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 PDFInfo
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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
Technical field
The present invention relates to industrial stokehold technical field, especially a kind of mould based on expansion state Kalman filter
Type predictive control algorithm.
Background technique
Expansion state observes (Extended state observer, ESO) device by disturbing the inside and outside lump in system
The new single order state of system is expanded into, observer parameter appropriate is chosen, obtaining all quantity of states of system includes lump disturbance quantity
Observation.Since in uncertain problems such as processing system unknown parameters, Unmarried pregnancy, unknown disturbances, advantage is bright for it
It is aobvious, therefore be gradually successfully applied in sorts of systems by the extensive attention of researcher.Existing research shows the observation of ESO
Performance is directly related to observer bandwidth, and bandwidth is bigger, and the accuracy of observation of quantity of state is higher, but also more sensitive to noise simultaneously.
However, existing the extended state observer not process noise in consideration system and measurement noise in design, and these noises
It is extensive physical presence again, to will affect the performance of observer.In addition, the gain one of general linear extended state observer
As adjusted by Bandwidth Method, Decoupling design need to be carried out when handling multi-variable system, it is complex.Therefore, document proposes one kind
Expansion state Kalman filter improves observer and exists in noise with Kalman's theory real-time optimization observer gain
When accuracy of observation.
Summary of the invention
Technical problem to be solved by the present invention lies in it is pre- to provide a kind of model based on expansion state Kalman filter
Control algolithm is surveyed, the state observation and Model Predictive Control problem of a kind of Nonlinear Uncertain Systems can be suitable for.
In order to solve the above technical problems, the present invention provides a kind of model prediction control based on expansion state Kalman filter
Algorithm processed, includes the following steps:
(1) it is a new quantity of state by mission nonlinear, uncertainty and external disturbance lump, expands original system
State-space model, 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 prediction
Controller.
Preferably, in step (1), consider that Discrete Nonlinear uncertain system is
Wherein, X (k) ∈ RmFor quantity of state, k is current sample time, Ad∈Rm×m, Bu∈Rm×p, Bf∈Rm×r, Cd∈Rq×m
For known system matrix, F (k) ∈ RrFor non-linear, uncertain in system and external disturbance lump item, nominal plant model
For known nonlinear function, process noise W (k) is m dimension irrelevant zero mean value gaussian random noise, covariance matrix Qw,y
(k)∈RqIt is measurement output vector, n (k) ∈ RqIt is measurement noise vector, covariance matrix Qn。
Preferably, in step (1), the lump in Discrete Nonlinear uncertain system model is disturbed into FkRegard amplification shape as
State, then system amplification state-space model be
Wherein, G (k)=F (k+1)-F (k) considers that the nominal plant model of G (k) is to preferably utilize model informationH is the sampling time,
Preferably, in step (1), for the amplification state space system model, expansion state Kalman filtering can be designed
Device is as follows:
Wherein, ' ∧ ' represents observation, KkAnd Pk+1It is the filter gain and the state error at k+1 moment at k moment respectively
Covariance estimation,Saturation function sat () is defined as
Sat (f, b)=max { min { f, b } ,-b }, b > 0, adjustment parameter
Preferably, in step (2), the specific design of model predictive controller is as follows:
In the state value and disturbed value that current sample time is observed based on expansion state Kalman filter, can must be
System state is in the prediction model of the following P sampling instant
Wherein,
Consider that system optimization performance index function is as follows
Wherein, Q and R is respectively error weight matrix and control weight matrix, XsFor state set-point, while meeting input, defeated
Out, state constraint is as follows:
Umin≤U(k)≤Umax
Ymin≤Y(k)≤Ymax
Xmin≤X(k)≤Xmax
The optimization problem is solved at every sampling moment obtains optimal control lawBy the first of optimal control law
Item is applied in control object, is updated State Viewpoint measured value in next sampling instant, is computed repeatedly optimal control law.
The invention has the benefit that being a new shape by mission nonlinear, uncertainty and external disturbance lump
State amount, design expansion state Kalman filter observe state value and lump disturbed value, avoid setting for nonlinear observer
Meter and thus bring stability problem；With Kalman's theory real-time optimization observer gain, observer is improved in mistake
Accuracy of observation in the presence of journey noise and measurement noise；Expansion state Kalman filter is mutually tied with model predictive controller
The shortcomings that closing, capable of overcoming the big inertia of system, large delay improves system response time；Simultaneously consider system input, output,
The restrict of quantity of state, control performance declines caused by avoiding because of damp constraint.
