CN111198500B - Time-lag sampling system anti-saturation control method with asymmetric saturated input constraint - Google Patents

Time-lag sampling system anti-saturation control method with asymmetric saturated input constraint Download PDF

Info

Publication number
CN111198500B
CN111198500B CN202010021010.9A CN202010021010A CN111198500B CN 111198500 B CN111198500 B CN 111198500B CN 202010021010 A CN202010021010 A CN 202010021010A CN 111198500 B CN111198500 B CN 111198500B
Authority
CN
China
Prior art keywords
saturation
time
lag
asymmetric
parameter
Prior art date
Legal status (The legal status is an assumption and is not a legal conclusion. Google has not performed a legal analysis and makes no representation as to the accuracy of the status listed.)
Active
Application number
CN202010021010.9A
Other languages
Chinese (zh)
Other versions
CN111198500A (en
Inventor
刘涛
耿新鹏
郝首霖
仲崇权
孟庆伟
朱理
Current Assignee (The listed assignees may be inaccurate. Google has not performed a legal analysis and makes no representation or warranty as to the accuracy of the list.)
Dalian University of Technology
Original Assignee
Dalian University of Technology
Priority date (The priority date is an assumption and is not a legal conclusion. Google has not performed a legal analysis and makes no representation as to the accuracy of the date listed.)
Filing date
Publication date
Application filed by Dalian University of Technology filed Critical Dalian University of Technology
Priority to CN202010021010.9A priority Critical patent/CN111198500B/en
Publication of CN111198500A publication Critical patent/CN111198500A/en
Application granted granted Critical
Publication of CN111198500B publication Critical patent/CN111198500B/en
Active legal-status Critical Current
Anticipated expiration legal-status Critical

Links

Images

Classifications

    • 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
    • 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
    • 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
    • G05B13/048—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 using a predictor

Abstract

A time-lag sampling system anti-saturation control method with asymmetric saturated input constraint belongs to the technical field of industrial process control. The invention provides an active disturbance rejection control design method of a discrete time domain for a production process with time-lag response and asymmetric saturation constraint of an actuator based on a discrete time domain transfer function model with time-lag parameters commonly used for describing a sampling system in practical engineering. An asymmetric saturation system is converted into a symmetric saturation constraint system through model transformation, and a reverse saturation extended state observer based on non-time-lag output prediction is provided by utilizing a developed generalized predictor structure. The observer and controller gains are solved analytically by configuring the characteristic root of the extended state observer and the desired poles of the closed-loop control system. Has better theoretical innovation and engineering application value.

