CN110376886A - A kind of Model Predictive Control Algorithm based on expansion state Kalman filter - Google Patents

A kind of Model Predictive Control Algorithm based on expansion state Kalman filter Download PDF

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CN110376886A
CN110376886A CN201910614372.6A CN201910614372A CN110376886A CN 110376886 A CN110376886 A CN 110376886A CN 201910614372 A CN201910614372 A CN 201910614372A CN 110376886 A CN110376886 A CN 110376886A
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沈炯
张怡
孙立
薛文超
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Southeast University
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    • 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
    • G05B13/042—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 in which a parameter or coefficient is automatically adjusted to optimise the performance

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Abstract

The invention discloses a kind of Model Predictive Control Algorithms based on expansion state Kalman filter, include the following steps: (1) by mission nonlinear, uncertainty and external disturbance lump be a new quantity of state, expand the state-space model of original system, design expansion state Kalman filter observation system quantity of state and lump disturbance quantity；(2) it is based on known state amount and disturbance quantity, while considering system input, output, state constraint, design a model predictive controller.The present invention is based on expansion state Kalman filter, it is proposed a kind of Model Predictive Control Algorithm based on expansion state Kalman filter, systematic procedure noise, measurement noise, input and output restricted problem can be solved simultaneously, observation performance of observer in the presence of noise is improved, control performance is improved.

