WO2023236786A1 - 用于叉车稳定控制的静态输出反馈控制方法及存储介质 - Google Patents

用于叉车稳定控制的静态输出反馈控制方法及存储介质 Download PDF

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WO2023236786A1
WO2023236786A1 PCT/CN2023/096459 CN2023096459W WO2023236786A1 WO 2023236786 A1 WO2023236786 A1 WO 2023236786A1 CN 2023096459 W CN2023096459 W CN 2023096459W WO 2023236786 A1 WO2023236786 A1 WO 2023236786A1
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forklift
fault
observer
output feedback
control method
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PCT/CN2023/096459
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English (en)
French (fr)
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王平
毕胜
张冬林
师学银
郑小东
夏光
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安徽合力股份有限公司
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Priority to EP23818951.8A priority Critical patent/EP4394537A1/en
Publication of WO2023236786A1 publication Critical patent/WO2023236786A1/zh

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    • G—PHYSICS
    • G05—CONTROLLING; REGULATING
    • G05B—CONTROL OR REGULATING SYSTEMS IN GENERAL; FUNCTIONAL ELEMENTS OF SUCH SYSTEMS; MONITORING OR TESTING ARRANGEMENTS FOR SUCH SYSTEMS OR ELEMENTS
    • G05B23/00—Testing or monitoring of control systems or parts thereof
    • G05B23/02—Electric testing or monitoring
    • G05B23/0205—Electric testing or monitoring by means of a monitoring system capable of detecting and responding to faults
    • G05B23/0218—Electric testing or monitoring by means of a monitoring system capable of detecting and responding to faults characterised by the fault detection method dealing with either existing or incipient faults
    • G05B23/0243—Electric testing or monitoring by means of a monitoring system capable of detecting and responding to faults characterised by the fault detection method dealing with either existing or incipient faults model based detection method, e.g. first-principles knowledge model
    • G—PHYSICS
    • G05—CONTROLLING; REGULATING
    • G05B—CONTROL OR REGULATING SYSTEMS IN GENERAL; FUNCTIONAL ELEMENTS OF SUCH SYSTEMS; MONITORING OR TESTING ARRANGEMENTS FOR SUCH SYSTEMS OR ELEMENTS
    • G05B23/00—Testing or monitoring of control systems or parts thereof
    • G05B23/02—Electric testing or monitoring
    • G05B23/0205—Electric testing or monitoring by means of a monitoring system capable of detecting and responding to faults
    • G05B23/0218—Electric testing or monitoring by means of a monitoring system capable of detecting and responding to faults characterised by the fault detection method dealing with either existing or incipient faults
    • G05B23/0224—Process history based detection method, e.g. whereby history implies the availability of large amounts of data
    • G05B23/024—Quantitative history assessment, e.g. mathematical relationships between available data; Functions therefor; Principal component analysis [PCA]; Partial least square [PLS]; Statistical classifiers, e.g. Bayesian networks, linear regression or correlation analysis; Neural networks
    • B—PERFORMING OPERATIONS; TRANSPORTING
    • B66—HOISTING; LIFTING; HAULING
    • B66F—HOISTING, LIFTING, HAULING OR PUSHING, NOT OTHERWISE PROVIDED FOR, e.g. DEVICES WHICH APPLY A LIFTING OR PUSHING FORCE DIRECTLY TO THE SURFACE OF A LOAD
    • B66F17/00—Safety devices, e.g. for limiting or indicating lifting force
    • B66F17/003—Safety devices, e.g. for limiting or indicating lifting force for fork-lift trucks
    • G—PHYSICS
    • G05—CONTROLLING; REGULATING
    • G05B—CONTROL OR REGULATING SYSTEMS IN GENERAL; FUNCTIONAL ELEMENTS OF SUCH SYSTEMS; MONITORING OR TESTING ARRANGEMENTS FOR SUCH SYSTEMS OR ELEMENTS
    • G05B13/00—Adaptive control systems, i.e. systems automatically adjusting themselves to have a performance which is optimum according to some preassigned criterion
    • G05B13/02—Adaptive control systems, i.e. systems automatically adjusting themselves to have a performance which is optimum according to some preassigned criterion electric
    • G05B13/04—Adaptive control systems, i.e. systems automatically adjusting themselves to have a performance which is optimum according to some preassigned criterion electric involving the use of models or simulators
    • G—PHYSICS
    • G05—CONTROLLING; REGULATING
    • G05B—CONTROL OR REGULATING SYSTEMS IN GENERAL; FUNCTIONAL ELEMENTS OF SUCH SYSTEMS; MONITORING OR TESTING ARRANGEMENTS FOR SUCH SYSTEMS OR ELEMENTS
    • G05B19/00—Programme-control systems
    • G05B19/02—Programme-control systems electric
    • G05B19/04—Programme control other than numerical control, i.e. in sequence controllers or logic controllers
    • G05B19/042—Programme control other than numerical control, i.e. in sequence controllers or logic controllers using digital processors
    • G05B19/0428—Safety, monitoring
    • G—PHYSICS
    • G05—CONTROLLING; REGULATING
    • G05B—CONTROL OR REGULATING SYSTEMS IN GENERAL; FUNCTIONAL ELEMENTS OF SUCH SYSTEMS; MONITORING OR TESTING ARRANGEMENTS FOR SUCH SYSTEMS OR ELEMENTS
    • G05B2219/00—Program-control systems
    • G05B2219/20—Pc systems
    • G05B2219/24—Pc safety
    • G05B2219/24065—Real time diagnostics

