CN104932531B - A kind of optimal anti-input saturation control method of quadrotor based on sliding formwork control - Google Patents
A kind of optimal anti-input saturation control method of quadrotor based on sliding formwork control Download PDFInfo
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Abstract
The invention discloses a kind of optimal anti-input saturation control methods of quadrotor based on sliding formwork control.Consider that there are actuator saturations for quadrotor, with reference to optimum control, propose a kind of sliding-mode control.Under the premise of ensureing that carrying performance index function J is optimal value, system sliding-mode surface parameter and switching time is calculated, and then by comparing switching time, design corresponding sliding-mode surface and sliding formwork control ratio, finally constitute optimal controller.The method of the present invention utilizes and solves inequality, simplify the design procedure of controller, according to performance index function, so that carried control law inputs the optimum control under saturation conditions for actuator, the control accuracy and response speed of quadrotor are effectively increased, controller design foundation can be provided to input the quadrotor of saturation with actuator.The present invention is used for the anti-input saturation control of the quadrotor with parameter uncertainty and external disturbance.
Description
Technical Field
The invention relates to an optimal input saturation resistance control method of a four-rotor aircraft based on sliding mode control, and belongs to the technical field of aircraft control.
Background
The four-rotor aircraft is an aircraft which is driven by a motor to rotate and can take off and land vertically. Compared with the conventional rotor craft, the structure is more compact, the lifting force can be generated, and the four rotors can mutually offset the reaction torque, so that special reaction torque paddles are not needed. As an unmanned aircraft, the four-rotor aircraft has a wide prospect in the fields of civil use and military use due to the unique advantages of the four-rotor aircraft. The quad-rotor aircraft then has the characteristics of non-linearity, strong coupling, and susceptibility to external disturbances. Therefore, a more robust control method is required to ensure the flight safety and flight quality. The system inevitably has the problems of parameter uncertainty and external interference due to the uncertainty of the four-rotor aircraft and the change of the flight environment, so that the controller needs to have strong robustness to avoid the adverse effect of the uncertainty and the interference on the aircraft.
At present, a plurality of new methods for robust control theory of a four-rotor aircraft exist, but better effect is often difficult to obtain in practical application. The existence of input constraint characteristics such as actuator saturation, dead zone and time lag is a main cause of the reduction of the actual performance of closed-loop control of the flight control system, and actuator saturation is the most common one. Due to the existence of input saturation, the actuator often cannot obtain a theoretical optimal value, and even the system is unstable. Therefore, the four-rotor aircraft is subjected to input saturation resistance control so as to eliminate the adverse effect of input saturation on the four-rotor aircraft, and then safe flight is realized, so that the four-rotor aircraft has important economic and social values.
Sliding mode variable structure control is a nonlinear control method. The control of the sliding mode is discontinuous, and in the control process, the structure of a closed-loop system is continuously changed to force the state of the system to move along a pre-designed sliding mode surface and gradually slide to a state balance point, namely, the state is gradually stable. The main advantage is that once the system state quantity reaches the sliding mode surface, the system is not influenced by parameter change and external disturbance. And the optimal control seeks an optimal control strategy under the condition of meeting certain constraint conditions, so that the performance index takes a maximum value or a minimum value. The two are widely applied to the flight control system, and effective strong robustness control is provided for the flight control system.
In order to eliminate the influence of system actuator input saturation on the performance of a flight control system and realize the global stability of the system, aiming at the flight control systems with actuator saturation constraint input constraint, a model following recombination control method is provided, and the tracking performance of the flight control system is improved. Guo Yuying then has designed a novel self-adaptation reconfiguration controller based on the switching of many models, has eliminated the influence of the input constraint that the system receives to system performance, has realized the global stability of system and has tracked the asymptotic of system state quantity. However, most of the methods do not consider system parameter uncertainty and nonlinearity, and for a four-rotor aircraft with a complex structure and serious parameter uncertainty and nonlinearity, the control effect is poor, and even the aircraft is unstable.
