CN111694276A - Robust control research method for uncertain fractional order switching system - Google Patents
Robust control research method for uncertain fractional order switching system Download PDFInfo
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- CN111694276A CN111694276A CN202010533978.XA CN202010533978A CN111694276A CN 111694276 A CN111694276 A CN 111694276A CN 202010533978 A CN202010533978 A CN 202010533978A CN 111694276 A CN111694276 A CN 111694276A
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- G05B—CONTROL OR REGULATING SYSTEMS IN GENERAL; FUNCTIONAL ELEMENTS OF SUCH SYSTEMS; MONITORING OR TESTING ARRANGEMENTS FOR SUCH SYSTEMS OR ELEMENTS
- G05B13/00—Adaptive control systems, i.e. systems automatically adjusting themselves to have a performance which is optimum according to some preassigned criterion
- G05B13/02—Adaptive control systems, i.e. systems automatically adjusting themselves to have a performance which is optimum according to some preassigned criterion electric
- G05B13/04—Adaptive control systems, i.e. systems automatically adjusting themselves to have a performance which is optimum according to some preassigned criterion electric involving the use of models or simulators
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Abstract
The invention aims to provide a robust control research method of an uncertain fractional order switching system, which researches the basic steps of the design of a state feedback controller of a common fractional order switching system on the basis of researching the stability criterion of the fractional order switching system; the general idea of designing a robust controller of an uncertain fractional order switching system is researched by analyzing various uncertain links in the system; researching the general steps of designing robust controllers under limited switching conditions and any switching conditions; a general method for controlling an integer order system by switching a plurality of fractional order controllers is researched, and a set of complete robust control theory of an uncertain fractional order switching system is provided.
Description
Technical Field
The invention relates to the field of robust control, in particular to a robust control research method of an uncertain fractional order switching system.
Background
The control of the fractional order system has been a leading issue in the research of control theory, and has been attracting much attention in recent years, but it is still in the initial stage of research, and many problems have not been involved or discussed in depth. In the current research, the switching control of the fractional order system and the robust control of the fractional order system are often studied separately, and few documents report the robust control problem of the fractional order switching system. With the rapid development of computer technology and digital signal processors, the robust control problem of fractional order switching systems is now that switching control strategies are widely adopted, that is, how to design a controller to ensure that the system can still meet certain control performance when various uncertain factors exist, and the problem becomes a main problem which must be solved when the system is in practical engineering.
Disclosure of Invention
The invention aims to provide a robust control research method of an uncertain fractional order switching system, which researches the stability criterion of the fractional order switching system on the basis of deeply researching the stability criterion of the fractional order system; then, the research model determines a general method for designing a controller of the fractional order switching system; then, carrying out system analysis on the uncertain fractional order switching control system, and analyzing the influence of parameter uncertainty on system stability and system performance; further researching the influence of a switching control strategy on the stability of the fractional order switching system, the performance influence of the fractional order switching system containing uncertainty, and the possible influence of different switching rules on the system performance; the general procedure for designing an uncertain fractional order switching system controller was investigated. And finally, modeling the motion control problem, analyzing uncertainty in the system, and researching the application problem of the robust controller containing the uncertain fractional order switching system.
The invention provides a robust control research method of an uncertain fractional order switching system, which comprises the following steps of (1) establishing a research model, determining a stability criterion of the fractional order switching system, and giving a linear matrix inequality expression form of the stability of the fractional order switching system by adopting the auxiliary design of tools such as a linear matrix inequality and the like; (2) on the basis of stability, a method similar to an integer order system is adopted, a public secondary Lyapunov function or a multiple Lyapunov function method is adopted to give a state feedback control law for determining a fractional order switching system on the basis of bounded real guiding theory; (3) given a corresponding H2/H∞Controlling the performance index; (4) and the fractional order controller is used for controlling the integer order motion control system to be applied by combining a space control technology and an inertia technology.
