CN110554601A - Design method and device of anti-interference PID controller - Google Patents
Design method and device of anti-interference PID controller Download PDFInfo
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Abstract
the invention provides a design method of an anti-interference PID controller, which comprises the steps of constructing an anti-interference PID control structure, wherein the anti-interference PID control structure comprises a prefilter and a PID feedback controller; for the established anti-interference PID control structure, carrying out equivalent transformation of a structure diagram through anti-interference control designed by a control system to obtain the structure of a pre-filter and the structure of a PID feedback controller; determining the final form of the anti-interference PID control structure according to the relative order of the controlled system; and selecting parameters of the anti-interference PID control structure. The invention also provides a design device of the anti-interference PID controller. The invention has the advantages that: the anti-interference PID controller designed by the technical scheme of the invention has active anti-interference capability and better robustness; meanwhile, the parameters are less selected, the physical significance is clear, and the control effect is excellent.
Description
Technical Field
the invention relates to the field of industrial control, in particular to a design method and a device of an anti-interference PID controller.
background
In industrial control, proportional-integral-derivative (PID) controllers are widely used because PID controllers have the characteristics of simple structure, strong robustness, and the like. Compared with the existing advanced control technology, for example: active Disturbance Rejection Control (ADRC), etc., PID control is considered as a control method with relatively poor performance.
At present, the research on PID control technology and application is very much, but an active disturbance rejection control scheme of a PID controller still remains blank, and the disturbance rejection control mechanism is still unclear. Although there are related patent technologies (for example, a method for setting a reduced-order active disturbance rejection controller parameter based On a PID controller disclosed in chinese patent application No. 201910035745.4 with application date of 2019.01.15) and a paper [ On The Characteristics of adaptive api interpolation ] both trying to establish a relationship between a PID controller and an active disturbance rejection controller, a setting formula of a PID controller is too complex, and in a feedback channel, other dynamic compensators are required in addition to The PID controller, so that both a disturbance rejection mechanism and a setting method of a controller parameter are to be improved.
Disclosure of Invention
the invention aims to solve the technical problem of providing a design method and a device of an anti-interference PID controller, and solves the problems that the setting formula of the existing PID controller is too complex, and other dynamic compensators are needed in a feedback channel besides the PID controller.
The invention is realized by the following steps: a method of designing an immunity PID controller, the method comprising the steps of:
Step S1, constructing an anti-interference PID control structure, wherein the anti-interference PID control structure comprises a prefilter F (S) and a PID feedback controller C (S); the pre-filter F(s) is used for realizing smooth filtering of a tracking signal, and the PID feedback controller C(s) is used for realizing closed-loop control of a control system;
step S2, carrying out equivalent transformation of a structure diagram on the established anti-interference PID control structure through anti-interference control designed by a control system, wherein the equivalent transformation comprises feedback equivalent transformation and equivalent unit feedback transformation to obtain the structure of a pre-filter F (S) and the structure of a PID feedback controller C (S);
step S3, determining the final form of the anti-interference PID control structure according to the relative order of the controlled system;
and step S4, selecting parameters of the anti-interference PID control structure.
Further, in step S2, the prefilter f (S) is configured to:
Wherein the content of the first and second substances,For a desired closed loop system, τca time constant representing a desired closed loop system;For disturbance estimation of the filter, tauqrepresenting the time constant of the disturbance observer.
Further, in step S2, the PID feedback controller c (S) is configured to:
the PID feedback controller C(s) has the form of PI-PD;
Wherein the PD controller is in the form of Cpd(s)＝kpd(1+kds) connected in series with the object G(s) to be controlled and G (∞) Cpd(∞)＝HR(∞) to realize high-frequency series compensation of controlled object G(s); the PI controller is in the form ofThe PI controller is an equivalent form of a disturbance observer, and the parameter of the PI controller is directly measured by taucAnd τqAnd (4) determining.
Further, the step S3 is specifically:
Determining a final form of the anti-interference PID control structure according to the relative order l ═ r.deg [ G ] of a controlled system, and specifically comprising:
When l is 1, there are:
Wherein, b*/a*High-frequency gain of controlled object G(s), i.e. G (∞) ═ b*/a*；
When l is 2, there are:
Wherein, b*/a*High-frequency gain of controlled object G(s), i.e. G (∞) ═ b*/a*；
When l is greater than 2, the controlled system is reduced in order and converted into the condition of l being 1 or l being 2 for processing.