Definitions

  • the invention relates to the field of vehicle safety control, and in particular to a static output feedback control method and storage medium for forklift stability control.
  • the present invention proposes a static output feedback control method and storage medium for forklift stability control, which can solve the above technical defects.
  • a static output feedback control method for forklift stability control including the following steps:
  • x(t) represents the state vector at time t;
  • f(t) ⁇ R s is the sensor fault vector;
  • d(t) ⁇ R nd is the unknown bounded disturbance vector;
  • matrices B d and D f is of appropriate dimensionality, and D f is assumed to be full column rank;
  • a residual signal L 2 is generated that is as sensitive to the fault f(t) as possible and insensitive to the disturbance d(t);
  • v(t) ⁇ R n+p is the auxiliary state vector of the observer; is the estimator of x(t); are unmeasurable premise variables; Si , E, and L are observer gains.
  • Equation (1-5) to design the control law of the reconfigured static output feedback controller:
  • the present invention also discloses a computer-readable storage medium that stores a computer program.
  • the computer program When executed by a processor, the computer program causes the processor to perform the steps of the above method.
  • the static output feedback control method and storage medium for forklift stability control of the present invention are expected to improve the fault tolerance of the counterbalanced forklift anti-rollover system, thereby ensuring the stability of the forklift anti-rollover system.
  • the purpose of improving the active safety of forklifts Specifically, when a sensor fails, the proposed state observer can estimate the sensor output signal and fault status, and the fault signal can be accurately received, and the output signal can be compensated and output in time according to the static output feedback control method. Then the system is subject to sensor failure The impact is minimal, ensuring the effectiveness of most functions of the controller.
  • Figure 1 is a diagram of the sensor fault-tolerant control system of the forklift anti-rollover system
  • Figure 2 is the fault fa signal and its estimated value signal diagram
  • Figure 3 is the fault fb signal and its estimated value signal diagram
  • Figure 4 is a fault-tolerant control input state diagram of static output feedback
  • Figure 5 shows the side slip angle of the forklift body and its estimated value when there is no fault tolerance
  • Figure 6 shows the forklift body yaw angular velocity and its estimated value without fault tolerance
  • Figure 7 shows the side slip angle of the forklift body and its estimated value under fault-tolerant control
  • Figure 8 shows the forklift body yaw angular velocity and its estimated value under fault-tolerant control.
  • the static output feedback control method for forklift stability control described in this embodiment includes setting a continuous-time fuzzy system model, a singular observer, a generalized observer, a residual generator, and static output feedback control device; specifically, it includes the following steps:
  • x(t) represents the state vector at time t;
  • f(t) ⁇ R s is the sensor fault vector;
  • d(t) ⁇ R nd is Unknown bounded perturbation vector;
  • matrices B d and D f have appropriate dimensions, and D f is assumed to be full column rank;
  • a residual signal L 2 is generated that is as sensitive to the fault f(t) as possible and insensitive to the disturbance d(t);
  • Step 11 When the forklift tire tilts, the tire itself will also deform. Similarly, when the forklift turns at high speed, the deformation of the forklift tire will also become larger, which will lead to a larger side slip angle of the tire. Because the forklift tire Not all force characteristic curves are approximately linear. Therefore, the present invention adopts a typical nonlinear tire model in vehicle research, which is more common in vehicle stability research, that is, the magic formula model. Therefore, the lateral forces F yf and F yr of the front and rear tires can be expressed as:
  • ⁇ f and ⁇ r are the slip angles of the front and rear tires of the forklift respectively.
  • Step 12 Based on the TS fuzzy model, for the estimation of the nonlinear characteristics of the front lateral force, the sliding area M 1 is used; for the estimation of the nonlinear characteristics of the rear lateral force, the sliding area M 2 is used; if
  • Step 13 The lateral force of the front and rear tires of the forklift is expressed as follows:
  • the overall forklift anti-rollover TS fuzzy model is as follows:
  • Step 15 An extended description system can be constructed for the counterbalanced forklift anti-rollover sensor failure system:
  • v(t) ⁇ R n+p is the auxiliary state vector of the singular observer of the system, is the above extension Describe the estimator of x(t) in the system. is an unmeasured premise variable, which depends partially or completely on the estimated state x(t). Now simplify the design of the observer to find the gains Si , E and L such that the state and fault error estimates conform to a stable generating system. In the above singular observer, the differential term of y(t) does not exist, so this kind of observer is easier to implement in practical engineering.