The further improvement lies in that: in the step 1, the stability criterion of the fractional order switching system is determined by a common quadratic Lyapunov function and a multiple Lyapunov function method through the congruent transformation of a matrix and the integral transformation method of a Gamma function and combining the stability criterion of the integer order switching system on the basis of the Riemann-Liouville or Caputo definition of fractional order calculus.
The further improvement lies in that: in step 2, the stability of the fractional order switching system in the Lyapunov stability frame is determined, then the controller stabilizing original system of the fractional order switching control system under any switching condition is analyzed, and the existence condition of a state feedback matrix meeting the stability theorem is given when the switching condition is limited.
The further improvement lies in that: and 3, decomposing the uncertainty of the fractional order switching system into two parts which meet the matching condition and do not meet the matching condition, giving a stable LMI solution of the robust controller of the uncertain fractional order switching system by using a method of a completeness condition and a multiple Lyapunov function when the system state matrix and the control input matrix exist simultaneously or only one matrix exists, and designing a state feedback array and a switching control mode corresponding to the robust state controller.
The further improvement lies in that: and 4, constructing more than two different fractional order switching controllers, and giving corresponding state feedback control laws and switching conditions based on the proposed robust control strategy of the fractional order switching control system to realize performance indexes such as high-precision positioning, quick response and the like.
The invention has the beneficial effects that: the basic steps of designing a state feedback controller of a general fractional order switching system are researched on the basis of researching the stability criterion of the fractional order switching system; the general idea of designing a robust controller of an uncertain fractional order switching system is researched by analyzing various uncertain links in the system; researching the general steps of designing robust controllers under limited switching conditions and any switching conditions; a general method of controlling an integer-order system by switching a plurality of fractional-order controllers is studied. The stability of the fractional order system is greatly different from that of the integer order system, and the structural form and the switching rule of the state feedback array in the design process of the controller are also different from those of the integer order system to a certain extent, so that the controller is more innovative.
Drawings
Fig. 1 is a schematic block diagram of a turntable control system.
FIG. 2 is a schematic block diagram of a servo system.
Fig. 3 is a balance equation.
Detailed Description
For the purpose of enhancing understanding of the present invention, the present invention will be further described in detail with reference to the following examples, which are provided for illustration only and are not to be construed as limiting the scope of the present invention.
The embodiment provides a robust control research method for an uncertain fractional order switching system, which is characterized in that: establishing a research model, determining a stability criterion of a fractional order switching system, and determining the stability criterion of the fractional order switching system on the basis of Riemann-Liouville or Caputo definition of fractional order calculus through the congruent transformation of a matrix, an integral transformation method of a Gamma function and the stability criterion of the integer order switching system by adopting a common secondary Lyapunov function and a multi-Lyapunov function method; the method comprises the following steps of providing a linear matrix inequality representation form of fractional order switching system stability by adopting auxiliary design of tools such as a linear matrix inequality; (2) on the basis of stability, a method similar to an integer order system is adopted, a bounded real guiding principle is adopted, a public secondary Lyapunov function or a multiple Lyapunov function method is adopted to give a state feedback control law for determining a fractional order switching system, the stability of the fractional order switching system in a Lyapunov stability frame is determined, a controller of the fractional order switching control system under any switching condition is analyzed, and the existence condition of a state feedback array meeting the stability theorem is given when the switching condition is limited; (3) given a corresponding H2/H∞Controlling performance indexes, decomposing uncertainty of the fractional order switching system into two parts which meet matching conditions and do not meet the matching conditions, when a system state matrix and a control input matrix exist at the same time or only one matrix exists, providing a stable LMI solution of a robust controller of the uncertain fractional order switching system by using a method of a completeness condition and a multiple Lyapunov function, and designing a state feedback array and a switching control mode corresponding to the robust state controller; (4) combining spatial control with inertial techniquesThe fractional order controller is used for controlling the integer order motion control system, more than two different fractional order switching controllers are constructed, and corresponding state feedback control laws and switching conditions are given based on the proposed robust control strategy of the fractional order switching control system, so that performance indexes such as high-precision positioning, quick response and the like are realized.