Further, the step S4 is specifically:
Determining a time constant τ based on rapidity index of control system designcand makeequal to desired closed loop system HR(s) a bandwidth; selectingAs a parameter of the disturbance rejection PID control structure, wherein,the bandwidth of the filter q(s) is estimated for the disturbance.
the invention is realized by the following steps: a design device of an anti-interference PID controller comprises a PID structure construction module, an equivalent transformation module, a form determination module and a parameter selection module;
The PID structure construction module is used for constructing an anti-interference PID control structure, and the anti-interference PID control structure comprises a prefilter F(s) and a PID feedback controller C(s); the pre-filter F(s) is used for realizing smooth filtering of a tracking signal, and the PID feedback controller C(s) is used for realizing closed-loop control of a control system;
the equivalent transformation module is used for carrying out equivalent transformation of a structure diagram on the established anti-interference PID control structure through anti-interference control designed by a control system, wherein the equivalent transformation comprises feedback equivalent transformation and equivalent unit feedback transformation to obtain the structure of a pre-filter F(s) and the structure of a PID feedback controller C(s);
the form determining module is used for determining the final form of the anti-interference PID control structure according to the relative order of the controlled system;
And the parameter selection module is used for selecting the parameters of the anti-interference PID control structure.
Further, in the equivalent transformation module, the prefilter f(s) is configured to:
Wherein the content of the first and second substances,For a desired closed loop system, τca time constant representing a desired closed loop system;For disturbance estimation of the filter, tauqRepresenting the time constant of the disturbance observer.
Further, in the equivalent transformation module, the PID feedback controller c(s) is configured to:
the PID feedback controller C(s) has the form of PI-PD;
Wherein the PD controller is in the form of Cpd(s)＝kpd(1+kds) connected in series with the object G(s) to be controlled and G (∞) Cpd(∞)＝HR(∞) to realize high-frequency series compensation of controlled object G(s); the PI controller is in the form ofThe PI controller is an equivalent form of a disturbance observer, and the parameter of the PI controller is directly measured by taucand τqAnd (4) determining.
further, the form determination module specifically includes:
Determining a final form of the anti-interference PID control structure according to the relative order l ═ r.deg [ G ] of a controlled system, and specifically comprising:
When l is 1, there are:
Wherein, b*/a*High-frequency gain of controlled object G(s), i.e. G (∞) ═ b*/a*；
when l is 2, there are:
wherein, b*/a*High-frequency gain of controlled object G(s), i.e. G (∞) ═ b*/a*；
When l is greater than 2, the controlled system is reduced in order and converted into the condition of l being 1 or l being 2 for processing.
Further, the parameter selection module specifically comprises:
determining a time constant τ based on rapidity index of control system designcand makeEqual to desired closed loop system HR(s) a bandwidth; selectingas a parameter of the disturbance rejection PID control structure, wherein,the bandwidth of the filter q(s) is estimated for the disturbance.
The invention has the following advantages: the anti-interference PID controller designed by the technical scheme of the invention has active anti-interference capability, and the parameters of the controller and the anti-interference performance have definite regulation relation; when the object model is inaccurate, the anti-interference PID controller can treat the uncertainty as the internal disturbance of the control system, so that the anti-interference PID controller designed by the technical scheme of the invention has better robustness; meanwhile, in the technical scheme designed by the invention, the parameters are less selected, the physical significance is clear, and the control effect is excellent.
drawings
The invention will be further described with reference to the following examples with reference to the accompanying drawings.
FIG. 1 is a schematic diagram of the anti-interference PID control structure of the present invention.
FIG. 2 is a schematic diagram of a magnetic levitation physical system in an embodiment of the present invention.
fig. 3a is a diagram illustrating the simulation effect of the control output of the magnetic levitation physical system in the embodiment of the present invention.
Fig. 3b is a diagram illustrating the simulation effect of the control input of the magnetic levitation physical system in the embodiment of the present invention.
FIG. 4a is a control output experimental graph of a magnetic levitation physical system in an embodiment of the present invention.