  • the generalized observer The norm is defined as:
  • the design task of the generalized observer is to generate a residual signal that is as sensitive to faults as possible and insensitive to disturbances, thereby making fault diagnosis robust.
  • the problem caused by residuals can be solved by Control to study (extend the H ⁇ control problem to nonlinear situations).
  • the residual signal generator is designed as follows:
  • Step 41 Minimize the interference signal r d (t) to the residual signal gain to design:
  • Theorem 1 If the positive definite symmetric matrices P 11 , P 12 , exists, as well as matrices N 1 , N 2 and a positive scalar ⁇ , then the state observer (1-2) can estimate the system state as well as sensor faults and minimize the scalar ⁇ under the following LMI constraints (see (2-8)).
  • Step 42 Obtain the observer gain through the following method:
  • Step 43 Give the attenuation level of the external interference signal residual:
  • the sensor estimate can be obtained through the above method while ensuring the integrity of the fault estimate.
  • a static output feedback controller is designed to target sensor faults and external interference.
  • the observer provides fault and state estimates, therefore, the corresponding control laws must be reallocated. Linear matrix inequalities will give sufficient conditions to ensure the stability of the closed system they produce.
  • the static output feedback controller is designed as follows:
  • Step 51 Based on parallel distributed compensation, the control law of static output feedback is designed as follows:
  • K i is the output feedback gain to be determined in the i-th local model
  • y c (t) represents the compensation output, which is defined as:
  • Step 52 Analyze the stability of the closed-loop system and the system state estimation error. It is generated by combining the above differential equation (2-9) with the following formula:
  • Step 53 Find the corresponding observer and controller to minimize the impact of external disturbance d(t) on the closed-loop system.
  • Lemma 1 Considering two real matrices X, Y and F(t) with appropriate dimensions, for any scalar ⁇ , the following inequality is proved: X T FY+Y T F T X ⁇ X T X+ ⁇ -1 Y T Y, ⁇ >0(2-22)
  • Step 54 Perform stability verification.
  • the above-mentioned effective control strategy is designed so that the forklift anti-rollover system can still ensure the stability of the entire system in the presence of sensor failure.
  • numerical simulations are performed to demonstrate the effectiveness and applicability of the proposed method to a fault-tolerant system for forklift anti-rollover sensors.
  • the T-S model constructed in the previous article is used to construct an observer, which represents a fault-tolerant system of forklift anti-rollover sensors with prerequisite variables that depend on unmeasurable state variables.
  • the vehicle parameters of the forklift considered are shown in Table 1.
  • a gyro sensor For the forklift anti-rollover system, a gyro sensor is used.
  • the gyro sensor can only measure the yaw angular velocity of the forklift.
  • K 1 [-0.0019 0.0020]
  • K 2 [-0.0020 0.0020] (2-44)
  • Figures 2, 3, and 4 respectively show the fault fa signal and its estimated value signal, the fault f b signal and its estimated value signal, and the fault-tolerant control input state of the static output feedback.
  • Figures 5 and 6 respectively show the side slip angle of the forklift body and its estimated value and the yaw angular velocity and its estimated value without fault tolerance.
  • Figures 7 and 8 respectively show the side slip angle of the forklift body and its estimated value and yaw rate under fault tolerance control. Angular velocity and its estimated value.
  • the present invention also discloses a computer-readable storage medium that stores a computer program.
  • the computer program When executed by a processor, the computer program causes the processor to perform the steps of any of the above methods.
  • the present invention also discloses a computer device, including a memory and a processor.
  • the memory stores a computer program.
  • the computer program When executed by the processor, it causes the processor to execute any of the above methods. A step of.
  • a computer program product containing instructions is also provided, which when run on a computer causes the computer to perform the steps of any of the methods in the above embodiments.
  • Non-volatile memory may include read-only memory (ROM), programmable ROM (PROM), electrically programmable ROM (EPROM), electrically erasable programmable ROM (EEPROM), or flash memory.
  • Volatile memory may include random access memory (RAM) or external cache memory.
  • RAM is available in many forms, such as static RAM (SRAM), dynamic RAM (DRAM), synchronous DRAM (SDRAM), double data rate SDRAM (DDRSDRAM), enhanced SDRAM (ESDRAM), synchronous chain Synchlink DRAM (SLDRAM), memory bus (Rambus) direct RAM (RDRAM), direct memory bus dynamic RAM (DRDRAM), and memory bus dynamic RAM (RDRAM), etc.
  • SRAM static RAM
  • DRAM dynamic RAM
  • SDRAM synchronous DRAM
  • DDRSDRAM double data rate SDRAM
  • ESDRAM enhanced SDRAM
  • SLDRAM synchronous chain Synchlink DRAM
  • Rambus direct RAM
  • DRAM direct memory bus dynamic RAM
  • RDRAM memory bus dynamic RAM