Description

Time-lag sampling system anti-saturation control method with asymmetric saturated input constraint
Technical Field
The invention relates to a control system of a chemical production process, provides a novel anti-saturation control method based on non-time-lag output prediction on the basis of active disturbance rejection control and anti-saturation control theories aiming at a production process with time-lag response and asymmetric saturation input constraint of an actuator in the chemical production, and belongs to the technical field of industrial process control.
Background
In industrial processes, there have been decades of research into actuator saturation phenomena. Saturation is often encountered in practical control systems due to limitations in the magnitude of the actuator amplitude. If some targeted processing is not performed on the control method, the control performance is reduced and even the whole system is unstable. Many researchers have been working on the control method of the saturation of the symmetric actuator, however, in practical application, the saturation of the asymmetric actuator often occurs, but only a few results are published at present. An asymmetric Lyapunov function was proposed to analyze the stability of the system as proposed in the reference Ansymmetric lyapunov function for linear systems with An asymmetric activator maintenance (International Journal of Robust and Nonlinear Control,2018, 28(5): 1624-.
Suppression of disturbances is one of the main control tasks in industrial processes as well. For engineering applications, more and more research is beginning to focus on exploring Active Disturbance Rejection Control (ADRC) strategies. In order to solve the actuator saturation problem, for a type of uncertain non-linear system which is interfered by external disturbance, an Anti-saturation ADRC design is proposed in the literature of Anti-wind design for uncertain non-linear systems sub-object to actuator failure and external distribution (International Journal of Robust and non-linear Control,2016,26(15): 3421-3438).
Furthermore, the time lag is another problem that limits the control performance and even causes the control system to be unstable. In recent years, considerable research effort has been devoted to time-lapse systems, such as convex combining methods, Wirtinger-based integral inequality methods, Generalized Free Weight Matrices (GFWM), and the like. However, at present, no relevant research is available on how to suppress disturbance in the production process with time-lag response and actuator asymmetric saturation constraint, and the problem has better theoretical innovation and engineering application value.
Disclosure of Invention
The invention aims to solve the technical problem of anti-interference control in the chemical production process with time-lag response and asymmetric saturation constraint of an actuator. In order to solve the problems, an active disturbance rejection and anti-saturation control structure based on non-time-lag output prediction is designed, and a unified anti-saturation control system design method capable of being used in a production process with time-lag response is provided.
The invention provides an active disturbance rejection control design method of a discrete time domain for a production process with time-lag response and actuator symmetric saturation constraint based on a discrete time domain transfer function model with time-lag parameters commonly used for describing a sampling system in practical engineering. By utilizing the developed generalized predictor structure, an anti-saturation extended state observer based on non-time-lag output prediction is provided. The observer and controller gains are solved analytically by configuring the characteristic root of the extended state observer and the desired poles of the closed-loop control system. The saturation compensation capability of the anti-saturation extended state observer is improved by adjusting parameters in the anti-saturation gain. The method has the outstanding advantages that the designed anti-saturation observer, the generalized predictor and the controller can be adjusted through adjustable parameters, and the method is beneficial to practical application. And according to the Lyapunov stability theorem, a time-lag correlation stability condition for ensuring the stability of the closed-loop system is provided.
The technical scheme of the invention is as follows:
(1) symmetrical transformation
The asymmetric actuator saturation constraint is converted into the symmetric actuator constraint through transformation, so that the original system can be described as a symmetric saturated input system additionally added with constant disturbance. Based on the transformed system, the increased constant perturbation and other perturbations of the system can be treated as augmented states, and the system is rewritten again to an augmented system with symmetric input saturation constraints. Based on this system, other control modules will be designed.