Fig. 4b is a control input experimental diagram of a magnetic levitation physical system in an embodiment of the present invention.
FIG. 5 is a flow chart of the implementation of a design method of an anti-interference PID controller according to the invention.
Fig. 6 is a schematic block diagram of a design device of an anti-interference PID controller according to the present invention.
Detailed Description
Referring to fig. 1 to 6, the design method and apparatus for an anti-interference PID controller of the present invention are shown, in order to overcome the problems that the setting formula of the existing PID controller is too complex and other dynamic compensators are needed in the feedback channel besides the PID controller; the invention obtains the anti-interference design method of the PID controller by establishing the association of the anti-interference control and the PID feedback control, and the general inventive concept of the invention is as follows: the design control system consists of a pre-filter and a PID feedback controller, wherein the pre-filter has the effect of smoothing filtering of an input signal so as to overcome the impact on the control system caused by the jump of the input signal; the PID feedback controller is in a PI-PD controller form, wherein the PD controller is used for realizing high-frequency compensation of an object, and the PI controller is an equivalent disturbance observer; the final form of the anti-interference PID controller is determined by the relative order of the objects, and the parameters of the anti-interference PID controller are selected and determined according to the anti-interference control principle. The anti-interference PID controller designed by the technical scheme of the invention has active anti-interference capability, and the parameters of the controller and the anti-interference performance have definite regulation relation; when the object model is inaccurate, the anti-interference PID controller can treat the uncertainty as the internal disturbance of the control system, so that the anti-interference PID controller designed by the technical scheme of the invention has better robustness; meanwhile, in the technical scheme designed by the invention, the parameters are less selected, the physical significance is clear, and the control effect is excellent.
the following detailed description will be made of a design method of an anti-interference PID controller according to a specific embodiment, as shown in fig. 1, where fig. 1 shows a process of deriving an anti-interference PID controller from a type of anti-interference controller; as can be seen from the figure 1, the original anti-interference control system takes G(s) as a controlled object and designs a pre-compensator Cpd(s) such that G(s) CpdDynamic behavior of(s) and desired closed loop transfer function HR(s) proximity (i.e., model matching is achieved), G(s) Cpd(s) and HRThe model error of(s) is an internal disturbance that the control system needs to overcome. In our design, we let G (∞) Cpd(∞)＝HR(∞) so as to ensure that the high-frequency disturbance inside the control system is approximately zero; at the same time to HR(s) inverting for estimating disturbances and feedback compensation; based on the principle, obtaining an equivalent two-degree-of-freedom feedback control structure, which comprises a prefilter F(s) and a feedback controller C(s);
as shown in fig. 5, the method comprises the steps of:
Step S1, constructing an anti-interference PID control structure, wherein the anti-interference PID control structure comprises a prefilter F (S) and a PID feedback controller C (S); the pre-filter F(s) is used for realizing smooth filtering of the tracking signal, and a transition process is arranged to prevent the control system impact problem caused by input signal jump; the PID feedback controller C(s) is used for realizing closed-loop control on the control system so as to reduce the tracking error of the control system and improve the robust stability of the control system;
step S2, carrying out equivalent transformation of a structure diagram on the established anti-interference PID control structure through anti-interference control designed by a control system, wherein the equivalent transformation comprises feedback equivalent transformation and equivalent unit feedback transformation to obtain the structure of a pre-filter F (S) and the structure of a PID feedback controller C (S);
Step S3, determining the final form of the anti-interference PID control structure according to the relative order of the controlled system;
And step S4, selecting parameters of the anti-interference PID control structure.
In step S2, the prefilter f (S) is configured to:
Wherein the content of the first and second substances,For a desired closed loop system, τcA time constant representing a desired closed loop system;For disturbance estimation of the filter, tauqRepresenting the time constant of the disturbance observer.
in step S2, the PID feedback controller c (S) is configured to:
The PID feedback controller C(s) has the form of PI-PD;
Wherein the PD controller is in the form of Cpd(s)＝kpd(1+kds) connected in series with the object G(s) to be controlled and G (∞) Cpd(∞)＝HRThe infinity is used for realizing high-frequency series compensation of the controlled object G(s), and the internal disturbance of the control system in a high-frequency section can be approximate to zero after the series compensation in the high-frequency section, so that the robust stability of the control system is greatly enhanced; the PI controller is in the form ofThe PI controller is an equivalent form of a disturbance observer, and the parameter of the PI controller is directly measured by taucAnd τqAnd (4) determining.