According to the characteristics of a continuous-discrete generalized fractional order system and a generalized system, some control methods widely applied to the continuous-discrete system and the generalized system are processed and then are also applicable to the continuous-discrete generalized piecewise affine system to some extent, so that the continuous-discrete generalized piecewise affine system is adopted as a main method and an experimental means depending on the implementation process.
As shown in fig. 1-3, through the construction of the actual turntable system, three free shafts of the three-shaft turntable adopted by the turntable system are all driven by the conventional direct current torque motor, wherein: the control azimuth axis adopts a traditional direct current torque motor (101), the pitching axis adopts two traditional direct current torque motors (102, 103), two motor windings of the pitching axis do not work simultaneously, and a two-stage series connection mode is adopted during wiring so as to ensure the synchronism of the pitching axis during working. The mathematical modeling of the three-axis turntable is carried out by adopting a physical derivation method, the controlled object is a table surface axis of the turntable, and the mathematical model of the load part can derive the kinetic equation of the three-axis turntable according to the mechanical principle of the three-axis turntable as follows:
。
in the above formula, the first and second carbon atoms are,
is the output torque of the motor and is,
the disturbance moment for the turntable surface shaft, the moment of inertia of the motor rotor, and the moment of inertia of the load,
is the rotation angle of the rotary table and the damping coefficient of the motor rotor,
is the damping coefficient of the load. Wherein: the additional torque generated by the free rotor of the motor and its load is expressed by the torque, also called motor disturbance torque, used later
Instead, the result is thus simplified
Wherein the content of the first and second substances,
，
. Through derivation, the output torque of the three motors is obtained, and an electrical equation of an internal system of the motor can be derived through a load dynamics equation.
The direct-current torque motor is used as a component of a driving system, and a model of the motor is summarized according to an electrical principle as follows
Is a coefficient of the electromagnetic torque and is,
is the current of the armature circuit of the motor,
for the input of the voltage to the motor,
in order to determine the angular velocity of rotation of the azimuth axis,
in order to induce an electromotive force, a magnetic field is generated,
is the back emf coefficient and is the resistance of the armature circuit.
And processing the electrical equation of the internal system of the motor and the output torque of the motor by adopting Laplace transformation to obtain a balance equation.
The direction angle of the three-axis turntable azimuth axis can be obtained by measurement, and the moment of the free axis in the turntable control system in the vertical direction of the table top can be obtained by measurement
As input to the control system, after the system has been in operation for some time, the angular velocity of the azimuth axis is maintained
At constant, the final control objective:
。
and debugging an actual turntable control system, verifying a main result by adopting a numerical simulation mode before debugging, acquiring data and arranging samples on the spot, and obtaining a static output feedback controller gain matrix and an observer performance matrix to be sought by adopting a mincx solver of an LMI toolbox in Matlab 7.0.
The purpose that the system has enough adjustment space to meet different performance requirements is finally achieved by carrying out non-fragile stable control on the system, so that the system is stabilized by utilizing state feedback control, and convenience is provided for fault diagnosis of the system.
Claims (5)
1. A robust control research method of an uncertain fractional order switching system is characterized in that: establishing a research model, determining a stability criterion of a fractional order switching system, and providing a linear matrix inequality expression form of the stability of the fractional order switching system by adopting the auxiliary design of tools such as a linear matrix inequality and the like; (2) in the stability groupOn the basis, a method similar to an integer order system is adopted, a public secondary Lyapunov function or a multiple Lyapunov function method is adopted to give a state feedback control law for determining a fractional order switching system based on a bounded real guiding principle; (3) given a corresponding H2/H∞Controlling the performance index; (4) and the fractional order controller is used for controlling the integer order motion control system to be applied by combining a space control technology and an inertia technology.