Detailed description of the invention
Fig. 1 is algorithm flow schematic diagram of the invention.
Fig. 2 is output quantity curve synoptic diagram in the embodiment of the present invention.
Fig. 3 is control amount curve synoptic diagram in the embodiment of the present invention.
Fig. 4 is quantity of state x in the embodiment of the present invention1Observation error curve synoptic diagram.
Fig. 5 is quantity of state x in embodiment in the present invention2Observation error curve synoptic diagram.
Fig. 6 is quantity of state x in embodiment in the present invention3Observation error curve synoptic diagram.
Fig. 7 is quantity of state x in embodiment in the present invention4Observation error curve synoptic diagram.
The observation error curve synoptic diagram that Fig. 8 is lump disturbance quantity F in embodiment in the present invention.
Specific embodiment
As shown in Figure 1, a kind of Model Predictive Control Algorithm based on expansion state Kalman filter, including walk as follows
It is rapid:
(1) it is a new quantity of state by mission nonlinear, uncertainty and external disturbance lump, expands original system
State-space model, 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 prediction
Controller.
In conjunction with the unmanned warship of drive lacking motion control as embodiment, filtered using of the invention based on expansion state Kalman
The Model Predictive Control Algorithm of wave device (Extended state kalman filter, ESKF), at the same be based on expansion state
The Model Predictive Control Algorithm of observer (Extended state observer, ESO) and be based on extended Kalman filter
The Model Predictive Control Algorithm of (Extended kalman filter, EKF) compares.
The unmanned warship motion model of drive lacking can be described as:
Wherein, x1,x2,x3And x4It is the unmanned warship course of drive lacking, course speed, course acceleration and direction griping respectively
Angle, control amount u are helm orders, and controlled volume y is unmanned warship course.D (t) represents external environment disturbance, and w (t) and n (t) are respectively to be
System process noise and measurement noise.K,T1,
T2,T3,TcIt is system parameter, K=0.5900, T with α1=0.9526, T2=0.0247, T3=0.2215, α=0.0001, Tc=
0.1000。
By the continuous model discretization, discrete time h=0.01s can obtain the separate manufacturing firms model of following form:
Wherein Cd=[1 00 0].
Assuming that system initial state is x=[0 00 0]T, control target is to make when external disturbance d (t) is definite value 10
Constant course is 20 °, and course speed, course acceleration, direction rudder angle of declination remain 0, i.e. xs=[20 00 0]T.System shape
State and input constraint are as follows: -30 °≤x4(k+i)≤30 °, -30 °≤u (k+i-1)≤30 °, -20 ° of h≤Δ u (k+i-1)≤
20°·h。σwAnd σnThe standard deviation of respectively process noise w (k) and measurement noise n (k), σw=0.001h, σn=0.001.
Expansion state Kalman filter parameter setting is as follows:
Model predictive controller parameter setting based on expansion state Kalman filter are as follows: prediction time domain P=200s, control
Time domain M=2s processed, error weight matrix Q=diag [105,102,102,102], weight matrix R=1 is controlled, duration t=20s is emulated.
In order to compare, while introducing the Model Predictive Control Algorithm based on extended state observer and being based on spreading kalman
The Model Predictive Control Algorithm of filter compares.Model predictive controller based on extended state observer and based on extension
The prediction time domain of the model predictive controller of Kalman filter, controls time domain, error weight matrix, control the setting of weight matrix with
The parameter setting of the model predictive controller based on expansion state Kalman filter in the present invention is identical.
In model predictive controller based on extended state observer, the construction and parameter setting of extended state observer are such as
Under:
Wherein, weFor extended state observer bandwidth, it is set as we=4.
