的发明丰富了半个多世纪以来的控制理论体系，为现有运行中的各类PID控制器的技术升级提供了有效的技术保障。本发明在非仿射非线性不确定控制系统以及飞行器控制领域具有广泛的应用前景。
图1是本发明的基于EAC-PI控制器的无人机UAV控制系统框架图；
图2是本发明的标称UAV系统跟踪控制结果中的空速跟踪轨迹图；
图3是本发明的标称UAV系统跟踪控制结果中的航迹倾斜角跟踪轨迹图；
图4是本发明的标称UAV系统跟踪控制结果中的航迹方位角跟踪轨迹图；
图5图是本发明的标称UAV系统跟踪控制结果中的UAV系统推力控制输入图；
图6是本发明的标称UAV系统跟踪控制结果中的UAV系统过载系数控制输入图；
图7是本发明的标称UAV系统跟踪控制结果中的UAV系统滚转角控制输入图；
图8是本发明的受扰UAV系统跟踪控制结果中的空速跟踪轨迹图；
图9是本发明的受扰UAV系统跟踪控制结果中的航迹倾斜角跟踪轨迹图；
图10是本发明的受扰UAV系统跟踪控制结果中的航迹方位角跟踪轨迹图；
图11是本发明的受扰UAV系统跟踪控制结果中的UAV系统推力控制输入图；
图12是本发明的受扰UAV系统跟踪控制结果中的UAV系统过载系数控制输入图；
图13是本发明的受扰UAV系统跟踪控制结果中的UAV系统滚转角控制输入图。
下面结合附图并通过具体实施方式来进一步说明本发明的技术方案。
1、从非仿射非线性不确定系统到反射线性不确定系统的映射思路
考虑无人机(UAV)系统：
其中：V、γ和χ分别是UAV的空速、航迹倾斜角和航迹方位角；T、n、μ分别为发动机推力、过载系数和滚转角；g为重力加速度；M为UAV的质量；D为阻力，且表示为：
其中，公式(2)的参数详细如表一所示：
表1 UAV基本参数
同时，还要考虑到UAV实际飞行安全要求，即滚转角μ应满足：|μ|≤90°；过载系数n应避免失速风险，n＜0.5ρV
2SC
Lmax/M。
为了便于分析，定义：y
1＝V，y
2＝γ，y
3＝χ，u
1＝T，u
2＝n，u
3＝μ。将公式(2)代入公式(1)，则有UAV系统如下：
其中，
c
12＝2kMg/(ρS)。
由UAV系统(3)可知，UAV是一个三输入三输出的非仿射非线性强耦合系统，针对该复杂系统的控制，本发明首先将每个通道的非仿射非线性不确定动态分别定义为三个总和扰动，即：
则UAV系统(3)简化为：
其中，b
j≠0是线性不确定系统(4)第j通道的控制增益，且b
1＝g/M，b
2＝1，b
3＝1。
显然，系统(4)是一个与UAV系统(3)完全等价的三输入三输出线性不确定系统，对系统(4)的控制等价于对UAV系统(3)的控制。只要总和扰动有界，即：|d
j|＜∞(j＝1,2,3)，那么，MIMO非仿射非线性不确定系统都可以表示为MIMO线性不确定系统(4)的形式，具有普遍意义。不仅如此，通过总和扰动定义，将一切已知或未知的不确定因素用总和扰动来表示，将 非仿射非线性不确定系统转换为线性不确定系统的思想，完全淡化了线性与非线性、确定与不确定性、时变与时不变性、仿射与非仿射等系统分类的概念，因而有效解决了半个多世纪以来控制论和模型论两大控制思想体系针对不同类型的被控系统如何施加有效控制方法遇到的各种难题，使任意复杂的非线性系统都转换为线性不确定系统，因而可以统一任意复杂非线性系统的控制方法。
如何对式(3)或式(4)所述的UAV系统施加有效控制，正是本发明的核心技术，即EAC-PI协同控制技术。
2、EAC-PI协同控制器设计
针对UAV系统(4)的控制问题，设第j通道(j＝1,2,3)的期望轨迹为y
dj，并定义跟踪控制误差为：
e
j＝y
dj-y
j (5)
且
则有
其中，b
1＝g/M，b
2＝1，b
3＝1。
根据公式(6)和(7)可建立第j通道的误差动态系统如下：
显然，误差系统(8)是一个二阶误差动态系统(Error Dynamics System,EDS)，为了使EDS稳定，定义EAC-PI协同控制律u
j为：
其中，z
j＞0和λ
j＞0是UAV系统第j通道EAC-PI控制器的速度因子和无量纲的增强因子，b
j是UAV第j通道的控制增益，且b
1＝g/M，b
2＝1，b
3＝1；
是第j通道的期望轨迹的微分，u