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Abstract

本发明公开一种用于叉车稳定控制的静态输出反馈控制方法及存储介质，其控制方法包括设置模糊系统模型、奇异观测器模块、广义观测器模块、残差发生器模块、用于叉车稳定控制的静态输出反馈控制方法模块。奇异观测器同时估计系统的状态和故障；广义观测器用于生成对故障尽可能敏感而对扰动不敏感的残差信号；残差发生器最大程度的减小了系统对扰动的敏感度，同时最大程度的提高了对故障的敏感度；用于叉车稳定控制的静态输出反馈控制方法利用观测器提供的故障和状态等可测信号控制动态系统。本发明能在系统发生故障后，能基于估计状态和故障向量，保证控制定律的重新配置，尽可能的恢复系统故障前的性能，大大提高了叉车横向稳定性和主动安全性。

Description

用于叉车稳定控制的静态输出反馈控制方法及存储介质 技术领域
本发明涉及车辆安全控制领域，具体涉及一种用于叉车稳定控制的静态输出反馈控制方法及存储介质。
背景技术
在叉车的主动安全技术领域，虽然防侧翻系统日益完善，但针对平衡重式叉车的防侧翻系统传感器故障的容错控制技术还未应用。若叉车防侧翻系统发生传感器故障，则系统不能正常的接收到所需要的叉车运行信息，系统便失去了运行过程中的运行状态，同时叉车在行驶过程中的安全性和稳定性不能得到保证。因此，叉车防侧翻系统容错控制必不可少。
发明内容
本发明提出的一种用于叉车稳定控制的静态输出反馈控制方法及存储介质，可解决上述技术缺陷。
为实现上述目的，本发明采用了以下技术方案：
一种用于叉车稳定控制的静态输出反馈控制方法，包括以下步骤：
利用式(1)构建连续时间的叉车防侧翻模糊系统模型：
式(1-1)中x(t)表示t时刻的状态向量；f(t)∈Rs是传感器故障向量；d(t)∈Rnd是未知有界扰动向量；矩阵Bd和Df为具有适当的维数，同时Df假定为满列秩；
通过设置连续时间的模糊系统模型以激励函数ui(ξ(t))为系统的输入，并且同时存在传感器故障和未知有界扰动；
通过设置奇异观测器用于同时估计平衡重式叉车防侧翻模糊系统的状态和输出故障
通过设置广义观测器用于测量连续时间内平衡重式叉车防侧翻系统的状态和故障估计，生成对故障f(t)尽可能敏感而对扰动d(t)不敏感的残差信号L2；
通过设置残差发生器利用残差信号L2控制去将H∞控制问题推广到非线性情形， 观察最小化干扰信号rd(t)得到残差信号L2的增益，找到相应的正定矩阵和正标量，进而渐进估计系统状态和传感器故障；
通过上述观察器提供的故障和状态估计，对控制定律进行重新配置，并通过LMIs形式给出足够的条件以保证所产生的闭环系统的稳定性。
进一步的，所述奇异观测器用于同时估计系统状态和输出故障如下：
式(1-2)中v(t)∈Rn+p是观测器的辅助状态向量；是x(t)的估计量；是不可测前提变量；Si、E、L为观测器增益。
进一步的，利用式(1-3))构建广义观测器H(t)∈L2，L2的范数定义为：
进一步的，利用式(1-4)构建残差发生器rd(t)
进一步的，利用式(1-5)设计重新配置的静态输出反馈控制器的控制律：
式(1-5)中Ki为待确定的输出反馈增益；yc(t)为补偿输出；为估计系统输出；l＝[0 Ip]。