(2) Anti-saturation extended state observer based on non-time-lag output prediction
The anti-saturation extended state observer provided by the invention is designed based on prediction output without time lag, which is different from the extended state observer design of the existing method directly based on output measurement. Furthermore, known model information is also applied to the design of the observer to improve the estimation performance of the system state. Furthermore, by adding the anti-saturation term, when the actuator is saturated, the observer can be compensated in real time, and the system can be ensured to stably operate in a saturation boundary. By arranging the characteristic root of the extended state observer to a desired position in the discrete time domain z-plane, the form of the observer gain can be solved analytically. By adjusting the parameters in the observer, the best compromise between closed loop system stability and immunity performance can be achieved.
(3) Closed loop controller design
The closed-loop controller designed by the invention comprises a feedback control part and a set point pre-filtering part, wherein the feedback controller is obtained by configuring a desired closed-loop system pole. The steady state gain of the system set point pre-filter is designed to be a steady state value of the inverse of the desired closed loop transfer function to achieve an steady state free tracking error. The controller has only one adjustment parameter that is adjusted by monotonically increasing or decreasing to achieve the desired set point tracking response performance.
(4) Generalized predictor design
The generalized predictor designed by the invention is a universal predictor structure which can be applied to open-loop stable, integral and unstable systems. The form of the predictor can be determined by a given formula given the predictor control parameters. The main advantage is that the predictor has only one tuning parameter, which can be tuned monotonically in the (0,1) range, thus achieving the best compromise between noise immunity and robust stability of the closed loop system.
The invention has the beneficial effects that: based on the design, the method has better tracking performance and anti-interference performance for the production process with time lag and actuator asymmetric saturation constraint, and greatly improves the control effect of past methods on asymmetric saturation constraint.
Drawings
FIG. 1 is a block schematic diagram of the control system of the present invention. In fig. 1, p (z) represents an actual controlled object, i.e., an industrial time-lag process; omega is the load interference of the input end of the controlled object; r, u and y are set point input signals, control inputs and measurement outputs, respectively; sigma is a symmetric saturation input signal, sat (-) represents an artificially designed actuator symmetric saturation constraint; SAT (·) represents the actual existing actuator asymmetric saturation constraint; kfIs a setpoint prefilter, the setpoint signal r being passed through KfGenerating a modified setpoint signal
Figure RE-GDA0002428210590000041
AESO is a model-based extended state observer; f1And F2Predictor filtering is used to predict the dead-lag output of the system; the saturation input is differed from the control input u, and the deviation signal is input into AESO to compensate the influence caused by saturation, so as to obtain a predicted value of the generalized system state; c (z) is a constant module for realizing the saturation of the productAnd the constraint translates into an asymmetric saturation constraint.
FIG. 2 shows the control effect of the method of the present invention for a specific controlled object, and compared with other two control algorithms, the method is obtained by using MATLAB software simulation. In fig. 2, the input signal is a unit amplitude step signal, and the disturbance signal ω is a step signal with an amplitude of 0.95. Wherein (a) represents the output response curves for different systems and (b) represents the corresponding control signal curves.
Detailed Description
For a better understanding of the technical solutions of the present invention, the following detailed description of the embodiments of the present invention is provided with reference to the accompanying drawings.
An anti-interference control method of a time-lag sampling system based on a predictor comprises the following steps:
the method comprises the following steps: symmetrical transformation
The system model is as follows
Figure RE-GDA0002428210590000051