Disclosure of Invention
The purpose of the invention is as follows: aiming at the prior art, an optimal input saturation resistance control method of the four-rotor aircraft based on sliding mode control is provided, and according to the optimal value of the performance index function J, the optimal sliding mode surface parameters and the sliding mode control law are selected to form a corresponding four-rotor aircraft controller, so that the influence of actuator saturation on the system performance is eliminated.
The technical scheme is as follows: an optimal input saturation resistance control method of a four-rotor aircraft based on sliding mode control is provided by combining optimal control when the four-rotor aircraft is considered to be saturated with an actuator, system sliding mode surface parameters and switching time are obtained through calculation on the premise that the performance index function J is guaranteed to reach an optimal value, then corresponding sliding mode surfaces and sliding mode control laws are designed through comparison of the switching time, and an optimal controller is finally formed, and the method comprises the following specific steps:
step 1), obtain four rotor crafts's control model:
wherein, F (x) ═ x2x3f(x)+Δf]T，G(x)＝[0 0 g(x)]T，Φ＝[0 0 d]TIn the formula: x ═ x1x2x3]TState variables representing the system, respectively representing the system displacement, speed and acceleration, u representing the system control input, g (x) and f (x) are nonlinear equations about the system state quantities, wherein g (x) satisfies | g (x) | < sigma, Δ f and d represent the parameter uncertainty and external interference existing in the system, and satisfies
Step 2), designing according to the flight safety and flight quality requirements of the four-rotor aircraftThe performance index function is used for reflecting the response speed and the control precision of the four-rotor aircraft, and the performance index comprises the initial time t0Error of displacement tracking e1；
Step 3), calculating each optimal sliding mode surface parameter and sliding mode surface switching time, and comprising the following steps:
step 3.1), taking the form of a sliding mode surface equation into consideration
Wherein α, A and B are scalar constants to be determinedThe number of α + β t is a full-range sliding state factor, and is required to meet α + β tf＝0，tfTime for switching the sliding mode surface;
step 3.2), combining a system model of the four-rotor aircraft and a sliding mode surface equation, the performance index function J can be converted into:
wherein,is composed of B and tfA co-determined scalar constant to be determined;
step 3.3), calculating the minimum value J of the performance index function JminAs shown in formula (4):
wherein
Step 3.4), according to the minimum value J of the performance index function JminCalculating corresponding optimal sliding mode surface parameters and switching time:
cop2≈2.7 (5)
step 4), obtaining the optimal sliding mode surface switching time t according to the step 3.4)fopJudging time and selecting a corresponding sliding mode surface;
step 4.1), when the time t is less than or equal to tfopSelecting a slip form surface s1As shown in formula (11):
s1＝α+βt+e3+Ae2+Be1(11)
step 4.2), otherwise, the time t is more than tfopSelecting a slip form surface s2As shown in formula (12):
s2＝e3+Ae2+Be1(12)
step 5), obtaining the optimal sliding mode surface switching time t according to the step 3.4)fopJudging time and selecting a corresponding sliding mode control law;
step 5.1), when the time t is less than or equal to tfopSelection of sliding mode control law u1As shown in formula (13):
step 5.2), otherwise, the time t is more than tfopSelection of sliding mode control law u2As shown in formula (14):
step 6), carrying out saturation input u on the sliding mode control law u obtained in the step 5) and the four-rotor aircraft actuatormaxComparing and judging whether the anti-input saturation control is successful or not, and forming a four-rotor aircraft controller when u is less than or equal to umaxThe four-rotor aircraft controller can be formed; and otherwise, calculating the optimal sliding mode parameters and the switching time again.
Has the advantages that: the invention provides an optimal input saturation resistance control method of a four-rotor aircraft based on sliding mode control, which considers that the four-rotor aircraft has actuator saturation and combines optimal control to provide the sliding mode control method. On the premise of ensuring that the performance index function J reaches an optimal value, calculating to obtain system sliding mode surface parameters and switching time, and then comparing the switching time to design a corresponding sliding mode surface and a corresponding sliding mode control law so as to finally form an optimal controller. Has the following specific advantages:
(1) by solving the inequality, a sliding mode control law meeting the input saturation constraint is obtained, the adverse effect of input saturation on the four-rotor aircraft is eliminated, and the input saturation constraint resistance is realized;
(2) the designed performance index function J is optimally solved to obtain corresponding optimal sliding mode surface parameters and a sliding mode control law, so that the control precision and the response speed of the four-rotor aircraft are improved, and the flight performance of the four-rotor aircraft is improved while input saturation resistance is achieved;
(3) the application of sliding mode control ensures that the quadrotor aircraft has strong robustness to uncertainty and external interference, and the introduction of sliding mode surface whole-course sliding state factors ensures the robustness of the sliding mode approaching stage, thereby realizing the global robustness.