Description

Model prediction control algorithm based on expansion state Kalman filter
Technical Field
The invention relates to the technical field of industrial process control, in particular to a model prediction control algorithm based on an expansion state Kalman filter.
Background
An Extended State Observer (ESO) expands internal and external lumped disturbances in a system into a new first-order state of the system, selects appropriate observer parameters, and obtains observed values of all state quantities of the system including the lumped disturbance quantities. The method has obvious advantages when the uncertain problems of unknown system parameters, unmodeled dynamics, unknown disturbance and the like are processed, so that the method is gradually paid attention by researchers and is successfully applied to various systems. Research has shown that the observation performance of the ESO is directly related to the observer bandwidth, and the larger the bandwidth is, the higher the observation accuracy of the state quantity is, but at the same time, the more sensitive it is to noise. However, existing extended state observers are not designed with consideration for process and measurement noise in the system, which is widely practical and affects observer performance. In addition, the gain of a general linear extended state observer is generally set by a bandwidth method, and decoupling design is required when a multivariable system is processed, so that the linear extended state observer is complex. Therefore, there is a document that proposes an extended state kalman filter, which optimizes the observer gain in real time by using the kalman theory, and improves the observation accuracy of the observer in the presence of noise.
Disclosure of Invention
The invention aims to solve the technical problem of providing a model predictive control algorithm based on an expansion state Kalman filter, which can be suitable for the problems of state observation and model predictive control of a nonlinear uncertain system.
In order to solve the technical problem, the invention provides a model predictive control algorithm based on an expansion state Kalman filter, which comprises the following steps:
(1) integrating system nonlinearity, uncertainty and external disturbance into a new state quantity, amplifying a state space model of an original system, and designing an expanded state Kalman filter observation system state quantity and an integrated disturbance quantity;
(2) and designing a model predictive controller based on the known state quantity and disturbance quantity and considering system input, output and state constraints simultaneously.
Preferably, in step (1), the discrete nonlinear uncertainty system is considered as
Wherein X (k) e RmIn order to be a state quantity,k is the current sampling instant, Ad∈Rm×m，Bu∈Rm×p，Bf∈Rm×r，Cd∈Rq×mFor a known system matrix, F (k) e RrIs a nominal model of the lumped terms of nonlinearity, uncertainty and external disturbance in the systemFor a known nonlinear function, the process noise W (k) is m-dimensional uncorrelated zero mean Gaussian random noise with a covariance matrix of Qw,y(k)∈RqIs the measurement output vector, n (k) e RqIs to measure the noise vector with a covariance matrix of Qn。
Preferably, in step (1), lumped disturbances F in the discrete nonlinear uncertainty system model are usedkWhen viewed as an amplification state, the system amplifies the state space model as
Wherein g (k) ═ F (k +1) -F (k), in order to better utilize the model information, the nominal model of g (k) is considered ash is the sampling time of the sample,
preferably, in step (1), the extended state kalman filter may be designed for the model of the augmented state space system as follows:
wherein ` Λ' represents an observed value, KkAnd Pk+1Respectively the filter gain at time k and the state error covariance estimate at time k +1,the saturation function sat (·) is defined as sat (f, b) ═ max { min { f, b }, -b }, b > 0, and the adjustment parameter
Preferably, in step (2), the model predictive controller is specifically designed as follows:
based on a state value and a disturbance value observed by an extended state Kalman filter at the current sampling moment, a prediction model of the system state at the future P sampling moments can be obtained as
Wherein,
consider the system optimization performance indicator function as follows
Wherein Q and R are an error weight matrix and a control weight matrix, respectively，XsFor the state set value, the input, output and state constraints are satisfied simultaneously as follows:
Umin≤U(k)≤Umax
Ymin≤Y(k)≤Ymax
Xmin≤X(k)≤Xmax
solving the optimization problem at each sampling time to obtain the optimal control lawAnd applying the first item of the optimal control law to the control object, updating the state observation value at the next sampling moment, and repeatedly calculating the optimal control law.
The invention has the beneficial effects that: the nonlinearity, the uncertainty and the external disturbance of the system are lumped into a new state quantity, and an expanded state Kalman filter is designed to observe a state value and a lumped disturbance value, so that the design of a nonlinear observer and the stability problem caused by the design are avoided; the Kalman theory is applied to optimize the gain of the observer in real time, so that the observation precision of the observer in the presence of process noise and measurement noise is improved; the Kalman filter in the expansion state is combined with the model prediction controller, so that the defects of large inertia and large delay of the system can be overcome, and the response speed of the system is improved; meanwhile, constraint limits of system input, output and state quantity are considered, and control performance reduction caused by actuator saturation is avoided.
Drawings
FIG. 1 is a schematic diagram of the algorithm flow of the present invention.
FIG. 2 is a graph illustrating an output curve according to an embodiment of the present invention.