In the present invention, the step S3 specifically includes:
determining a final form of the anti-interference PID control structure according to a relative order l ═ r.deg [ G ], wherein the final form is mainly divided into three cases of l ═ 1, l ═ 2 and l > 2, and the method specifically comprises the following steps:
When l is 1, there are:
wherein, b*/a*High-frequency gain of controlled object G(s), i.e. G (∞) ═ b*/a*；
when l is 2, there are:
wherein, b*/a*high-frequency gain of controlled object G(s), i.e. G (∞) ═ b*/a*；
When l is greater than 2, the controlled system is reduced in order and converted into the condition of l being 1 or l being 2 for processing. That is, when the controlled object is a high-order object, the controlled system needs to be subjected to a reduced-order process first to convert the high-order object into a low-order object for processing.
In the present invention, the step S4 specifically includes:
determining a time constant τ based on rapidity index of control system designcand makeEqual to desired closed loop system HR(s) a bandwidth; selectingAs a parameter of the disturbance rejection PID control structure, wherein,Estimating the bandwidth of the filter q(s) for the disturbance; wherein the content of the first and second substances,Andthe larger the multiple relationship between the two, the better the immunity control performance.
As shown in fig. 6, corresponding to the method, the invention further provides a design apparatus of an anti-interference PID controller, which includes a PID structure construction module, an equivalent transformation module, a form determination module, and a parameter selection module;
The PID structure construction module is used for constructing an anti-interference PID control structure, and the anti-interference PID control structure comprises a prefilter F(s) and a PID feedback controller C(s); the pre-filter F(s) is used for realizing smooth filtering of a tracking signal, and the PID feedback controller C(s) is used for realizing closed-loop control of a control system;
the equivalent transformation module is used for carrying out equivalent transformation of a structure diagram on the established anti-interference PID control structure through anti-interference control designed by a control system, wherein the equivalent transformation comprises feedback equivalent transformation and equivalent unit feedback transformation to obtain the structure of a pre-filter F(s) and the structure of a PID feedback controller C(s);
The form determining module is used for determining the final form of the anti-interference PID control structure according to the relative order of the controlled system;
And the parameter selection module is used for selecting the parameters of the anti-interference PID control structure.
In the present invention, in the equivalent transformation module, the prefilter f(s) is configured to:
Wherein the content of the first and second substances,for a desired closed loop system, τcA time constant representing a desired closed loop system;For disturbance estimation of the filter, tauqRepresenting the time constant of the disturbance observer.
in the equivalent transformation module, the PID feedback controller c(s) is configured to:
The PID feedback controller C(s) has the form of PI-PD;
Wherein the PD controller is in the form of Cpd(s)＝kpd(1+kds) connected in series with the object G(s) to be controlled and G (∞) Cpd(∞)＝HR(∞) to realize high-frequency series compensation of controlled object G(s); the PI controller is in the form ofthe PI controller is an equivalent form of a disturbance observer, and the parameter of the PI controller is directly measured by taucAnd τqand (4) determining.
in the present invention, the form determination module specifically includes:
Determining a final form of the anti-interference PID control structure according to the relative order l ═ r.deg [ G ] of a controlled system, and specifically comprising:
When l is 1, there are:
Wherein, b*/a*High-frequency gain of controlled object G(s), i.e. G (∞) ═ b*/a*；
When l is 2, there are:
Wherein, b*/a*High-frequency gain of controlled object G(s), i.e. G (∞) ═ b*/a*；
When l is greater than 2, the controlled system is reduced in order and converted into the condition of l being 1 or l being 2 for processing.
In the present invention, the parameter selection module specifically includes:
determining a time constant τ based on rapidity index of control system designcAnd makeEqual to desired closed loop system HR(s) a bandwidth; selectingas a parameter of the disturbance rejection PID control structure, wherein,The bandwidth of the filter q(s) is estimated for the disturbance.
