CN107942665B - Modular active disturbance rejection control method for angular rate proportional-integral feedback - Google Patents
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Abstract
The invention relates to a modular active disturbance rejection control method aiming at angular rate proportional-integral feedback, which comprises the following four steps: 1. equivalently establishing a dynamic model of the tracking error of the rigid body angular rate according to a rigid body angular rate control system based on proportional-integral feedback control: 2. designing a total uncertainty estimator according to a rigid body angular rate control system based on proportional-integral feedback control and the angular rate tracking error dynamic model obtained in the step 1 to obtain the total uncertainty in the rigid body angular rate control system; 3. the parameters of the 'total uncertainty' estimator (5) designed in step 2 are designed: 4. the estimated value of the total uncertainty in the rigid body angular rate control system is obtained by using the total uncertainty estimator (5) in the step 2
Modular active disturbance rejection control inputs with "total uncertainty" compensation are designed.
Description
Technical Field
The invention belongs to the field of design of rigid body angular rate control methods, and particularly relates to a proportional-integral feedback control method and a modular active-disturbance-rejection control method of a rigid body angular rate control system.
Background
Proportional-integral feedback control methods are very classical and efficient feedback control methods for first order control systems and have been widely used in practical industrial control system processes. The document w.l. bialkowski, "The control handbook," New York,1996 mentions that 98% of The control loops employ a single-input single-output proportional-integral feedback control method. Control engineers often have more experience in parameter adjustment of proportional-integral feedback control methods and master more theoretical methods. Therefore, the parameters of the proportional-integral feedback control method used in the actual control system are often subjected to a great deal of debugging by engineers, and the selected values can be considered to be optimal to some extent. In addition, many of the parameters of the proportional-integral feedback control methods that have been used in practical control systems are fixed or protected in the control equipment after being adjusted, and are difficult to change. In summary, proportional-integral feedback control is used in a large number of practical industrial products, and the control parameters are often selected by optimization, and the values are also fixed or protected in the control device.
However, the characteristics of the actual control system and the external environment change with time, and many models of the control system change in an unknown manner after a long or short period of time, and the unknown change is probably not considered when the control parameters are adjusted, so that the performance of the control system is reduced and even the control system is unstable. In the problem of angular rate control of a rigid body, the influence of uncertainty changes inside and outside the actual control system on the control system is particularly significant. For example, in the problem of angular rate control of an aircraft, a series of uncertain changes brought by the internal and external environments of the aircraft, such as equipment aging of flight instruments, wide changes of the flight altitude of the aircraft, air pressure and temperature, interference of natural factors such as wind, light and electricity in the flight environment, and the like, all bring great challenges to the angular rate control link which only depends on the inherent proportional-integral feedback control method. In the problem of angular rate control of the mechanical arm, factors such as abrasion of internal parts of the mechanical arm, friction of joints of the mechanical arm, interference of the external environment and the like are severe tests on the robustness of the used proportional-integral feedback control method. There is an urgent and important practical need for improving the proportional-integral feedback control method that has been used in the rigid body angular rate control to meet the requirement of resisting uncertainty inside and outside the control system. For the design of rigid body angular rate control, the corresponding core problem is how to increase a control module or a loop to greatly improve the capability of the whole control system for dealing with uncertainty under the condition of not changing the structure and parameters of the existing proportional-integral feedback control method.
Disclosure of Invention
The technical problem solved by the invention is as follows: aiming at a rigid body angular rate control system and a proportional-integral feedback control method which is already put into use, the modularized active disturbance rejection control method for enhancing the control system to cope with nonlinear unknown dynamic and external disturbance is provided under the condition of not changing the existing control structure and parameters of the system.