j既是第j通道EAC-PI协同控制器输出协同控制力，又是第j通道被控对象的协同控制力输入。
与传统PI控制器模型：u＝k
pe
j+k
pe
j0相比，可得EAC-PI控制器的增益整定规则：
由整定规则(10)可知，速度因子不仅是EAC-PI控制器中两个增益k
p和k
i之间的重要联系 因子，而且也是k
p和k
i的当量转换因子。此外，增强因子的主要作用是调整比例环节的控制力，当0＜λ
j＜1时,降低比例环节的控制力作用，否则，增强比例环节的控制力作用。
3、闭环控制系统稳定性分析
定理1：假设综合扰动有界：|d
j|＜∞(j＝1,2,3)，则当且仅当z
j＞0、λ
j＞0时，由EAC-PI控制器(9)组成的闭环控制系统是全局鲁棒稳定的，而且EAC-PI控制器具有良好的抗扰动鲁棒性。
证明：
(1)稳定性分析
将EAC-PI控制器(9)带入公式(8)所示的误差动态系统(EDS)，则有：
显然，误差系统(11)是一个在有界扰动|d
j|＜∞激励下的动态系统。考虑到初始状态:
对误差动态系统(11)取单边拉普拉斯变换，则有:
整理得闭环控制系统为：
显然，闭环控制系统(13)的第一项是零输入响应，第二项是零状态响应。其系统传输函数为：
由于系统(14)的特征根为
因此，当z
j＞0、0＜λ
j＜1时，系统(14)在左半复平面存在一对共轭复根：
因而误差系统(11)或(13)是一致稳定的；当z
j＞0、λ
j＝1时，系统(14)在左半复平面的实轴上存在一个重实根：s
1,2＝-λ
jz
j，因而误差系统(11)或(13)是逐渐稳定的；z
j＞0、λ
j＞1时，系统(14)在左半复平面的实轴上存在两个实根：
因而，误差系统(11)或(13)也是逐渐稳定的，总之，只要z
j＞0、λ
j＞0，系统误差(11)或(13)总是稳定的，由于系统的稳定性与被控对象的模型无关，因而全局是稳定的。
(2)、抗扰动鲁棒性分析
①当z
j＞0、0＜λ
j＜1时，系统(14)的单位冲激响应为：
其中，
显然，有：
②当z
j＞0、λ
j＝1时，系统(14)的单位冲激响应为：
显然也有：
③当z
j＞0、λ
j＞1时，系统(14)的单位冲激响应为：
其中,
k
1＝0.5(λ
j-ξ
j)/ξ
j，k
2＝-0.5(λ
j+ξ
j)/ξ
j。
显然也有：
总之，只要z
j＞0、λ
j＞0，则必有：
由于
因此，有：
由于z
j＞0、λ
j＞0时，
因此，只要总和扰动有界：|d
j|＜∞(j＝1,2,3)，则必有
成立，即MIMO被控系统第j通道的跟踪误差e
j(t)可以从任意不为零的初始状态
一致趋近稳定的平衡点零点，可以实现精确控制。
上述理论分析表明，当z
j＞0、λ
j＞0时，由AC-PI控制器组成的闭环控制系统是全局鲁棒稳定的；只要总和扰动有界：|d
j|＜∞，则MIMO被控系统第j通道的跟踪误差e
j(t)可以从任意不为零的初始状态渐近趋近稳定的平衡点零点。由于e
j(t)从任意不为零的初始状态趋近稳定的平衡点零点只与|d
j|＜∞有关，而与总和扰动d
j的具体模型无关，因此，EAC-PI协同控制器具有良好的抗扰动鲁棒性。
4、速度因子整定方法
定理1表明：当z
j＞0、λ
j＞0时，公式(10)的增益整定规则可以保证由EAC-PI控制器 (9)组成的闭环控制系统的全局稳定性，因而，z
j具有很大的整定裕度。为了使EAC-PI协同控制器具有快的响应速度和强的抗扰动能力，则要求z
j越大越好。但是，z
j太大很可能会因积分饱和引起超调和振荡现象，因此，要求合理整定EAC-PI的速度因子z
j，具体方法如下：
由传统PI控制器可知，比例增益k
p与积分增益k
i的关系为：
k
i＝k
p/T
i (19)
其中，k
p＞0是一个无属性的独立比例增益，T
i是PI控制器的独立积分时间常数。
正因为k
p是一个无物理属性的独立变量，T
i是一个独立时间变量，因而，积分增益k
i＝k
p/T
i也是一个无物理属性的独立变量，因此，k
p与k
i之间的表面关系k
i＝k
p/T
i实际上是无约束力的松散关系。
此外，k
p究竟具有什么物理属性？k
p和T
i是否存在内在必然关系？k
p和T