The technical solution of the present invention is further described below with reference to a specific embodiment:
as shown in fig. 2, an actual magnetic levitation physical system manufactured by high-tech company is taken as an example, and the magnetic levitation physical system mainly comprises a master PC computer, an electromagnetic coil device, a motion control data card PCI-1711, a steel ball, a current amplifier, a laser sensor and a converter. Since the steel ball is at different set point positions and the transfer function shown has a certain difference, the linear transfer function for the magnetic levitation physical system can be described as:
the magnetic suspension physical system is mainly described as the relation between the system input current and the output position of a steel ball, and works in the real-time environment of MATLAB/SIMULINK, and the sampling time is 0.001 s. The technical scheme of the invention is used for designing the anti-interference PID controller:
1. Establishing an anti-interference PID control structure;
2. A prefilter and a PID feedback controller;
3. determining the form of an anti-interference PID controller; since the described magnetic levitation physical system is l ═ 2, therefore:
wherein the parameter a*＝0.0311，b*＝77.8421；
4. Selecting parameters of an anti-interference PID controller; determining tau according to corresponding performance requirements of the magnetic levitation physical systemc1/20; meanwhile, the time constant tau of the disturbance estimation filter is selectedqThe selection principle isAnd as the effect is better when the multiple difference is larger, the tau is finally determinedq＝1/200。
Referring to FIGS. 3a and 3b, FIGS. 3a and 3b show the same τcSelecting different tau under the condition of parametersqA simulation effect graph of the control output (y) and the control input (u) d of (a); from fig. 3a and 3b we can see that by reducing τqthe control effect can be improved, and the tracking and interference resistance performance can be improved. The effect is shown in fig. 4a and 4b, fig. 4a is magneticthe control output experiment chart of the suspension physical system, the control input experiment chart of the magnetic suspension physical system is shown in figure 4b, and the parameter selected in the experiment is tauc＝1/20，τq1/400, it can be seen from fig. 4a and 4b that the design scheme of the disturbance rejection PID controller proposed by the present invention can be well applied to practical systems, and has excellent control performance, simple structure and easy implementation.
In summary, the invention has the advantages that: the anti-interference PID controller designed by the technical scheme of the invention has active anti-interference capability, and the parameters of the controller and the anti-interference performance have definite regulation relation; when the object model is inaccurate, the anti-interference PID controller can treat the uncertainty as the internal disturbance of the control system, so that the anti-interference PID controller designed by the technical scheme of the invention has better robustness; meanwhile, in the technical scheme designed by the invention, the parameters are less selected, the physical significance is clear, and the control effect is excellent.
although specific embodiments of the invention have been described above, it will be understood by those skilled in the art that the specific embodiments described are illustrative only and are not limiting upon the scope of the invention, and that equivalent modifications and variations can be made by those skilled in the art without departing from the spirit of the invention, which is to be limited only by the appended claims.
Claims (10)
1. A design method of an anti-interference PID controller is characterized by comprising the following steps: the method comprises the following steps:
step S1, constructing an anti-interference PID control structure, wherein the anti-interference PID control structure comprises a prefilter F (S) and a PID feedback controller C (S); the pre-filter F(s) is used for realizing smooth filtering of a tracking signal, and the PID feedback controller C(s) is used for realizing closed-loop control of a control system;
Step S2, carrying out equivalent transformation of a structure diagram on the established anti-interference PID control structure through anti-interference control designed by a control system, wherein the equivalent transformation comprises feedback equivalent transformation and equivalent unit feedback transformation to obtain the structure of a pre-filter F (S) and the structure of a PID feedback controller C (S);
step S3, determining the final form of the anti-interference PID control structure according to the relative order of the controlled system;
And step S4, selecting parameters of the anti-interference PID control structure.
2. The design method of an anti-interference PID controller according to claim 1, characterized in that: in the step S2, the prefilter f (S) is configured to:
wherein the content of the first and second substances,for a desired closed loop system, τca time constant representing a desired closed loop system;for disturbance estimation of the filter, tauqRepresenting the time constant of the disturbance observer.
3. The design method of the disturbance rejection PID controller according to claim 2, wherein: in step S2, the PID feedback controller c (S) is configured to:
The PID feedback controller C(s) has the form of PI-PD;
wherein the PD controller is in the form of Cpd(s)＝kpd(1+kds) connected in series with the object G(s) to be controlled and G (∞) Cpd(∞)＝HR(∞) to realize high-frequency series compensation of controlled object G(s); the PI controller is in the form ofthe PI controller is an equivalent form of a disturbance observer, and the parameter of the PI controller is directly measured by taucAnd τqand (4) determining.