再一方面，本发明还公开一种计算机可读存储介质，存储有计算机程序，所述计算机程序被处理器执行时，使得所述处理器执行如上述方法的步骤。
由上述技术方案可知，本发明的用于叉车稳定控制的静态输出反馈控制方法及存储介质，以期待能提高平衡重式叉车防侧翻系统的容错能力，从而保证叉车防侧翻系统的稳定性，提高叉车主动安全性的目的。具体的说，在传感器发生故障时，所提出的状态观测器能够估计传感器输出的信号及故障状态，其故障信号能够被准确的接收，并根据静态输出反馈控制方法对输出信号及时进行补偿输出，那么系统受传感器故障 的影响极小，保证了控制器绝大部分功能有效性。
与现有技术相比，本发明的有益效果在于：
1、能保证在系统前提变量不可测的情况下，仍然可以得到相应的状态和故障向量。
2、在系统发生故障后，能基于估计状态和故障向量，保证控制定律的重新配置，尽可能的恢复系统故障前的性能。
3、提高了叉车防侧翻系统的容错能力，大大提高了叉车横向稳定性和主动安全性。
附图说明
图1为叉车防侧翻系统传感器故障容错控制系统图；
图2为故障fa信号及其估计值信号图；
图3为故障fb信号及其估计值信号图；
图4为静态输出反馈的容错控制输入状态图；
图5为无容错时叉车车身侧偏角及其估计值图；
图6为无容错时叉车车身横摆角速度及其估计值图；
图7为容错控制下叉车车身侧偏角及其估计值图；
图8为容错控制下叉车车身横摆角速度及其估计值图。
具体实施方式
为使本发明实施例的目的、技术方案和优点更加清楚，下面将结合本发明实施例中的附图，对本发明实施例中的技术方案进行清楚、完整地描述，显然，所描述的实施例是本发明一部分实施例，而不是全部的实施例。
实施例1：
如图1所示，本实施例所述的用于叉车稳定控制的静态输出反馈控制方法，包括设置连续时间的模糊系统模型、奇异观测器、广义观测器、残差发生器、静态输出反馈控制器；具体的说包括以下步骤：
利用式(1)构建连续时间的叉车防侧翻模糊系统模型：
式(1-1)中x(t)表示t时刻的状态向量；f(t)∈Rs是传感器故障向量；d(t)∈Rnd是 未知有界扰动向量；矩阵Bd和Df为具有适当的维数，同时Df假定为满列秩；
通过设置连续时间的模糊系统模型以激励函数ui(ξ(t))为系统的输入，并且同时存在传感器故障和未知有界扰动；
通过设置奇异观测器用于同时估计平衡重式叉车防侧翻模糊系统的状态和输出故障
通过设置广义观测器用于测量连续时间内平衡重式叉车防侧翻系统的状态和故障估计，生成对故障f(t)尽可能敏感而对扰动d(t)不敏感的残差信号L2；
通过设置残差发生器利用残差信号L2控制去将H∞控制问题推广到非线性情形，观察最小化干扰信号rd(t)得到残差信号L2的增益，找到相应的正定矩阵和正标量，进而渐进估计系统状态和传感器故障；
通过上述观察器提供的故障和状态估计，对控制定律进行重新配置，并通过LMIs形式给出足够的条件以保证所产生的闭环系统的稳定性。
以下分别具体说明，按如下步骤设计连续时间的模糊系统模型：
步骤11、叉车轮胎在车身发生倾斜时其轮胎自身也跟着发生形变，同样的，当叉车在高速转弯时，叉车的轮胎变形也会变大，进而导致轮胎的侧偏角较大，由于叉车轮胎的力特性曲线并非都能近似线性化。故本发明采用了车辆研究中典型的非线性轮胎模型，在车辆稳定性性研究中更为常见，即魔术公式模型，因此前后轮胎的侧向力Fyf，Fyr可以表示为：