Where G (z) is a time-lag independent transfer function, N (z) and D (z) are the corresponding numerator and denominator, and z is a variable of the discrete domain transfer function. d is the nominal time lag.
Definition of
Figure RE-GDA0002428210590000052
Is the nominal system state associated with g (z). The corresponding state space is implemented as Cm(zI-Am)-1BmWherein
Figure RE-GDA0002428210590000053
Cm＝[1 b1/b0 … bn-2/b0 bn-1/b0]And I is an identity matrix. (2)
Correspondingly, the state space of the sampling system with input time lag and asymmetric saturation constraint of the actuator is described as
Figure RE-GDA0002428210590000054
Where y (k) represents the process output at the k-th time instant in the discrete time domain, u (k) represents the process input at the k-th time instant, ω (k) represents the interference signal at the k-th time instant, φ (k) represents the initial condition, aiAnd bi(i-0, 1,2, …, n-1) is a parameter of the system transfer function, and d represents the process lag. SAT (u (k)) is a saturation function, which is defined as
Figure RE-GDA0002428210590000061
Wherein alpha is more than 0, beta is more than or equal to 0 and is the upper and lower bounds of asymmetric saturation bound constraint.
Definition of xn+1＝b0Where ω (k) is the state of augmentation, then one spatial expression of the state of augmentation for more than one system can be expressed as
Figure RE-GDA0002428210590000062
Wherein
Figure RE-GDA0002428210590000063
h(k)＝b0[ω(k+1)-ω(k)],
Figure RE-GDA0002428210590000064
Figure RE-GDA0002428210590000065
To handle asymmetric actuator saturation, a symmetric transformation is used based on the system (2).
Order to
SAT(u(k))＝sat(σ(k))+δ (6)
Where sat (σ (k)) is a symmetric saturation function defined as
Figure RE-GDA0002428210590000066
The constant part is defined as
Figure RE-GDA0002428210590000067
Where r (z) represents the setpoint tracking signal.
Can be easily verified
Figure RE-GDA0002428210590000068
Based on the above transformation, the system (2) can be rewritten as
Figure RE-GDA0002428210590000071
Defining an expanded state
Figure RE-GDA0002428210590000072
The amplification expression of the above system is
Figure RE-GDA0002428210590000073
Step two: anti-saturation extended state observer design based on non-time-lag output prediction
Considering the nominal time-lag independent system defined by G (z), to handle actuator saturation, the following anti-saturation extended state observer is designed
Figure RE-GDA0002428210590000074
WhereinLAWIs the gain of the reverse saturation compensation, LoIs the gain of the observer and is,
Figure RE-GDA0002428210590000075
representing a predicted time-lag-free output, σ (k) being a control input, which can be obtained by configuring the desired position of the feature in (10) according to the z-plane, i.e.
|zI-(Ae-LoCe)|＝(z-ωo)n+1＝0 (12)
Wherein ω isoE (0,1) is a tuning parameter. The corresponding observer gain vector is
Figure RE-GDA0002428210590000076
To improve the reverse saturation behaviour, LAWIs designed as
Figure RE-GDA0002428210590000077
Wherein lawIs the only adjustable parameter in the anti-saturation gain.
In view of the actual implementation, it is proposed to select the initial values of the adjustment parameters as: omegao∈[0.9,0.99]， law∈[0.1,1]×(10-3\10-8). Then by adjusting these two parameters monotonically, a compromise can be reached before estimating performance, anti-saturation compensation performance and robustness.
Step three: anti-disturbance controller design
As in fig. 1, in the form of a controller,
Figure RE-GDA0002428210590000081
wherein
Figure RE-GDA0002428210590000082
Is a closed-loop anti-interference feedback controller,
Figure RE-GDA0002428210590000083
is a modified reference signal. The controller is applied to a generalized system (4), and a closed-loop system characteristic equation can be written,
|zI-(Ae-BeK0)|＝(z-1)[zn+(an-1+kn)zn-1+…+(a0+k1)]＝0 (16)
assigning a desired closed loop system pole to
Zn+(an-1+kn)zn-1+…+(a0+k1)＝(z-ωc)n (17)
Wherein ω iscE (0,1) is a tuning parameter. The controller parameters are accordingly available
Figure RE-GDA0002428210590000084
In consideration of practical application, it is recommended that the initial value be selected to be ωc∈[0.9,0.95]Then monotonously adjusting the parameter ωcA compromise between noise immunity and robust stability of the closed loop system may be achieved.
Step four: generalized predictor design
In view of the above time-lag independent implementation of the observer, a generalized predictor is used herein to obtain a time-lag independent system output prediction. The generalized predictor is filtered by two filters F in FIG. 11And F2And (4) forming. (1) The nominal system in the formula can be decomposed into
Figure RE-GDA0002428210590000085
Wherein
Figure RE-GDA0002428210590000091
Figure RE-GDA0002428210590000092
m is the number of zeros in G (z), λ ∈ (0,1) is an adjustable parameter, H (z) is a strictly regular filter, (A)g,bg,cg) Is that