Consider a rigid body angular rate control system based on proportional-integral feedback control:
where x (t) ∈ R is the angular velocity of the rigid body at time t, x (τ) ∈ R is the angular velocity of the rigid body at time τ, f (x, t) ∈ R is the sum of uncertain unknown dynamics in the control system, including unknown internal nonlinear dynamics and unknown external disturbances, u (t) ∈ R is the control input, and u (t) u in a rigid body angular velocity control system based on proportional-integral feedback controlPI(t)，uPI(t) ∈ R is the designed proportional-integral feedback control input, b ∈ R is the control input gain, kp∈ R is the proportional feedback gain of the designed proportional-integral feedback control input, ki∈ R is the integral feedback gain of the designed proportional-integral feedback control input, R ∈ R is the reference signal for the angular velocity of the rigid body t0Is the initial value of the running time of the rigid body angular rate control system t ∈ t0And ∞) is the operating time of the rigid body angular rate control system.
For a rigid body angular rate control system (1) based on proportional-integral feedback control, the design goals of the control inputs u (t) are: without changing the designed proportional-integral feedback control input uPI(t) providing a control input u (t) with greater robustness to the uncertain unknown dynamic sum f (x, t) in the control system, thereby enabling the angular velocity x (t) of the rigid body at time t to track a given angular velocity reference signal r.
The technical solution of the invention comprises the following four steps:
step (I): equivalently establishing a dynamic model of the tracking error of the rigid body angular rate according to a rigid body angular rate control system (1) based on proportional-integral feedback control:
the tracking error, which defines the angular rate of the rigid body, is:
establishing an equivalent angular rate tracking error dynamic model according to a rigid body angular rate control system (1) based on proportional-integral feedback control, wherein the expression is as follows:
wherein
Is an estimated value of control input gain, is a parameter to be regulated, and is delta (e (t), R, t) ∈ R is 'total uncertainty' in the rigid body angular rate control system, and the expression of delta (e (t), R, t) is as follows:
step (II): according to a rigid body angular rate control system (1) based on proportional-integral feedback control and an angular rate tracking error dynamic model (3) obtained in the step (I), a total uncertainty estimator is designed to obtain the total uncertainty in the rigid body angular rate control system, and the specific steps are as follows:
designing an "Total uncertainty" estimator
Where β∈ R is the tunable parameter of the "Total uncertainty" estimator, ξ (t) ∈ R is the state value in the "Total uncertainty" estimator,
is the output value of the 'total uncertainty' estimator at the time t, and is relative to the rigid body angleAn estimate of "total uncertainty" δ (e (t), r, t) in a rate control system.
Remarking: the advantages of this patent over the prior art are not reflected in the form of an "overall uncertainty" estimator (5), but in its two parameters
And β, see step (III) and advantages 1-3 of this patent.
Step (three): designing parameters of the total uncertainty estimator (5) designed in the step (two):
firstly, selecting parameters
Satisfy the requirement of
Wherein k isp∈ R is the proportional feedback gain of the designed proportional-integral feedback control input, ki∈ R is the integral feedback gain of the designed proportional-integral feedback control input.
According to the selected
To design the parameters β to satisfy
Where L ∈ R is the upper bound of the partial derivative of the uncertain unknown dynamic sum f (x (t), t) to the rigid body angular rate x (t), L1∈ R is the lower bound on the absolute value of the control input gain.
Step (IV): the estimated value of the total uncertainty in the rigid body angular rate control system is obtained by the total uncertainty estimator (5) in the step (two)
Design belt "Total uncertainty "compensated modular active disturbance rejection control input:
inputting a designed modularized active disturbance rejection control input (8) with 'total uncertainty' compensation into a rigid body angular rate control system (1) based on proportional-integral feedback control to obtain the rigid body angular rate control system based on proportional-integral feedback control and modularized active disturbance rejection control:
the invention designs a total uncertainty estimator (5) and a modular active disturbance rejection control input (8) with total uncertainty compensation aiming at a rigid body angular rate control system (1) based on proportional-integral feedback control, and obtains a rigid body angular rate control system (9) based on proportional-integral feedback control and modular active disturbance rejection control. The invention discloses a modularized active disturbance rejection control method for an enhanced control system to cope with nonlinear unknown dynamic and external disturbance under the condition of not changing a designed proportional-integral feedback control method.