i与被控对象的什么特性有关？这三个问题是近百年来国内外学者一直忽视的三个关键科学问题，因而也是引起PI控制器的整定难题。为了有效解决这些关键科学问题，本发明根据EAC-PI控制器的整定规则(10)以及传统PI控制器的增益关系：k
i＝k
p/T
i，得到了一个重要的理论结果：
z
j＝2λ
j/T
i (20)
显然，z
j是T
i的倒数，即z
j的量纲是/秒，因而称其为速度因子。T
i越小，z
j则越大，否则反之。如果将积分时间常数T
i近似作为被控对象的时间尺度τ，即T
i≈τ，则有：
z
j≈2λ
j/τ (21)
由式(21)可知，时间尺度τ越小，表明被控对象的动态特性越快，因此要求EAC-PI控制器的速度因子z
j也越大，否则反之。显然，速度因子z
j不仅是EAC-PI控制器(9)的内在核心耦合因子和EAC-PI控制器增益整定规则(10)的当量换算因子，而且还与反映被控对象快慢的间尺度τ建立了确定的外在联系(21)，因此，完全可以根据被控对象的快慢特性来整定速度因子z
j的取值范围。
5、协同控制力的限幅处理方法
由于实际物理系统的执行机构往往存在饱和现象，当控制饱和发生时，系统的跟踪性能下降，甚至会引起系统失控，因此，必须对控制力进行限幅处理。考虑到积分饱和是引起控制力饱和的主要原因，因此，首先考虑对积分环节控制力进行限幅处理，再考虑对EAC-PI的控制力u
j进行限幅处理，即：为了有效避免动态过程中的积分饱和现象并考虑到输入受限的系统，对第j通道的积分环节控制力：u
jI＝z
2
je
j0/b
j和控制力u
j分别进行限幅处理：
|u
jI|≤0.5u
jm，|u
j|≤u
jm
其中，u
jm＞0是第j通道控制输入的最大幅值。
基于EAC-PI控制器的无人机UAV控制系统框图如图1。
6、本发明的一种大型无人机UAV的EAC-PI协同控制方法的性能测试与分析
为了验证本发明一种EAC-PI控制方法的有效性，针对某大型无人机UAV系统(1)或(3)的控制问题进行下列仿真实验，UAV系统(1)或(3)的相关参数参见表1，UAV初始条件如下：
V(0)＝90m/s，γ(0)＝χ(0)＝0°，T(0)＝1kN，n(0)＝1，μ(0)＝0°
设期望轨迹为：
三个EAC-PI控制器相关仿真条件设置如下：
速度因子：z
1＝40，z
2＝400，z
3＝40；
增强因子：λ
1＝10，λ
2＝20，λ
3＝20；
积分环节控制力限幅：|u
1I|≤0.5T
max，|u
2I|≤0.5n
max，|u
3I|≤0.01π；
控制力限幅：|u
1|≤T
max，|u
2|≤n
max，|u
3|≤0.45π；
控制通道增益：b
1＝g/M，b
2＝1，b
3＝1。
下面分两种情况进行仿真验证：一是标称UAV系统，即UAV模型精确已知的情况；二是受扰UAV系统，即UAV模型存在气动参数不确定和执行器故障情况。
仿真实验1：标称UAV系统跟踪控制实验
针对系统(1)或(3)所示的MIMO受控对象UAV系统进行指令跟踪控制实验，使用本发明的EAC-PI控制方法，仿真结果如图2-图7。图2-图7表明，基于EAC-PI控制器的UAV控制系统不仅具有很快的响应速度和很高的控制精度，而且具有良好的鲁棒稳定性，因而是一种有效的控制方法。
仿真实验2：受扰UAV系统跟踪控制实验
当UAV执行飞行任务时，飞行环境等因素的影响可能导致气动参数不确定以及执行器失效等问题。其中，如果UAV因战斗受损或执行器引起故障，则期望过载系数n与实际过载系数n
a之间有n
a＝(1-k
n)n，且k
n为过载失效系数，满足0≤k
n<1；如果UAV没有发生故障，则k
n＝0。因此，下面设受扰UAV系统相关参数如下：
设在UAV飞行过程中，k
n＝0.25，气动参数C
D0和k存在-30％不确定，即
Δk＝-0.3k，并考虑发动机最大推力也降低30％的情况下，即ΔT
max＝-0.3T
max。
在上述飞行条件下，三个EAC-PI协同控制器的相关参数与标称UAV系统的完全相同，仿真结果如图8-图13。图8-图13表明，当UAV存在参数不确定和执行器故障时，本发明的EAC-PI控制方法不仅仍然具有很快的响应速度和很高的控制精度，而且还具有良好的鲁棒稳定性，进一步表明了本发明一种大小无人机的强自耦PI控制方法是一种全局稳定的强抗扰控制方法。