Figure RE-GDA0002428210590000093
Is implemented with minimal state space.
For practical applications, the measurement noise is taken into account, where H (z) is designed to
Figure RE-GDA0002428210590000094
It is characterized by no static gain, [ (1-lambda)qzq]/(1-z)qFor all-pass filtering, to reduce sensitivity to noise, the order q is user-determined and related to the noise level.
Next, an auxiliary transfer function is defined,
Figure RE-GDA0002428210590000095
the time lag independent output is predicted as
Figure RE-GDA0002428210590000096
Wherein
Figure RE-GDA0002428210590000097
Wherein
Figure RE-GDA0002428210590000098
Respectively representing transfer functions
Figure RE-GDA0002428210590000099
U (z) is the control input, y (z) represents the actual output of the process, noting that λ e (0,1) is the filtering F1(z)，F2(z) by adjusting this parameter monotonically, a trade-off between prediction performance and robustness can be obtained.
Step five: setpoint tracking controller
To achieve smooth setpoint tracking performance without overshoot, setpoint tracking Kf(z) is designed as follows
Figure RE-GDA00024282105900000910
Based on the AESO and feedback control rate designed above, the transfer function for the closed loop system for setpoint tracking is derived as
Figure RE-GDA0002428210590000101
Wherein N (z) is a molecule of P (z), Td＝N(z)/(z-ωc)nIs a transfer function for disturbance rejection feedback control.
Note TdCan be decomposed into a Minimum Phase (MP) part (consisting of zeros and poles inside the unit circle) and a non-minimum phase (NMP) part (consisting of zeros outside the unit circle), respectivelyd-MPAnd Td-NMPThe definition, that is,
Td-ADRC(z)＝Td-MP(z)Td-NMP(z)， (25)
based on the internal model control theory, the expected transfer function for the set point tracking is designed as
Figure RE-GDA0002428210590000102
Wherein λfE (0,1) is an adjustable parameter, nf≥deg(Td-MP) +1 is the user-specified order of execution, ngIs a positive integer satisfying
Figure RE-GDA0002428210590000103
Is biregular, i.e. its numerator is the same order as the denominator.
Substituting equation (24) into equation (26) results in a setpoint tracking controller
Figure RE-GDA0002428210590000104
Wherein
Figure RE-GDA0002428210590000105
Figure RE-GDA0002428210590000106
For making Td-NMPBecomes an all-pass filter. For example, if there is a non-minimum phase zero, i.e., Td-NMP＝z-z0，|z0If the ratio of the absolute value is greater than 1,
Figure RE-GDA0002428210590000107
is selected as
Figure RE-GDA0002428210590000108
Suggesting an adjustable parameter lambdafIs selected within the interval 0.95,0.99]Then, this parameter is monotonically adjusted so that a trade-off is made between setpoint tracking speed and robustness.
Step six: simulation verification
Consider an application case of Tan and Fu in the literature Linear active distribution-reflection control: analysis and tuning via IMC (IEEE Transactions on Industrial Electronics,2016, 63(4):2350-,
Figure RE-GDA0002428210590000111
for control execution, the sampling period is taken as T being 0.02(s), and the corresponding discrete model is
Figure RE-GDA0002428210590000112
For comparison with the above document, at similar setpoint tracking speeds and disturbance response peaks, the AESO and feedback controller K0Respectively to omegao0.9139 and ωc0.9418. Accordingly, the gain vector and feedback control law of the AESO can be calculated
L0＝[0.1114 0.1193 0.00032],
K0＝[-662.4063 687.2931 7634.4596].
According to equation (26), let λf＝0.96，nf4, the setpoint controller is designed as
Figure RE-GDA0002428210590000113
Given a nominal time lag d of 20, λ of 0.986 and m of 1, the time-lag-independent output predictor is designed according to equation (21) as
Figure RE-GDA0002428210590000114
Wherein
Figure RE-GDA0002428210590000115
Figure RE-GDA0002428210590000121
Figure RE-GDA0002428210590000122
Assuming that the input constraint for asymmetric saturation is 1 and 0.5, the control gain vector is designed according to (13) anti-saturation
LAW＝[0 0 0.00035]
In the reference, three sets of contrast controllers are set up according to the control method thereof
(a) At the same input saturation limit, b-4/3, ωc＝1,ωo＝10；
(b) Under the saturation boundary without input, b is 4/3, omegac＝1,ωo＝10；
(c) At the same input saturation limit, b-4/3, ωc＝10/13,ωo＝10
Note that (a) and (b) have the same parameter settings, but different input saturation constraints. At the same time, to avoid input saturation, (c) the speed of the set point tracking is turned down.
For control testing, a unit step signal was added to the system at t-0(s) and a step load disturbance of amplitude 0.95 was added to the process input at t-20(s). The control results are shown in FIG. 2. It can be seen that the control method of the present invention has better set point tracking performance and anti-interference performance.