In model predictive controller based on extended Kalman filter, the construction and parameter of extended Kalman filter are set
It sets as follows:
Wherein
A kind of Model Predictive Control Algorithm structural representation based on expansion state Kalman filter proposed in the present invention
Figure is as shown in Figure 1.Fig. 2 and Fig. 3 is respectively output quantity curve and control amount curve in the embodiment of the present invention, it can be seen that
In the presence of extraneous definite value disturbance, process noise, measurement noise, in the case where meeting quantity of state and input quantity constrains, controlled volume
Setting value can be quickly and accurately reached, and control amount variation is gentle, has no frequent fluctuation.Fig. 4, Fig. 5, Fig. 6, Fig. 7 and Fig. 8 points
It Wei not expansion state Kalman filter, extended state observer and expansion Kalman filter observation in the embodiment of the present invention
Obtained quantity of state x1,x2,x3,x4With the observation error curve of lump disturbance quantity F.As can be seen that Extended Kalman filter in figure
There are stable state observed deviations for estimation of the device to quantity of state and disturbance quantity.Although the stable state observed deviation of extended state observer is 0,
But observation is more sensitive to noise, will cause controller frequent fluctuation.And expansion state Kalman filter combines expansion
The advantages of state observer and Kalman filter, observation is affected by noise less, and stable state observation error is 0, thus sees
It is best to survey effect.
The present invention is based on expansion state Kalman filter, propose a kind of model based on expansion state Kalman filter
Predictive control algorithm can solve systematic procedure noise, measurement noise, input and output restricted problem simultaneously, improve observer and exist
Observation performance in the presence of noise improves control performance.
Claims (5)
1. a kind of Model Predictive Control Algorithm based on expansion state Kalman filter, which comprises the steps of:
(1) it is a new quantity of state by mission nonlinear, uncertainty and external disturbance lump, expands the shape of original system
State space model, 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 CONTROL
Device.
2. the Model Predictive Control Algorithm as described in claim 1 based on expansion state Kalman filter, which is characterized in that
In step (1), consider that Discrete Nonlinear uncertain system is
Wherein, X (k) ∈ RmFor quantity of state, k is current sample time, Ad∈Rm×m, Bu∈Rm×p, Bf∈Rm×r, Cd∈Rq×mFor
Know sytem matrix, F (k) ∈ RrFor non-linear, uncertain in system and external disturbance lump item, nominal plant modelFor
Know that nonlinear function, process noise W (k) are m dimension irrelevant zero mean value gaussian random noise, covariance matrix Qw,y(k)
∈RqIt is measurement output vector, n (k) ∈ RqIt is measurement noise vector, covariance matrix Qn。
3. the Model Predictive Control Algorithm as described in claim 1 based on expansion state Kalman filter, which is characterized in that
In step (1), the lump in Discrete Nonlinear uncertain system model is disturbed into FkRegard amplification state as, then system expands state
Spatial model is
Wherein, G (k)=F (k+1)-F (k) considers that the nominal plant model of G (k) is to preferably utilize model informationH is the sampling time, C=[Cd 0]。
4. the Model Predictive Control Algorithm as claimed in claim 3 based on expansion state Kalman filter, which is characterized in that
In step (1), for the amplification state space system model, it is as follows that expansion state Kalman filter can be designed:
Wherein, ' ∧ ' represents observation, KkAnd Pk+1It is filter gain and the state error association side at k+1 moment at k moment respectively
Difference estimation,Saturation function sat () be defined as sat (f,
B)=max { min { f, b } ,-b }, b > 0, adjustment parameter
5. the Model Predictive Control Algorithm as described in claim 1 based on expansion state Kalman filter, which is characterized in that
In step (2), the specific design of model predictive controller is as follows:
In the state value and disturbed value that current sample time is observed based on expansion state Kalman filter, system shape can be obtained
State is in the prediction model of the following P sampling instant
Wherein,
Consider that system optimization performance index function is as follows
Wherein, Q and R is respectively error weight matrix and control weight matrix, XsFor state set-point, while meeting input, output, shape
Modal constraint is as follows:
Umin≤U(k)≤Umax
Ymin≤Y(k)≤Ymax
Xmin≤X(k)≤Xmax
The optimization problem is solved at every sampling moment obtains optimal control lawThe first item of optimal control law is applied
It is added in control object, updates State Viewpoint measured value in next sampling instant, compute repeatedly 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 |
| 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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| 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 |
| 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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