2. The robust control research method of the uncertain fractional order switching system as claimed in claim 1, wherein: in the step 1, the stability criterion of the fractional order switching system is determined by a common quadratic Lyapunov function and a multiple Lyapunov function method through the congruent transformation of a matrix and the integral transformation method of a Gamma function and combining the stability criterion of the integer order switching system on the basis of the Riemann-Liouville or Caputo definition of fractional order calculus.
3. The robust control research method of the uncertain fractional order switching system as claimed in claim 1, wherein: in step 2, the stability of the fractional order switching system in the Lyapunov stability frame is determined, then the controller stabilizing original system of the fractional order switching control system under any switching condition is analyzed, and the existence condition of a state feedback matrix meeting the stability theorem is given when the switching condition is limited.
4. The robust control research method of the uncertain fractional order switching system as claimed in claim 1, wherein: and 3, decomposing the uncertainty of the fractional order switching system into two parts which meet the matching condition and do not meet the matching condition, giving a stable LMI solution of the robust controller of the uncertain fractional order switching system by using a method of a completeness condition and a multiple Lyapunov function when the system state matrix and the control input matrix exist simultaneously or only one matrix exists, and designing a state feedback array and a switching control mode corresponding to the robust state controller.
5. The robust control research method of the uncertain fractional order switching system as claimed in claim 1, wherein: and 4, constructing more than two different fractional order switching controllers, and giving corresponding state feedback control laws and switching conditions based on the proposed robust control strategy of the fractional order switching control system to realize performance indexes such as high-precision positioning, quick response and the like.
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| CN112658920A (en) * | 2020-12-17 | 2021-04-16 | 安徽工程大学 | Special pneumatic control-based piston skirt porous grinding machine and force control method thereof |
Citations (4)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN104639001A (en) * | 2015-01-22 | 2015-05-20 | 广州市香港科大霍英东研究院 | Servo motor control method integrating sliding mode control and fractional order neural network control |
| CN105204341A (en) * | 2015-09-25 | 2015-12-30 | 西安石油大学 | Robust tracking control method of network control system based on switching control theory |
| CN107070336A (en) * | 2017-02-24 | 2017-08-18 | 沈阳工业大学 | The two patterns paste fractional order System with Sliding Mode Controller and method of permanent magnet linear synchronous motor |
| CN107248822A (en) * | 2017-07-17 | 2017-10-13 | 南京信息工程大学 | Inverter control method based on Fractional Order PID discrete sliding mode structure changes |
-
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Patent Citations (4)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN104639001A (en) * | 2015-01-22 | 2015-05-20 | 广州市香港科大霍英东研究院 | Servo motor control method integrating sliding mode control and fractional order neural network control |
| CN105204341A (en) * | 2015-09-25 | 2015-12-30 | 西安石油大学 | Robust tracking control method of network control system based on switching control theory |
| CN107070336A (en) * | 2017-02-24 | 2017-08-18 | 沈阳工业大学 | The two patterns paste fractional order System with Sliding Mode Controller and method of permanent magnet linear synchronous motor |
| CN107248822A (en) * | 2017-07-17 | 2017-10-13 | 南京信息工程大学 | Inverter control method based on Fractional Order PID discrete sliding mode structure changes |
Non-Patent Citations (2)
| Title |
|---|
| XUEFENG ZHANG等: "Stability and robust stabilization of uncertain switched fractional order systems", 《ISA TRANSACTIONS》 * |
| 王荣浩等: "具有时变时滞不确定切换系统的鲁棒H∞可靠控制", 《南京航空航天大学学报》 * |
Cited By (1)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN112658920A (en) * | 2020-12-17 | 2021-04-16 | 安徽工程大学 | Special pneumatic control-based piston skirt porous grinding machine and force control method thereof |
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