FIG. 3 is a graph illustrating a control quantity curve according to an embodiment of the present invention.
FIG. 4 shows a state quantity x in an embodiment of the present invention1Schematic diagram of the observation error curve of (1).
FIG. 5 shows the state quantities x in the embodiment of the present invention2Schematic diagram of the observation error curve of (1).
FIG. 6 shows the state quantities x in the embodiment of the present invention3Is shown by the observation error curveIntention is.
FIG. 7 shows the state quantities x in the embodiment of the present invention4Schematic diagram of the observation error curve of (1).
FIG. 8 is a schematic view of an observation error curve of the lumped disturbance F in the embodiment of the present invention.
Detailed Description
As shown in fig. 1, a model predictive control algorithm based on an extended state kalman filter includes the following steps:
(1) integrating system nonlinearity, uncertainty and external disturbance into a new state quantity, amplifying a state space model of an original system, and designing an expanded state Kalman filter observation system state quantity and an integrated disturbance quantity;
(2) and designing a model predictive controller based on the known state quantity and disturbance quantity and considering system input, output and state constraints simultaneously.
By combining the motion control of the under-actuated unmanned ship as an embodiment, the model predictive control algorithm based on the Extended State Kalman Filter (ESKF) of the present invention is adopted, and is compared with the model predictive control algorithm based on the Extended State Observer (ESO) and the model predictive control algorithm based on the Extended Kalman Filter (EKF).
The motion model of the under-actuated unmanned ship can be described as follows:
wherein x is1,x2,x3And x4The control quantity u is a steering command, and the controlled quantity y is the unmanned ship course. d (t) represents the external environment disturbance, w (t) and n (t) are the system process noise and the measurement noise respectively.K,T1,T2,T3,TcAnd α is a system parameter, K ═0.5900,T1＝0.9526,T2＝0.0247,T3＝0.2215,α＝0.0001,Tc＝0.1000。
Discretizing the continuous model, wherein the discrete time h is 0.01s, a discrete state space model of the following form can be obtained:
wherein Cd＝[1 0 0 0]。
Suppose the system initial state is x ═ 0000]TThe control objective is to make the heading constant at 20 DEG while keeping the heading speed, heading acceleration and heading deflection angle at 0, namely x, when the external disturbance d (t) is a constant value of 10s＝[20 0 0 0]T. The system state and input constraints are: x is more than or equal to minus 30 degrees4(k+i)≤30°，-30°≤u(k+i-1)≤30°，-20°·h≤Δu(k+i-1)≤20°·h。σwAnd σnThe standard deviation, σ, of the process noise w (k) and the measurement noise n (k), respectivelyw＝0.001·h，σn＝0.001。
The extended state kalman filter parameters are set as follows:
the model predictive controller parameters based on the extended state kalman filter are set as: the prediction time domain P is 200s, the control time domain M is 2s, and the error weight matrix Q is diag [10 ═ d [ ]5,102,102,102]The control weight matrix R is 1, and the simulation time duration t is 20 s.
For comparison, a model predictive control algorithm based on an extended state observer and a model predictive control algorithm based on an extended Kalman filter are introduced for comparison. The model prediction controller based on the extended state observer and the model prediction controller based on the extended Kalman filter are used for predicting time domain, control time domain and error weight matrix, and the setting of the control weight matrix is the same as the parameter setting of the model prediction controller based on the extended state Kalman filter in the invention.
In the model predictive controller based on the extended state observer, the structure and parameters of the extended state observer are set as follows:
wherein, weTo expand the state observer bandwidth, set to we＝4。
In the model prediction controller based on the extended Kalman filter, the structure and the parameter setting of the extended Kalman filter are as follows:
wherein
The structural schematic diagram of the model predictive control algorithm based on the extended state Kalman filter is shown in FIG. 1. Fig. 2 and fig. 3 are an output quantity curve and a control quantity curve, respectively, in the embodiment of the present invention, it can be seen that, in the presence of disturbance of an external limit value, process noise, and measurement noise, under the condition that the constraints of a state quantity and an input quantity are satisfied, a controlled quantity can quickly and accurately reach a set value, and the control quantity changes smoothly without frequent fluctuation. Fig. 4, fig. 5, fig. 6, fig. 7, and fig. 8 are respectively a state quantity x observed by the extended state kalman filter, the extended state observer, and the extended kalman filter in the embodiment of the present invention1,x2,x3,x4And an observation error curve of the total disturbance quantity F. As can be seen in the figure, the estimation of the state quantity and the disturbance quantity by the extended Kalman filter has steady-state observation deviation. Although the steady state observation deviation of the extended state observer is 0, the observation value is sensitive to noise, and frequent fluctuation of the controller is caused. The extended state Kalman filter combines the advantages of the extended state observer and the Kalman filter, the observation value is not greatly influenced by noise, and the steady state observation error is 0, so the observation effect is best.
The invention provides a model prediction control algorithm based on an extended state Kalman filter, which can simultaneously solve the problems of system process noise, measurement noise and input/output constraint, improve the observation performance of an observer in the presence of noise and improve the control performance.