Claims (1)

1. The anti-saturation control method of the time-lag sampling system with the asymmetric saturated input constraint is characterized by comprising the following steps of:
the method comprises the following steps: symmetrical transformation
The system model is as follows
Figure RE-FDA0002448265950000011
Wherein G (z) is a time-lag independent transfer function, N (z) and D (z) are the corresponding numerator and denominator, z being a variable of the discrete domain transfer function; d is the nominal time lag;
definition of
Figure RE-FDA0002448265950000012
Is the nominal system state associated with g (z); the corresponding state space is implemented as Cm(zI-Am)-1BmWherein
Figure RE-FDA0002448265950000013
Cm＝[1 b1/b0…bn-2/b0 bn-1/b0]I is an identity matrix; (2)
correspondingly, the state space of the sampling system with input time lag and asymmetric saturation constraint of the actuator is described as
Figure RE-FDA0002448265950000014
Where y (k) represents the process output at the k-th time instant in the discrete time domain, u (k) represents the process input at the k-th time instant, ω (k) represents the interference signal at the k-th time instant, φ (k) represents the initial condition, aiAnd biN-1 is a parameter of the system transfer function; SAT (u (k)) is a saturation function, which is defined as
Figure RE-FDA0002448265950000021
Wherein alpha is more than 0, beta is more than or equal to 0 and is an upper bound and a lower bound of asymmetric saturation bound;
definition of xn+1＝b0Where ω (k) is the state of augmentation, then one spatial expression of the state of augmentation for the above system is expressed as
Figure RE-FDA0002448265950000022
Wherein
Figure RE-FDA0002448265950000023
h(k)＝b0[ω(k+1)-ω(k)]，
Figure RE-FDA0002448265950000024
Figure RE-FDA0002448265950000025
To handle asymmetric actuator saturation, a symmetric transformation is used based on the system (2);
order to
SAT(u(k))＝sat(σ(k))+δ (6)
Where sat (σ (k)) is a symmetric saturation function defined as
Figure RE-FDA0002448265950000026
The constant part is defined as
Figure RE-FDA0002448265950000027
Wherein r (z) represents a setpoint tracking signal;
can verify
Figure RE-FDA0002448265950000031
Based on the above transformation, the system (2) is rewritten as
Figure RE-FDA0002448265950000032
Defining an expanded state
Figure RE-FDA0002448265950000033
The amplification expression of the above system is
Figure RE-FDA0002448265950000034
Step two: anti-saturation extended state observer design based on non-time-lag output prediction
Considering the nominal time-lag independent system defined by G (z), to handle actuator saturation, the following anti-saturation extended state observer is designed
Figure RE-FDA0002448265950000035
Wherein L isAWIs the gain of the reverse saturation compensation, LoIs the gain of the observer and is,
Figure RE-FDA0002448265950000036
representing a predicted time-lag-free output, σ (k) being a control input, obtainable by configuring a desired position of a feature in (11) according to the z-plane, i.e.
|zI-(Ae-LoCe)|＝(z-ωo)n+1＝0 (12)
Wherein ω isoE (0,1) is a setting parameter; the corresponding observer gain vector is
Figure RE-FDA0002448265950000037
To improve the reverse saturation behaviour, LAWIs designed as
Figure RE-FDA0002448265950000038
Wherein lawIs the only adjustable parameter in the anti-saturation gain;
in view of the actual implementation, the initial values of the adjustment parameters are selected as: omegao∈[0.9,0.99]，law∈[0.1,1]×(10-3\10-8) (ii) a Then, by adjusting the two parameters monotonously, a compromise is obtained before estimating the performance, the anti-saturation compensation performance and the robustness;
step three: anti-disturbance controller design
In the form of a controller as follows,
Figure RE-FDA0002448265950000041
wherein
Figure RE-FDA0002448265950000042
Is a closed-loop anti-interference feedback controller,
Figure RE-FDA0002448265950000043
is a modified reference signal; the controller is applied to a generalized system (5), and a closed-loop system characteristic equation is written as