Compared with the prior art, the invention has the advantages that:
1. in a rigid body angular rate control system, due to factors such as equipment aging and external environment change, the control performance of a designed and operated proportional-integral feedback control method is reduced, but the integral replacement of control hardware and software has the defects of high cost and low feasibility. The invention can only utilize the measurement value of the angular velocity of the rigid body, the nonlinear uncertain dynamics of the rigid body angular velocity control system and the range information of the external disturbance on the premise of not changing the designed proportional-integral feedback control method, and the performance of the whole control system is improved by designing a total uncertainty estimator and adding a total uncertainty compensation module on the basis of the used proportional-integral feedback control method;
2. the problem of adjusting control parameters is an important issue in engineering control. The modular active disturbance rejection control method provided by the invention provides a method for adjusting two parameters in a total uncertainty estimator, and quantitatively and explicitly provides the adjusting ranges of the two parameters in the modular active disturbance rejection control method according to the parameter characteristics of the designed proportional-integral feedback control method and the boundary information of nonlinear unknown dynamic change conditions and control input gains. The parameter adjusting theory can reduce the cost of manpower, physics and time spent on adjusting parameters in actual engineering;
3. the modularized active disturbance rejection control method for proportional-integral feedback control designed by the invention can improve the robustness of the control system to internal nonlinear uncertain dynamics and external disturbance. When the control system has internal nonlinear uncertain dynamics and external disturbance, the invention designs a modular active disturbance rejection control structure with compensation 'total uncertainty' by utilizing an estimated value provided by a 'total uncertainty' estimator, thereby improving the performance of the rigid body angular rate control system under the uncertain condition.
Drawings
FIG. 1 is a flow chart of the method of the present invention.
Fig. 2 is a control block diagram of the method of the present invention.
Fig. 3 is a response curve of the angular velocity of the rigid body (first uncertainty case).
Fig. 4 is a response curve of the angular velocity of the rigid body (second uncertainty case).
Fig. 5 is a response curve for the angular velocity of the rigid body (third uncertainty case).
Description of the symbols
t0: initial value of operation time of rigid body angular rate control system;
t is the operating time of the rigid body angular rate control system, t ∈ [ t ]0,∞)；
R is the reference signal of the rigid body angular rate, R ∈ R;
x (t) the angular velocity of the rigid body at time t, x (t) ∈ R;
u (t) control input of the rigid body angular rate control system at time t, u (t) ∈ R;
uPI(t): designed proportional-integral feedback control input, uPI(t)∈R；
f (x (t), t) the sum of uncertain unknown dynamics of the rigid body inside and outside at time t, f (x (t), t) ∈ R;
e (t) tracking error of rigid body angular rate at time t, e (t) ∈ R;
δ (e (t), r, t): the "total uncertainty" of the rigid body angular rate control system at time t,
δ(e(t),r,t)∈R；
ξ (t) value of the state of the "Total uncertainty" estimator at time t, ξ (t) ∈ R;
kp: designed proportional-integral feedback control of input proportional feedback gain, kp∈R；
ki: designed integral feedback gain, k, of proportional-integral feedback control inputi∈R；
b, control input gain of the rigid body angular rate control system, b ∈ R;
β second tunable parameter of the "Total uncertainty" estimator, β∈ R;
l: uncertain unknown dynamic sums f (x (t), t) of rigid body angular rate control systems to the upper bound of the partial derivatives of the state quantities x, i.e.
L1: the lower bound of the absolute value of the control input gain of the rigid body angular rate control system, i.e., | b | ≧ L1.