7、结论
尽管基于控制论策略的PID控制器、SMC以及ADRC是目前控制工程领域广泛使用的三大主流控制器，然而，传统PID控制器的局限性也十分明显，其一是增益参数要求随工况状态的变化而变化，因而存在参数整定的困难；其二是较差的非线性控制能力；其三是较弱的抗扰动能力。尽管各种改进型的PID控制器，如自适应PID控制器、非线性PID控制器、参数自学习非线性PID控制器、模糊PID控制器、最优PID控制器、神经元PID控制器、专家PID控制器等在很大程度上克服了传统PID控制器的参数整定问题，并具备一定的非线性控制能力，然而，现有改进型PID控制器的计算量大，存在实时性欠佳和抗扰动能力较差的局限性；SMC尽管鲁棒稳定性能好，然而，在高频抖振与抗扰动能力之间存在不可调和的矛盾；ADRC尽管鲁棒稳定性能好，然而，却存在过多的增益参数，相关非线性函数的计算量过大，控制系统结构较复杂，而且无法从理论上分析控制系统的稳定性。
与现有三大主流控制器相比，本发明的一种强自耦比例-积分(EAC-PI)控制方法集中了三大主流控制器的各自优势并消除了其各自的局限性，即：既具备PID结构简单的优势，又具备SMC良好的鲁棒稳定性优势，还具备ADRC抗扰动能力强的优势；既有效避免了PID增益整定困难的问题，又有效解决了SMC在高频抖振与抗扰动能力之间不可调和的难题，还有效避免了ADRC增益参数过多、计算量过大的难题。EAC-PI控制方法的发明丰富了半个多世纪以来的控制理论体系，为现有运行中的各类PID控制器的技术升级提供了有效的技术保障。
以上结合具体实施例描述了本发明的技术原理。这些描述只是为了解释本发明的原理，而不能以任何方式解释为对本发明保护范围的限制。基于此处的解释，本领域的技术人员不需要付出创造性的劳动即可联想到本发明的其它具体实施方式，这些方式都将落入本发明的保护范围之内。
Claims (3)
- 一种大型无人机UAV的强自耦PI协同控制方法，其特征在于：具体步骤如下：步骤A：测量获取无人机UAV的期望轨迹y dj、微分信号和UAV的实际输出y j，并以此建立其跟踪误差e j和跟踪误差的积分e j0；
包括使用如下计算公式分别建立跟踪误差和跟踪误差的积分：
其中，e j表示跟踪误差；e j0表示跟踪误差的积分，j＝1,2,3是UAV的通道序号。 - 根据权利要求1所述一种大型无人机UAV的强自耦PI协同控制方法，其特征在于：步骤B：根据步骤A获得无人机UAV的跟踪误差e j，根据跟踪误差e j、跟踪误差的积分e j0和期望轨迹的微分信号创建EAC-PI协同控制律u j，具体包括使用如下公式获取EAC-PI的协同控制律：
其中，z j表示UAV第j通道EAC-PI控制器的速度因子，z j＞0；λ j表示UAV第j通道EAC-PI控制器的无量纲的增强因子，λ j＞0；b j表示第j通道的控制增益，且b 1＝g/M,b 2＝1,b 3＝1；u j表示第j通道EAC-PI协同控制器的输出协同控制力。 - 根据权利要求2所述一种大型无人机UAV的强自耦PI协同控制方法，其特征在于：步骤C：根据步骤B建立的UAV第j通道EAC-PI协同控制律模型，并通过对第j通道的积分控制力和协同控制力u j分别进行限幅处理，避免动态过程中的积分饱和现象，并满足输入受限系统的要求；
根据EAC-PI控制器模型控制无人机，具体包括使用如下公式进行限幅处理：|u jI|≤0.5u jm，|u j|≤u jm其中，u jm表示第j通道协同控制输入的最大幅值，u jm＞0。
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| CN105137999A (zh) * | 2015-07-23 | 2015-12-09 | 北京航空航天大学 | 一种具有输入饱和的飞行器跟踪控制直接法 |
| CN108845491A (zh) * | 2018-07-02 | 2018-11-20 | 曾喆昭 | 大时滞系统的智慧pi复合控制方法 |
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