|zI-(Ae-BeK0)|＝(z-1)[zn+(an-1+kn)zn-1+…+(a0+k1)]＝0 (16)
Assigning a desired closed loop system pole to
zn+(an-1+kn)zn-1+…+(a0+k1)＝(z-ωc)n (17)
Wherein ω iscE (0,1) is a setting parameter; obtaining controller parameters accordingly
Figure RE-FDA0002448265950000044
Considering practical application, the initial value is selected to be omegac∈[0.9,0.95]Then monotonously adjusting the parameter ωcObtaining the compromise between the anti-interference performance and the robust stability of the closed-loop system;
step four: generalized predictor design
Taking into account the time-lag independent execution of the observer above, a generalized predictor is used to obtain a time-lag independent system output prediction; generalized predictor with two filters F1And F2Composition is carried out; (1) the nominal system in the formula is decomposed into
Figure RE-FDA0002448265950000045
Wherein
Figure RE-FDA0002448265950000051
Figure RE-FDA0002448265950000052
Where m is the number of zeros in G (z), λ ∈ (0,1) is an adjustable parameter, H (z) is a strictly regular filter, (A)g,bg,cg) Is that
Figure RE-FDA0002448265950000053
State space minimum implementation of (c);
for practical applications, the measurement noise is taken into account, where H (z) is designed to
Figure RE-FDA0002448265950000054
It is characterized by no static gain, [ (1-lambda)qzq]/(1-z)qIs all-pass filtering, is used forReducing sensitivity to noise, the order q being user-determined and related to the noise level;
next, an auxiliary transfer function is defined
Figure RE-FDA0002448265950000055
The time lag independent output is predicted as
Figure RE-FDA0002448265950000056
Wherein
Figure RE-FDA0002448265950000057
Wherein
Figure RE-FDA0002448265950000058
Respectively representing transfer functions
Figure RE-FDA0002448265950000059
U (z) is a control input, y (z) represents the actual output of the process; note that λ ∈ (0,1) is the filter F1(z)，F2(z) a unique adjustable parameter that, by monotonically adjusting this parameter, results in a trade-off between prediction performance and robustness;
step five: setpoint tracking controller
To achieve smooth setpoint tracking performance without overshoot, setpoint tracking Kf(z) is designed as follows
Figure RE-FDA00024482659500000510
The fixed point signal r passes through KfGenerating a modified setpoint signal
Figure RE-FDA0002448265950000061
Based on the AESO and feedback control rate designed above, the transfer function for the closed loop system for setpoint tracking is derived as
Figure RE-FDA0002448265950000062
Wherein N (z) is a molecule of P (z), Td＝N(z)/(z-ωc)nIs a transfer function for disturbance rejection feedback control;
note TdCan be decomposed into a minimum phase MP part consisting of zeros and poles inside the unit circle, and a non-minimum phase NMP part consisting of zeros outside the unit circle, respectively Td-MPAnd Td-NMPThe definition, that is,
Td-ADRC(z)＝Td-MP(z)Td-NMP(z)， (25)
based on the internal model control theory, the expected transfer function for the set point tracking is designed as
Figure RE-FDA0002448265950000063
Wherein λfE (0,1) is an adjustable parameter, nf≥deg(Td-MP) +1 is the user-specified order of execution, ngIs a positive integer satisfying
Figure RE-FDA0002448265950000064
Is ditormonal, i.e., its numerator is the same order as the denominator;
substituting equation (24) into equation (26) results in a setpoint tracking controller
Figure RE-FDA0002448265950000065
Wherein
Figure RE-FDA0002448265950000066
Figure RE-FDA0002448265950000067
For making Td-NMPBecomes an all-pass filter; when there is a non-minimum phase zero, i.e. Td-NMP＝z-z0，|z0If | is greater than 1, selecting
Figure RE-FDA0002448265950000068
Is composed of
Figure RE-FDA0002448265950000069
Adjustable parameter lambdafIs selected within the interval 0.95,0.99]Then, this parameter is monotonically adjusted so that a trade-off is made between setpoint tracking speed and robustness.
CN202010021010.9A 2020-01-09 2020-01-09 Time-lag sampling system anti-saturation control method with asymmetric saturated input constraint Active CN111198500B (en)