The specific implementation mode is as follows:
to test the applicability of the modular auto-disturbance rejection control method for the body angular rate proportional-integral feedback control, we performed simulation experiments. Consider a rigid body angular rate control system based on proportional-integral feedback control:
with three types of unknown uncertainty dynamics f (x, t) as follows:
the first case is a nominal control system, which does not contain internal uncertain dynamics and external disturbances; in the second case, the unknown uncertainty dynamics is a typical external disturbance: step disturbance; the third unknown uncertainty dynamics is a composite of the nonlinear system dynamics and the periodic external disturbance.
The proportional feedback gain and integral feedback gain of the control input gain and the existing proportional-integral feedback control input of the rigid body angular rate control system are as follows:
b＝5,kp＝1,ki＝0.05. (12)
the initial value of the control system and the reference signal satisfy:
x(0)＝0,u(0)＝0,r＝1. (13)
defining a state tracking error according to step (one) of the present invention
Establishing an angular rate tracking error dynamic model equivalent to a rigid body angular rate control system based on proportional-integral feedback control:
designing the 'Total uncertainty' estimator according to the step (two) of the invention
Wherein
Is the output value of the 'total uncertainty' estimator at time t, which is an estimate of the 'total uncertainty' δ (e (t), r, t) in a rigid body angular rate control system.
According to the formula (6) and the formula (7) designed according to the parameters in the step (three) of the invention, the parameters of the 'total uncertainty' estimator are designed
According to step (four) of the invention, the output value of the estimator (16) at time t is used
Design modular active disturbance rejection control input with "total uncertainty" compensation:
the designed modular active disturbance rejection control input (18) with 'total uncertainty' compensation is then input into the rigid body angular rate control system (10) based on proportional-integral feedback control.
Fig. 3-5 are simulation results of a proportional-integral feedback control method and a modular active-disturbance-rejection control method for proportional-integral feedback control under a third uncertainty.
In the first case, the control system is a nominal system, free of internal uncertainties and external disturbances. The proportional-integral feedback control method in the simulation is consistent with a system state quantity response curve corresponding to a modularized active disturbance rejection control method aiming at the proportional-integral feedback control, the dynamic response time of a closed loop system is 0.8 second, and the steady-state error is 0.005 radian/second.
In the second case, the uncertain dynamics in the system are external step response signals. And under the condition that the running time is less than 10 seconds, the system is not influenced by uncertainty, and the proportional-integral feedback control method is consistent with a system state response curve corresponding to the modularized active disturbance rejection control method aiming at the proportional-integral feedback control. And when the running time is 10 seconds, an external step disturbance signal enters the system, and only by means of a designed proportional-integral feedback control method, the tracking error of the control system reaches a peak value of 0.1 radian/second when the running time is 10.7 seconds, the tracking error of the control system slowly attenuates, and when the running time is 40 seconds, the tracking error of the control system still has a magnitude of 0.025 radian/second. Under the modularized active disturbance rejection control method aiming at proportional-integral feedback control, the tracking error of the control system reaches the peak value of 0.05 radian/second at the operation time of 10.4 seconds, then rapidly decreases, and is stabilized at 0.005 radian/second after the operation time of 11.2 seconds.
In the third case, the uncertain dynamics in the control system is a composite of the nonlinear system dynamics and the periodic external disturbances. Under the designed proportional-integral feedback control method, the overshoot of the system reaches 0.41 radian/second, the tracking error of the system is slowly attenuated, and the tracking error of the system still fluctuates in the range of-0.03 radian/second to 0.07 radian/second when the running time is 30 seconds to 40 seconds. Under the modularized active disturbance rejection control method aiming at proportional-integral feedback control, the overshoot of the system is 0.07 radian/second, the tracking error of the system is rapidly reduced, and the system is stabilized between-0.005 radian/second and 0.01 radian/second after the running time is 1.5 seconds.
Combining the simulation results of fig. 3-5, the modular active disturbance rejection control method for proportional-integral feedback control exhibits the same closed-loop response characteristics as the proportional-integral feedback control method in a nominal system. Under the condition that the system has uncertain unknown dynamics, the modularized active disturbance rejection control method aiming at the proportional-integral feedback control can greatly improve the performance of the designed proportional-integral feedback control system.