式中，αf和αr分别为叉车前后轮胎的侧偏角。另外，对于上式中参数Di，Li，Gi和Vi(i＝f,r)，它们的取值影响因素较多，其中关键的主要包括行进速度，车轮附着力，以及车轮力特性。
步骤12、基于T-S模糊模型，对于前侧向力的非线性特性的估计，使用滑动区域M1；后侧向力的非线性特性估计，使用滑动区域M2；如果|αf|属于M1，则：
如果|αf|属于M2，则：
式(2-3)、(2-4)中，Cfi(i＝1,2)和Cri(i＝1,2)分别为前后轮胎的侧偏刚度，其值影响因素较多，包括轮胎宽度、载荷质量、车轮附着力以及车速。
步骤13、叉车前后轮胎的侧向力表示如下：
式(2-5)中，λi(|αf|)(i＝1,2)是关于变量|αf|的加权函数，这些加权函数满足以下属性：0≤λi(|αf|)≤1和
步骤14、假设叉车前后轮胎的侧偏角很小，可以得到αf＝β-(aω/vx)和αr＝δ-β-(bω/vx)。考虑叉车动力学模型，则整体的叉车防侧翻T-S模糊模型如下：
式(2-6)中u(t)＝F(t)，和z(t)＝[LTR]分别为上述系统模型的状态，控制输入，干扰输入和控制输出，相关矩阵如下：



步骤15、对平衡重式叉车防侧翻传感器故障系统可构造扩展描述系统：




平衡重式叉车防侧翻故障系统中，控制器的正常工作至关重要，传感器故障将会导致控制器的传感器输入信号出现偏差，严重时甚至没有信号输入。因此，如果传感器发生故障后，其故障信号能够被准确的接收，并根据控制器输出信号及时进行补偿输出，那么控制器将不受传感器故障的影响，保证控制器正常工作。
具体实施中为了同时估计系统的状态和故障，如下设计了奇异观测器结构:
式(1-2)中v(t)∈Rn+p是系统奇异观察器的辅助状态向量，是上述扩展 描述系统中x(t)的估计量。是不可测前提变量，其部分或完全取决于估计状态x(t)。现在简化设计观察器为寻找增益Si，E和L，以使状态和故障误差估计符合一个稳定的生成系统。上述奇异观测器中，y(t)的微分项并未存在，因此在实际工程中这种观测器更易实现。
系统模型中设想了传感器故障和未知干扰，为了研究连续时间下的叉车防侧翻传感器故障系统模型的故障估计以及状态估计，将对各种一般的情况进行分析。
具体实施中，广义观测器范数定义为：
在上述情况下，广义观测器的设计任务在于生成对故障尽可能敏感而对扰动不敏感的残差信号，从而使故障诊断具有鲁棒性。实际上，残差产生的问题可以通过控制来研究(将H∞控制问题推广到非线性情形)。
在具体实施中，按如下步骤设计残差信号发生器：
步骤41、通过最小化干扰信号rd(t)到残差信号的增益来设计：
为此，提出以下定理：
定理1：若正定对称矩阵P11、P12、存在，以及矩阵N1、N2和正标量η，则状态观测器(1-2)可以估计系统状态以及传感器故障，并且在以下LMI约束下(见(2-8))将标量γ最小化。



步骤42、通过以下方法获得观测器增益：
式(2-9)中，Ω∈Rn.p和两个自由矩阵，可用得到非奇异矩阵E：

步骤43、给出外部的干扰信号残差的衰减水平：
假设Df具有完整的列秩，则可以通过上述方法获得传感器的估计值，同时保证了故障估计值的完好性。
为了针对叉车防侧翻传感器故障容错系统，实现容错控制，针对传感器故障和外部干扰，设计了一种静态输出反馈控制器。如图1所示，观测器提供了故障和状态估计，因此，相应的控制律必须要进行重新分配。线性矩阵不等式将给出足够的条件以保证其产生的闭关系统的稳定性。
在具体实施中，按如下步骤设计静态输出反馈控制器：
步骤51、基于并行分布补偿，静态输出反馈的控制律设计如下：
式(2-13)中Ki为第i个局部模型中待确定的输出反馈增益，yc(t)代表补偿输出被定义为：