Priority Applications (1)

Application Number Priority Date Filing Date Title
CN202010021010.9A CN111198500B (en) 2020-01-09 2020-01-09 Time-lag sampling system anti-saturation control method with asymmetric saturated input constraint

Applications Claiming Priority (1)

Application Number Priority Date Filing Date Title
CN202010021010.9A CN111198500B (en) 2020-01-09 2020-01-09 Time-lag sampling system anti-saturation control method with asymmetric saturated input constraint

Publications (2)

Publication Number Publication Date
CN111198500A CN111198500A (en) 2020-05-26
CN111198500B true CN111198500B (en) 2021-06-08

Family

ID=70747146

Family Applications (1)

Application Number Title Priority Date Filing Date
CN202010021010.9A Active CN111198500B (en) 2020-01-09 2020-01-09 Time-lag sampling system anti-saturation control method with asymmetric saturated input constraint

Country Status (1)

Country Link
CN (1) CN111198500B (en)

Families Citing this family (1)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN112180727B (en) * 2020-10-01 2023-03-14 天水师范学院 Multi-rate sampling control method and system for large-time-lag nonlinear system and application

Family Cites Families (5)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
US9645558B2 (en) * 2012-09-29 2017-05-09 Operation Technology, Inc. Dynamic parameter tuning using particle swarm optimization
CN107037734A (en) * 2017-06-26 2017-08-11 青岛格莱瑞智能控制技术有限公司 One kind has a variety of uncertain factor nonlinear system tenacious tracking control methods
CN107908107A (en) * 2017-11-13 2018-04-13 大连理工大学 Disturbance rejection control method of the time lag sampling system based on fallout predictor
CN108490765B (en) * 2018-01-27 2020-12-11 天津大学 Design method of active disturbance rejection controller with anti-integral compensation
CN110879582B (en) * 2019-12-20 2020-11-03 大连理工大学 Time-lag sampling system anti-saturation control method with actuator symmetric saturation constraint

Also Published As

Publication number Publication date
CN111198500A (en) 2020-05-26

Similar Documents

Publication Publication Date Title
CN105487385B (en) Based on model-free adaption internal model control method
CN110879582B (en) Time-lag sampling system anti-saturation control method with actuator symmetric saturation constraint
Kwon et al. Receding horizon tracking control as a predictive control and its stability properties
Wang et al. Cascade optimal control for tracking and synchronization of a multimotor driving system
Du et al. Disturbance rejection for input-delay system using observer-predictor-based output feedback control
Parvathy et al. A survey on active disturbance rejection control
CN107908107A (en) Disturbance rejection control method of the time lag sampling system based on fallout predictor
CN111198500B (en) Time-lag sampling system anti-saturation control method with asymmetric saturated input constraint
Huba et al. Noise attenuation motivated controller design. Part I: Speed control
Yan et al. Adaptive control of uncertain hammerstein systems with monotonic input nonlinearities using auxiliary nonlinearities
Ikpe Aniekan et al. Comparative analysis of a PID controller using Ziegler Nichols and auto turning method
Tavakoli et al. Kalman filter-smoothed random walk based centralized controller for multi-input multi-output processes
Sethi et al. Design of fractional order MRAPIDC for inverted pendulum system
Missaghie et al. Sensitivity reducing observers for optimal feedback control
Pedro et al. State feedback control of MIMO systems with multiple time delays
Guo et al. Adaptive sliding mode active disturbance rejection control of PMLSM based on simulated annealing particle swarm optimization algorithm
Lino et al. Feedback-Feedforward Position and Speed Control of DC Motors by Fractional-Order PI ν Controllers
Anwar Design of PID controller for high-order process via IMC scheme in frequency domain
Lima et al. First-order dead-time compensation with feedforward action
Tan et al. Robust design and tuning for a modified IMC structure
Wu et al. Active disturbance rejection control based simplified decoupling for two-input-two-output processes
Ota et al. Simultaneous design of reference model and controller for VRFT using closed-loop step response data
Feng et al. Improved Adaptive Dynamic Surface Control for a Class of Uncertain Nonlinear Systems
Albertos et al. Control of input/output delayed and disturbed unstable plants
Ghany et al. Practical implementation for fuzzy self tuning of optimal PID controller to servo permanent magnet synchronous motor

Legal Events

Date Code Title Description
PB01 Publication
PB01 Publication
SE01 Entry into force of request for substantive examination
SE01 Entry into force of request for substantive examination
GR01 Patent grant
GR01 Patent grant