Claims (1)
1. A modularized active disturbance rejection control method aiming at angular rate proportional-integral feedback is characterized in that a rigid body angular rate control system based on proportional-integral feedback control is utilized:
where x (t) ∈ R is the angular velocity of the rigid body at time t, x (τ) ∈ R is the angular velocity of the rigid body at time τ, f (x, t) ∈ R is the sum of uncertain unknown dynamics in the control system, including unknown internal nonlinear dynamics and unknown external disturbances, u (t) ∈ R is the control input, and u (t) u in the rigid body angular velocity control system based on proportional-integral feedback controlPI(t)，uPI(t) ∈ R is the designed proportional-integral feedback control input, b ∈ R is the control input gain, kp∈ R is the proportional feedback gain of the designed proportional-integral feedback control input, ki∈ R is the integral feedback gain of the designed proportional-integral feedback control input, R ∈ R is the reference signal for the angular velocity of the rigid body, t0Is the initial value of the running time of the rigid body angular rate control system t ∈ t0And ∞) is the operating time of the rigid body angular rate control system;
for a rigid body angular rate control system (1) based on proportional-integral feedback control, the design goals of the control inputs u (t) are: without changing the designed proportional-integral feedback control input uPI(t) providing a control input u (t) having a stronger robustness to the uncertain unknown dynamic sum f (x, t) in the control system, thereby enabling the angular velocity x (t) of the rigid body at time t to track a given angular velocity reference signal r;
the method is characterized in that: the modularized active disturbance rejection control method for the angular rate proportional-integral feedback comprises the following four steps:
step (I): equivalently establishing a dynamic model of the tracking error of the rigid body angular rate according to a rigid body angular rate control system (1) based on proportional-integral feedback control:
the tracking error, which defines the angular rate of the rigid body, is:
establishing an equivalent angular rate tracking error dynamic model according to a rigid body angular rate control system (1) based on proportional-integral feedback control, wherein the expression is as follows:
wherein
Is an estimated value of control input gain, is a parameter to be regulated, and is delta (e (t), R, t) ∈ R is 'total uncertainty' in the rigid body angular rate control system, and the expression of delta (e (t), R, t) is as follows:
step (II): according to a rigid body angular rate control system (1) based on proportional-integral feedback control and an angular rate tracking error dynamic model (3) obtained in the step (I), a total uncertainty estimator is designed to obtain the total uncertainty in the rigid body angular rate control system, and the specific steps are as follows:
designing an "Total uncertainty" estimator
Where β∈ R is the tunable parameter of the "Total uncertainty" estimator, ξ (t) ∈ R is in the "Total uncertainty" estimatorIs set to a value of (a) in (b),
is the output value of the 'total uncertainty' estimator at the time t, and is the estimated value of 'total uncertainty' delta (e (t), r, t) in the rigid body angular rate control system;
step (three): designing parameters of the total uncertainty estimator (5) designed in the step (two):
firstly, selecting parameters
Satisfy the requirement of
Wherein k isp∈ R is the proportional feedback gain of the designed proportional-integral feedback control input, ki∈ R is the integral feedback gain of the designed proportional-integral feedback control input;
according to the selected
To design the parameters β to satisfy
Where L ∈ R is the upper bound of the partial derivative of the uncertain unknown dynamic sum f (x (t), t) to the rigid body angular rate x (t), L1∈ R is the lower bound of the absolute value of the control input gain;
step (IV): the estimated value of the total uncertainty in the rigid body angular rate control system is obtained by the total uncertainty estimator (5) in the step (two)
Design modular active disturbance rejection control input with "total uncertainty" compensation:
inputting a designed modularized active disturbance rejection control input (8) with 'total uncertainty' compensation into a rigid body angular rate control system (1) based on proportional-integral feedback control to obtain the rigid body angular rate control system based on proportional-integral feedback control and modularized active disturbance rejection control:
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