静态输出反馈的目标是只利用可测信号的知识来控制动态系统。因此，要求决策变量只依赖于控制输入信号u(t)、实际输出信号y(t),并且最终依赖于可测量的状态变量。在不可测量的前提变量的情况下，仍然可以设计一个稳定的静态输出反馈控制器。 在下面的容错控制律的结构计算中，同时考虑了观测器中导出的状态和传感器故障信号估计
步骤52、分析该闭环系统的稳定性，系统状态估计误差由上述微分方程(2-9)结合下述公式生成：
将静态输出反馈控制律(2-13)带入上述公式，可以得出结论为：
加减公式(2-17)可重写为：
式(2-18)中因此，上述LMI约束公式相当于：
使用以下公式在状态空间表示中重写整个模型：



定义增广状态向量：
获得以下闭环系统：
步骤53、找出相应的观测器和控制器，使外部干扰d(t)对闭环系统的影响最小，该问题的出现，导致必须解决由以下定理提供的线性矩阵不等式约束下的标准控制。
引理1：考虑两个具有适当维数的实矩阵X,Y以及F(t)，对于任意的标量δ，证明了以下不等式：
XTFY+YTFTX≤δXTX+δ-1YTY,δ>0(2-22)
引理2：如果存在对称的正定矩阵P11，P12，P2i，矩阵Q1，Q2和正标量ψ，且δi，i＝1,…，7满足i，j＝1,2,…,r且i≠j的以下条件，则具有基于奇异观测器的叉车防侧翻传感器故障容错控制系统渐近稳定。
minψ(2-23)
Wii<0(2-24)
其中：




Y(2,2)＝-diag(δ1+δ5δ2(δ3+δ4+δ2)-1×δ3δ4δ1 -1δ6δ7(δ5+δ6+δ7)-1)(2-30)
然后通过上述公式(2-9)中Ω以及下式获得观测器增益。

步骤54、进行稳定性证明。
为了获得不保守的条件，采用以下非二次Lyapunov函数：
上式中Λi＝diag[P1P2i]，其中P1，P2i是对称正定矩阵。具有容错控制的闭环系统是稳定的，并且如果则η可以限制从d(t)到e(t)的增益。Lyapunov函数V(xa(t))的导数表示为：
这个条件是负定的，如果
其中：
式(2-36)中：
使用上述所提出的引理1，存在正标量δi，i＝1,…，7
使：
式(2-38)中：
在BMI项和上应用Schur补码，定理2中提出的充分线性矩阵不等式条件成立。
实施例2：
针对叉车防侧翻传感器故障容错系统，设计上述有效的控制策略，使得叉车防侧翻系统在存在传感器故障的情况下，仍然能够保证整个系统的稳定。在本节中，通过数值模拟来证明所提出的方法对叉车防侧翻传感器故障容错系统的有效性和适用性。前文中构建的T-S模型用于构建观测器，表示具有取决于不可测量状态变量为前提变量的叉车防侧翻传感器故障容错系统。在设计中，考虑的叉车整车参数见表1。
表1
考虑故障信号f(t)＝(fa(t),fb(t))T影响系统输出行为，并描述如下：

对于叉车防侧翻系统使用了陀螺仪传感器，陀螺仪传感器只能测量叉车的横摆角速度，对于横向速度使用建议的观测器估计，解决上述定理(2)中的线性矩阵不等式约束下的优化问题，得到以下标称衰减水平ψ＝0.843的观察器和控制器增益矩阵。