4. the design method of the disturbance rejection PID controller according to claim 2, wherein: the step S3 specifically includes:
Determining a final form of the anti-interference PID control structure according to the relative order l ═ r.deg [ G ] of a controlled system, and specifically comprising:
When l is 1, there are:
wherein, b*/a*high-frequency gain of controlled object G(s), i.e. G (∞) ═ b*/a*；
When l is 2, there are:
wherein, b*/a*high-frequency gain of controlled object G(s), i.e. G (∞) ═ b*/a*；
When l is greater than 2, the controlled system is reduced in order and converted into the condition of l being 1 or l being 2 for processing.
5. the design method of the disturbance rejection PID controller according to claim 2, wherein: the step S4 specifically includes:
determining a time constant τ based on rapidity index of control system designcand makeequal to desired closed loop system HR(s) a bandwidth; selectingas a parameter of the disturbance rejection PID control structure, wherein,The bandwidth of the filter q(s) is estimated for the disturbance.
6. a design device of an anti-interference PID controller is characterized in that: the system comprises a PID structure construction module, an equivalent transformation module, a form determination module and a parameter selection module;
The PID structure construction module is used for constructing an anti-interference PID control structure, and the anti-interference PID control structure comprises a prefilter F(s) and a PID feedback controller C(s); the pre-filter F(s) is used for realizing smooth filtering of a tracking signal, and the PID feedback controller C(s) is used for realizing closed-loop control of a control system;
the equivalent transformation module is used for carrying out equivalent transformation of a structure diagram on the established anti-interference PID control structure through anti-interference control designed by a control system, wherein the equivalent transformation comprises feedback equivalent transformation and equivalent unit feedback transformation to obtain the structure of a pre-filter F(s) and the structure of a PID feedback controller C(s);
The form determining module is used for determining the final form of the anti-interference PID control structure according to the relative order of the controlled system;
and the parameter selection module is used for selecting the parameters of the anti-interference PID control structure.
7. The design device of an anti-interference PID controller according to claim 6, characterized in that: in the equivalent transformation module, the prefilter f(s) is configured to:
Wherein the content of the first and second substances,for a desired closed loop system, τca time constant representing a desired closed loop system;For disturbance estimation of the filter, tauqRepresenting the time constant of the disturbance observer.
8. The design device of an anti-interference PID controller according to claim 7, characterized in that: in the equivalent transformation module, the PID feedback controller c(s) is configured to:
The PID feedback controller C(s) has the form of PI-PD;
wherein the PD controller is in the form of Cpd(s)＝kpd(1+kds) connected in series with the object G(s) to be controlled and G (∞) Cpd(∞)＝HR(∞) to realize high-frequency series compensation of controlled object G(s); the PI controller is in the form ofThe PI controller is an equivalent form of a disturbance observer, and the parameter of the PI controller is directly measured by taucAnd τqAnd (4) determining.
9. The design device of an anti-interference PID controller according to claim 7, characterized in that: the form determination module is specifically:
Determining a final form of the anti-interference PID control structure according to the relative order l ═ r.deg [ G ] of a controlled system, and specifically comprising:
when l is 1, there are:
Wherein, b*/a*high-frequency gain of controlled object G(s), i.e. G (∞) ═ b*/a*；
when l is 2, there are:
wherein, b*/a*High-frequency gain of controlled object G(s), i.e. G (∞) ═ b*/a*；
When l is greater than 2, the controlled system is reduced in order and converted into the condition of l being 1 or l being 2 for processing.
10. the design device of an anti-interference PID controller according to claim 7, characterized in that: the parameter selection module specifically comprises:
Determining a time constant τ based on rapidity index of control system designcand makeEqual to desired closed loop system HR(s) a bandwidth; selectingAs a parameter of the disturbance rejection PID control structure, wherein,the bandwidth of the filter q(s) is estimated for the disturbance.
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| CN111965969A (en) * | 2020-08-19 | 2020-11-20 | 华侨大学 | Double closed-loop anti-interference PID control method and system for speed and position of direct current motor |
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