The method used by the invention is used as an input saturation resistant control method of the four-rotor aircraft, has certain application significance, is easy to realize, has good control effect, and can effectively improve the control precision and the reaction speed of the four-rotor aircraft. The method has strong operability and convenient and reliable application.
Drawings
FIG. 1 is a flow chart of a method of the present invention;
FIG. 2 is an experimental setup Qball-X4 quad-rotor craft developed by Quanser to study quad-rotor craft control;
FIG. 3 is a coordinate axis system and symbol convention for Qball-X4;
FIG. 4 is a schematic view of the position control system in the direction of the predetermined X axis of Qball-X4;
FIG. 5 is a Qball-X4 desired displacement tracking curve and an actual displacement tracking curve;
FIGS. 6-7 are plots of the Qball-X4 displacement tracking error e1, velocity tracking error e2, and acceleration tracking error e 3;
FIG. 8 is a Qball-X4 actuator input u curve.
Detailed Description
The invention is further explained below with reference to the drawings.
As shown in fig. 1, an optimal input saturation resistance control method for a four-rotor aircraft based on sliding mode control considers that the four-rotor aircraft has actuator saturation, combines optimal control, and provides a sliding mode control method, wherein system sliding mode surface parameters and switching time are obtained by calculation on the premise of ensuring that a performance index function J reaches an optimal value, and then corresponding sliding mode surfaces and sliding mode control laws are designed by comparing the switching time, so that an optimal controller is finally formed, and the method comprises the following specific steps:
step 1), obtain four rotor crafts's control model:
wherein, F (x) ═ x2x3f(x)+Δf]T，G(x)＝[0 0 g(x)]T，Φ＝[0 0 d]TIn the formula: x ═ x1x2x3]TState variables representing the system, respectively representing the system displacement, speed and acceleration, u representing the system control input, g (x) and f (x) are nonlinear equations about the system state quantities, wherein g (x) satisfies | g (x) | < sigma, Δ f and d represent the parameter uncertainty and external interference existing in the system, and satisfies
Step 2), designing according to the flight safety and flight quality requirements of the four-rotor aircraftThe performance index function is used for reflecting the response speed and the control precision of the four-rotor aircraft, and the performance index comprises the initial time t0Error of displacement tracking e1；
Step 3), calculating each optimal sliding mode surface parameter and sliding mode surface switching time, and comprising the following steps:
step 3.1), taking the form of a sliding mode surface equation into consideration
Wherein α, A and B are scalar constants to be determined, α + β t is a full-range sliding factor, and the requirement of α + β t is satisfiedf＝0，tfTime for switching the sliding mode surface;
step 3.2), combining a system model of the four-rotor aircraft and a sliding mode surface equation, the performance index function J can be converted into:
wherein,is composed of B and tfA co-determined scalar constant to be determined;
step 3.3), calculating the minimum value J of the performance index function JminAs shown in formula (4):
wherein
Step 3.4), according to the minimum value J of the performance index function JminCalculating corresponding optimal sliding mode surface parameters and switching time:
cop2≈2.7 (5)
step 4), obtaining the optimal sliding mode surface switching time t according to the step 3.4)fopJudging time and selecting a corresponding sliding mode surface;
step 4.1), when the time t is less than or equal to tfopSelecting a slip form surface s1As shown in formula (11):
s1＝α+βt+e3+Ae2+Be1(11)
step 4.2), otherwise, the time t is more than tfopSelecting a slip form surface s2As shown in formula (12):
s2＝e3+Ae2+Be1(12)
step 5), obtaining the optimal sliding mode surface switching time t according to the step 3.4)fopJudging time and selecting a corresponding sliding mode control law;
step 5.1), when the time t is less than or equal to tfopSelection of sliding mode control law u1As shown in formula (13):
step 5.2), otherwise, the time t is more than tfopSelection of sliding mode control law u2As shown in formula (14):
step 6), carrying out saturation input u on the sliding mode control law u obtained in the step 5) and the four-rotor aircraft actuatormaxComparing and judging whether the anti-input saturation control is successful or not, and forming a four-rotor aircraft controller when u is less than or equal to umaxThe four-rotor aircraft controller can be formed; otherwise, it is repeatedAnd calculating the optimal sliding mode parameters and switching time.