K1＝[-0.0019 0.0020],K2＝[-0.0020 0.0020](2-44)
作为本发明的一个实施例，图2、图3图4分别为故障fa信号及其估计值信号、故障fb信号及其估计值信号、静态输出反馈的容错控制输入状态。图5、图6分别为无容错时叉车车身侧偏角及其估计值和横摆角速度及其估计值，图7、图8分别为容错控制下叉车车身侧偏角及其估计值和横摆角速度及其估计值。
对于使用静态输出反馈容错控制策略的案例，可以注意到，当系统传感器发生故障时，尽管系统存在故障和外部干扰，叉车防侧翻系统仍然保持了稳定，保持其侧偏角及横摆角速度在发生故障时，其最值波动不超过未使用静态输出反馈容错控制策略的角度最值的3％。因此，表明了本文提出的静态输出反馈容错控制策略是有效的。
又一方面，本发明还公开一种计算机可读存储介质，存储有计算机程序，所述计算机程序被处理器执行时，使得所述处理器执行如上述任一方法的步骤。
再一方面，本发明还公开一种计算机设备，包括存储器和处理器，所述存储器存储有计算机程序，所述计算机程序被所述处理器执行时，使得所述处理器执行如上述任一方法的步骤。
在本申请提供的又一实施例中，还提供了一种包含指令的计算机程序产品，当其在计算机上运行时，使得计算机执行上述实施例中任一方法的步骤。
可理解的是，本发明实施例提供的系统与本发明实施例提供的方法相对应，相关 内容的解释、举例和有益效果可以参考上述方法中的相应部分。
本领域普通技术人员可以理解实现上述实施例方法中的全部或部分流程，是可以通过计算机程序来指令相关的硬件来完成，所述的程序可存储于一非易失性计算机可读取存储介质中，该程序在执行时，可包括如上述各方法的实施例的流程。其中，本申请所提供的各实施例中所使用的对存储器、存储、数据库或其它介质的任何引用，均可包括非易失性和/或易失性存储器。非易失性存储器可包括只读存储器(ROM)、可编程ROM(PROM)、电可编程ROM(EPROM)、电可擦除可编程ROM(EEPROM)或闪存。易失性存储器可包括随机存取存储器(RAM)或者外部高速缓冲存储器。作为说明而非局限，RAM以多种形式可得，诸如静态RAM(SRAM)、动态RAM(DRAM)、同步DRAM(SDRAM)、双数据率SDRAM(DDRSDRAM)、增强型SDRAM(ESDRAM)、同步链路(Synchlink)DRAM(SLDRAM)、存储器总线(Rambus)直接RAM(RDRAM)、直接存储器总线动态RAM(DRDRAM)、以及存储器总线动态RAM(RDRAM)等。
以上实施例仅用以说明本发明的技术方案，而非对其限制；尽管参照前述实施例对本发明进行了详细的说明，本领域的普通技术人员应当理解：其依然可以对前述各实施例所记载的技术方案进行修改，或者对其中部分技术特征进行等同替换；而这些修改或者替换，并不使相应技术方案的本质脱离本发明各实施例技术方案的精神和范围。

Claims (6)

  1. 一种用于叉车稳定控制的静态输出反馈控制方法，其特征在于，包括以下步骤：
    利用式(1-1)构建连续时间的叉车防侧翻模糊系统模型：
    式(1-1)中x(t)表示t时刻的状态向量；f(t)∈Rs是传感器故障向量；d(t)∈Rnd是未知有界扰动向量；矩阵Bd和Df为具有适当的维数，同时Df假定为满列秩；
    通过设置连续时间的模糊系统模型以激励函数ui(ξ(t))为系统的输入，并且同时存在传感器故障和未知有界扰动；
    通过设置奇异观测器用于同时估计平衡重式叉车防侧翻模糊系统的状态和输出故障
    通过设置广义观测器用于测量连续时间内平衡重式叉车防侧翻系统的状态和故障估计，生成对故障f(t)尽可能敏感而对扰动d(t)不敏感的残差信号L2；
    通过设置残差发生器利用残差信号L2控制去将H∞控制问题推广到非线性情形，观察最小化干扰信号rd(t)得到残差信号L2的增益，找到相应的正定矩阵和正标量，进而渐进估计系统状态和传感器故障；
    通过上述观察器提供的故障和状态估计，对控制定律进行重新配置，并通过LMIs形式给出足够的条件以保证所产生的闭环系统的稳定性。
  2. 根据权利要求1所述的用于叉车稳定控制的静态输出反馈控制方法，其特征在于：所述奇异观测器用于同时估计叉车防侧翻模糊系统的状态和输出故障如下：
    式(1-2)中v(t)∈Rn+p是观测器的辅助状态向量；是的估计量；是不可测前提变量；Si、E、L为观测器增益。
  3. 根据权利要求1所述的用于叉车稳定控制的静态输出反馈控制方法，其特征在于：利用式(1-3))构建广义观测器H(t)∈L2，L2的范数定义为：
  4. 根据权利要求1所述的用于叉车稳定控制的静态输出反馈控制方法，其特征在于：利用式(1-4)构建残差发生器rd(t),
  5. 根据权利要求1所述的用于叉车稳定控制的静态输出反馈控制方法，其特征在于：利用式(1-5)设计重新配置的静态输出反馈控制器的控制律：
    式(1-5)中Ki为待确定的输出反馈增益；yc(t)为补偿输出；为估计系统输出；l＝[0 Ip]。
  6. 一种计算机可读存储介质，存储有计算机程序，所述计算机程序被处理器执行时，使得所述处理器执行如权利要求1至5中任一项所述方法的步骤。
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CN114967656A (zh) * 2022-06-09 2022-08-30 安徽合力股份有限公司 用于叉车稳定控制的静态输出反馈控制方法及存储介质

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