Claims (5)

1. A model prediction control algorithm based on an extended state Kalman filter is characterized by comprising the following steps:
(1) integrating system nonlinearity, uncertainty and external disturbance into a new state quantity, amplifying a state space model of an original system, and designing an expanded state Kalman filter observation system state quantity and an integrated disturbance quantity;
(2) and designing a model predictive controller based on the known state quantity and disturbance quantity and considering system input, output and state constraints simultaneously.
2. The extended-state kalman filter-based model predictive control algorithm according to claim 1, wherein in step (1), the discrete nonlinear uncertainty system is considered as
Wherein X (k) e RmIs the state quantity, k is the current sampling time, Ad∈Rm×m，Bu∈Rm×p，Bf∈Rm×r，Cd∈Rq×mFor a known system matrix, F (k) e RrIs a nominal model of the lumped terms of nonlinearity, uncertainty and external disturbance in the systemFor a known nonlinear function, the process noise W (k) is m-dimensional uncorrelated zero mean Gaussian random noise with a covariance matrix of Qw,y(k)∈RqIs the measurement output vector, n (k) e RqIs to measure the noise vector with a covariance matrix of Qn。
3. The extended-state Kalman filter-based model prediction control algorithm of claim 1, characterized in that in step (1), lumped disturbances F in the discrete nonlinear uncertainty system model are treatedkWhen viewed as an amplification state, the system amplifies the state space model as
Wherein g (k) ═ F (k +1) -F (k), in order to better utilize the model information, the nominal model of g (k) is considered ash is the sampling time of the sample, C＝[Cd 0]。
4. the extended state kalman filter-based model predictive control algorithm of claim 3, wherein in step (1), the extended state kalman filter is designed for the extended state space system model as follows:
wherein ` Λ' represents an observed value, KkAnd Pk+1Respectively the filter gain at time k and the state error covariance estimate at time k +1,the saturation function sat (-) is defined as sat (f, b) ═ max { min { f, b }, -b }, b > 0, and the adjustment is adjustedParameter(s)
5. The extended-state kalman filter-based model predictive control algorithm according to claim 1, wherein in step (2), the model predictive controller is specifically designed as follows:
based on a state value and a disturbance value observed by an extended state Kalman filter at the current sampling moment, a prediction model of the system state at the future P sampling moments can be obtained as
Wherein,
consider the system optimization performance indicator function as follows
Wherein Q and R are an error weight matrix and a control weight matrix, XsFor the state set value, the input, output and state constraints are satisfied simultaneously as follows:
Umin≤U(k)≤Umax
Ymin≤Y(k)≤Ymax
Xmin≤X(k)≤Xmax
solving the optimization problem at each sampling time to obtain the optimal control lawAnd applying the first item of the optimal control law to the control object, updating the state observation value at the next sampling moment, and repeatedly calculating the optimal control law.
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CN111208438A (en) * 2020-03-05 2020-05-29 东南大学 Method for cooperatively estimating residual capacity of lithium-ion battery and sensor deviation based on neural network and unscented Kalman filter
CN112269317A (en) * 2020-11-04 2021-01-26 天津大学 Bilateral teleoperation control method based on extended Kalman filter
CN112637884A (en) * 2020-12-08 2021-04-09 广西电网有限责任公司电力科学研究院 Model prediction control method of WSN (Wireless sensor network) based on extended state observer
CN113034904A (en) * 2021-03-05 2021-06-25 交通运输部公路科学研究所 ETC data-based traffic state estimation method and device
CN113341765A (en) * 2021-06-10 2021-09-03 江苏舜高智能科技有限公司 Coal-fired power plant CO for strictly controlling carbon emission2Flexible regulation and control method for trapping system
CN113495486A (en) * 2021-08-06 2021-10-12 南京工业大学 Model prediction control method based on extended state observer for structural thermal test
CN115860450A (en) * 2022-12-07 2023-03-28 北京和利时工业软件有限公司 Prediction control method, device and medium based on state space model
CN116224802A (en) * 2023-03-31 2023-06-06 上海理工大学 Vehicle team longitudinal composite control method based on interference observer and pipeline model prediction

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CN111208438B (en) * 2020-03-05 2022-03-08 东南大学 Method for cooperatively estimating residual capacity of lithium-ion battery and sensor deviation based on neural network and unscented Kalman filter
CN111208438A (en) * 2020-03-05 2020-05-29 东南大学 Method for cooperatively estimating residual capacity of lithium-ion battery and sensor deviation based on neural network and unscented Kalman filter
CN112269317A (en) * 2020-11-04 2021-01-26 天津大学 Bilateral teleoperation control method based on extended Kalman filter
CN112269317B (en) * 2020-11-04 2024-03-15 天津大学 Bilateral teleoperation control method based on extended Kalman filter
CN112637884A (en) * 2020-12-08 2021-04-09 广西电网有限责任公司电力科学研究院 Model prediction control method of WSN (Wireless sensor network) based on extended state observer
CN113034904A (en) * 2021-03-05 2021-06-25 交通运输部公路科学研究所 ETC data-based traffic state estimation method and device
CN113034904B (en) * 2021-03-05 2022-06-24 交通运输部公路科学研究所 ETC data-based traffic state estimation method and device
CN113341765B (en) * 2021-06-10 2023-10-27 江苏舜高智能科技有限公司 Coal-fired power plant CO with strictly controlled carbon emission 2 Flexible control method for trapping system
CN113341765A (en) * 2021-06-10 2021-09-03 江苏舜高智能科技有限公司 Coal-fired power plant CO for strictly controlling carbon emission2Flexible regulation and control method for trapping system
CN113495486A (en) * 2021-08-06 2021-10-12 南京工业大学 Model prediction control method based on extended state observer for structural thermal test
CN113495486B (en) * 2021-08-06 2023-11-24 南京工业大学 Model prediction control method for structural thermal test based on extended state observer
CN115860450A (en) * 2022-12-07 2023-03-28 北京和利时工业软件有限公司 Prediction control method, device and medium based on state space model
CN116224802A (en) * 2023-03-31 2023-06-06 上海理工大学 Vehicle team longitudinal composite control method based on interference observer and pipeline model prediction
CN116224802B (en) * 2023-03-31 2023-12-05 上海理工大学 Vehicle team longitudinal composite control method based on interference observer and pipeline model prediction

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