The foregoing is only a preferred embodiment of the present invention, and it should be noted that, for those skilled in the art, various modifications and decorations can be made without departing from the principle of the invention, and these modifications and decorations should also be regarded as the protection scope of the present invention,
the effectiveness of the implementation is illustrated in the following by a practical case simulation.
An experimental device Qball-X4 developed by Quanser company for studying control of a four-rotor aircraft was used as an application study object, and Qball-X4 is shown in FIG. 2. A Qball-X4 quad-rotor vehicle has six-dimensional variables (X, Y, Z, psi, theta, phi) where X, Y, Z are position variables, psi is yaw angle, theta is pitch angle, and phi is roll angle. The Qball-X4 body coordinate system OXYZ is established as shown in FIG. 3. Assuming that the pitch angle theta, the roll angle phi and the yaw angle psi of the Qball aircraft are all zero, the Qball performs the flat flight motion. Without loss of generality, the linear motion control is only carried out in the X axis direction, and the displacement, the speed and the acceleration of the linear motion control in the X axis direction are taken as system state quantities, and FIG. 4 is a schematic diagram of a position control system in the preset X axis direction of Qball-X4.
Qball-X4 satisfies the following equation of state:
F(x)＝[x2x3x1x2+Δf]T
G(x)＝[0 0 1]T
Φ＝[0 0 d]T
considering the common parameter uncertainty form in the aircraft and the external interference (such as airflow disturbance) easily encountered in the flight process, the parameter uncertainty existing in the system in the experiment isMeanwhile, the system is subjected to external interference d ═ 0.6sin (10 t).
The tracking signal of Qball on the X-axis is required to be: x is the number of1dSin (t +2.2), because the power supply of Qball is two three-core 2500mAh lithium batteries, the measured input quantity of the actuator needs to meet the restriction requirement that u is less than or equal to 10 v.
Taking the state quantity vector of the system at the initial moment as:
x0＝[x10x20x30]T＝[1.8085 -0.5885 -0.8085]T
according to the method, the Qball-X4 four-rotor aircraft with actuator input saturation is controlled, and the results of input saturation resistance control are shown in the figures 5-8. FIG. 5 is a Qball-X4 required displacement tracking curve and an actual displacement tracking curve; FIGS. 6-7 are plots of the Qball-X4 displacement tracking error e1, velocity tracking error e2, and acceleration tracking error e 3; FIG. 8 is a Qball-X4 actuator input u curve.
As can be seen from fig. 5, at the initial time, there is an initial error in the displacement tracking of the Qball in the X axis, and there is a parameter uncertainty and an external disturbance at the same time. Fig. 6 and 7 show that, in this case, the input saturation resistance control method of the quadrotor based on sliding mode control and optimal control can ensure that the Qball can still quickly track the specified target displacement, speed and acceleration, so that the tracking errors of the displacement, speed and acceleration are quickly converged to zero. The Qball-X4 control input curve of fig. 8 shows that the sliding mode control law, i.e. the absolute value of the input quantity of the actuator is always smaller than the input constraint value condition, and is kept in the range of 10v, and it can be calculated that the minimum value of the performance index of the system under the control is J1min0.95. The input saturation resistant control method of the four-rotor aircraft based on sliding mode control and optimal control can not only eliminate the malignant influence of input saturation on the four-rotor aircraft, but also ensure the control precision and the reaction speed of the aircraftAnd (4) degree.
Claims (1)
1. An optimal input saturation resistance control method of a four-rotor aircraft based on sliding mode control is characterized by comprising the following steps: considering that the four-rotor aircraft has actuator saturation, combining with optimal control, providing a sliding mode control method, calculating to obtain system sliding mode surface parameters and switching time on the premise of ensuring that the performance index function J reaches an optimal value, and then designing corresponding sliding mode surfaces and sliding mode control laws by comparing the switching time to finally form an optimal controller, wherein the method comprises the following specific steps:
step 1), obtain four rotor crafts's control model:
wherein, F (x) ═ x2x3f(x)+Δf]T，G(x)＝[0 0 g(x)]T，Φ＝[0 0 d]TIn the formula: x ═ x1x2x3]TState variables representing the system, respectively representing the system displacement, speed and acceleration, u representing the system control input, g (x) and f (x) are nonlinear equations about the system state quantities, wherein g (x) satisfies | g (x) | < sigma, Δ f and d represent the parameter uncertainty and external interference existing in the system, and satisfies
Step 2), designing according to the flight safety and flight quality requirements of the four-rotor aircraftThe performance index function is used for reflecting the response speed and the control precision of the four-rotor aircraft, and the performance index comprises the initial time t0Error of displacement tracking e1；
Step 3), calculating each optimal sliding mode surface parameter and sliding mode surface switching time, and comprising the following steps:
step 3.1), taking the form of a sliding mode surface equation into consideration
Wherein α, A and B are scalar constants to be determined, α + β t is a full-range sliding factor, and the requirement of α + β t is satisfiedf＝0，tfTime for switching the sliding mode surface;
step 3.2), combining a system model of the four-rotor aircraft and a sliding mode surface equation, the performance index function J can be converted into:
wherein,is composed of B and tfA co-determined scalar constant to be determined;
step 3.3), calculating the minimum value J of the performance index function JminAs shown in formula (4):
wherein
Step 3.4), according to the minimum value J of the performance index function JminCalculating corresponding optimal sliding mode surface parameters and switching time:
cop2≈2.7 (5)
step 4), obtaining the optimal sliding mode surface switching time t according to the step 3.4)fopPerforming time judgment and selecting correspondingA slip form surface;
step 4.1), when the time t is less than or equal to tfopSelecting a slip form surface s1As shown in formula (11):
s1＝α+βt+e3+Ae2+Be1(11)
step 4.2), otherwise, the time t is more than tfopSelecting a slip form surface s2As shown in formula (12):
s2＝e3+Ae2+Be1(12)
step 5), obtaining the optimal sliding mode surface switching time t according to the step 3.4)fopJudging time and selecting a corresponding sliding mode control law;
step 5.1), when the time t is less than or equal to tfopSelection of sliding mode control law u1As shown in formula (13):
step 5.2), otherwise, the time t is more than tfopSelection of sliding mode control law u2As shown in formula (14):
step 6), carrying out saturation input u on the sliding mode control law u obtained in the step 5) and the four-rotor aircraft actuatormaxComparing and judging whether the anti-input saturation control is successful or not, and forming a four-rotor aircraft controller when u is less than or equal to umaxThe four-rotor aircraft controller can be formed; and otherwise, calculating the optimal sliding mode parameters and the switching time again.
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| CN105911866B (en) * | 2016-06-15 | 2019-01-22 | 浙江工业大学 | Finite time full-order sliding mode control method of four-rotor unmanned aerial vehicle |
| CN106597851B (en) * | 2016-12-15 | 2019-04-30 | 南京航空航天大学 | A kind of robust Fault-Tolerant Control method of small drone flight control system |
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| CN106774273B (en) * | 2017-01-04 | 2019-01-01 | 南京航空航天大学 | For the algorithm based on sliding mode prediction fault tolerant control method of time_varying delay control system actuator failures |
| CN108345212A (en) * | 2017-01-24 | 2018-07-31 | 南京航空航天大学 | A kind of robust H of the Three Degree Of Freedom helicopter based on sliding formwork∞Control method |
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| CN108267956B (en) * | 2018-01-23 | 2019-05-28 | 蓝箭航天空间科技股份有限公司 | Flight control method based on sliding formwork control |
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