A system setting value tracking accuracy control method based on variable input

Abstract

The invention relates to the field of automatic control technology, and discloses a system setting value tracking accuracy control method based on variable input, comprising the following steps: establishing a linear time-invariant system model and a steady-state equation of the system under steady-state conditions, obtaining a state variable of the system and an error equation of the state variable of the system under steady-state conditions; obtaining an original controller equation and analyzing it, and when the system parameters of the controlled object are inconsistent with the actual parameters of the system, establishing a control equation of the actual parameters of the system, introducing a negative slope function, establishing a new control function after introducing the negative slope, and establishing a new controller equation based on the control equation of the actual parameters of the system, replacing the actual parameters of the system and the state variables of the system under steady-state conditions, obtaining an optimal control equation and solving it, and substituting the obtained solution into the original controller to realize control of the controlled object; the method greatly reduces the influence of the actual parameters of the system and improves the tracking accuracy of the system for the setting value.

Description

Technical Field

[0001] The present invention relates to the field of automatic control technology, and in particular to a system setting value tracking accuracy control method based on variable input. Background Art

[0002] Currently, in the field of automatic control, it is necessary to design a controller to control specific quantities of the controlled object's system in order to track a set value. When designing a controller, the system model of the controlled object is first constructed and the system parameters (i.e., parameters of the controlled object, such as mass, friction coefficient, capacitance and inductance) are identified. If the actual system parameters are consistent with the identified parameters, the control is relatively accurate. However, the actual system parameters and the identified parameters are often inconsistent, mainly due to system aging and errors in batch production. When existing design methods do not match the system parameters with the identified parameters, the actual system's tracking accuracy of the set value is low. Summary of the Invention

[0003] In response to the above-mentioned deficiencies in the prior art, the present invention provides a system setting value tracking accuracy control method based on variable input, which is used to solve the problem in the prior art that when the system parameters are inconsistent with the identified parameters, the actual system has low tracking accuracy of the setting values, thereby improving the system's tracking accuracy of the setting values.

[0004] In order to achieve the above-mentioned object of the invention, the technical solution adopted by the present invention is:

[0005] A system setting value tracking accuracy control method based on variable input includes the following steps:

[0006] S1. Based on the system parameters of the controlled object, the control input and state variables of the system, a linear time-invariant system model is established;

[0007] S2. Based on the system parameters of the controlled object, when the system is in a steady-state condition, the steady-state equation of the system under the steady-state condition is established according to the state variables and control input of the system under the steady-state condition;

[0008] S3. Obtaining the state variables of the system and the error equations of the state variables of the system under steady-state conditions based on the linear time-invariant system model established in step S1 and the steady-state equations of the system under steady-state conditions established in step S2;

[0009] S4. Designing the original controller as proportional feedback of the error based on the control input of the system, the control input of the system under steady-state conditions, the state variable of the system obtained in step S3, and the error equation of the state variable of the system under steady-state conditions to obtain the original controller;

[0010] S5. Analyze the original controller obtained in step S4. When the system parameters of the controlled object are inconsistent with the actual system parameters of the controlled object, establish control equations of the actual system parameters and control equations of the system parameters respectively.

[0011] S6. Perform steady-state analysis based on the control equations of the actual system parameters and the control equations of the system parameters established in step S5. By introducing a negative slope function, the system parameters of the controlled object and the state variables of the system under steady-state conditions are set to variable values, and a new control function after the negative slope is introduced is established.

[0012] S7. Based on the new control function after introducing the negative slope established in step S6 and the control equation of the actual system parameters, a new controller equation is established, and the actual system parameters of the controlled object and the state variables of the system under steady-state conditions are replaced to obtain the optimal control equation and solve the control input of the system under steady-state conditions and substitute it into the original controller to realize control of the controlled object.

[0013] Furthermore, the linear time-invariant system model in step S1 is:

[0014]

[0015] in, represents the output variable of the system, represents the state variables of the system, represents the first-order derivative of the system's state variables, 、 、 、 They represent the system parameters of the controlled object, represents the control input of the system, express dimensional real space, Represents the real number space.

[0016] Furthermore, step S2 specifically includes:

[0017] Based on the system parameters of the controlled object, if the system output setting value under steady-state conditions is , the state variables of the system under steady-state conditions are , the control input of the system under steady-state conditions is , then the steady-state equation of the system under steady-state conditions is established, namely:

[0018] .

[0019] Furthermore, step S3 specifically includes:

[0020] The linear time-invariant system model established in step S1 and the steady-state equation of the system under steady-state conditions established in step S2 are subjected to difference processing to obtain the error equation between the state variables of the system and the state variables of the system under steady-state conditions, namely:

[0021]

[0022] in, It represents the error between the state variables of the system and the state variables of the system under steady-state conditions, It represents the first derivative of the error between the state variable of the system and the state variable of the system under steady-state conditions.

[0023] Furthermore, the original controller obtained in step S4 is:

[0024]

[0025] in, Represents the proportional parameter of a conventional proportional controller.

[0026] Furthermore, step S5 specifically includes:

[0027] S51. Calculate the state variables of the system under steady-state conditions, namely:

[0028] ;

[0029] S52: Analyze the original controller obtained in step S4 based on the state variables of the system under steady-state conditions calculated in step S51. When the system parameters of the controlled object are inconsistent with the actual system parameters of the controlled object, establish the control equations of the system parameters and the control equations of the actual system parameters, respectively. Specifically,

[0030] based on , when the system parameters of the controlled object are inconsistent with the actual system parameters of the controlled object, then:

[0031]

[0032] in, Represents the actual system parameters of the controlled object;

[0033] when System parameters in is the identity matrix, the system parameters When is a zero matrix, the control equation of the system parameters is established, namely:

[0034] ;

[0035] when System parameters in is the identity matrix, the system parameters When it is a zero matrix, the control equation of the actual parameters of the system is established, that is:

[0036] .

[0037] Furthermore, step S6 specifically includes:

[0038] S61, based on 、 ,draw Curve Curve and The system tracking accuracy diagram of the curve change is obtained respectively. Curve and The horizontal coordinate of the intersection point of the curve, Curve and The horizontal coordinates of the intersection points of the lines;

[0039] S62, based on the obtained Curve and The horizontal coordinate of the intersection point of the curve, Curve and The abscissa of the intersection of the curves is obtained by introducing a negative slope function, setting the system parameters of the controlled object and the state variables of the system under steady-state conditions to variable values, and establishing a new control function after the introduction of the negative slope, namely:

[0040]

[0041] in, Represents the new control function after the negative slope is introduced, represents a negative slope function, Indicates the intersection of curves.

[0042] Furthermore, step S7 specifically includes:

[0043] S71, according to the control equation of the new control function after introducing the negative slope established in step S6 and the actual parameters of the system, by setting and Equal, establish a new control equation, namely:

[0044] ;

[0045] S72. According to the new control equation, the actual system parameters of the controlled object are Replaced with the system parameters of the controlled object , the state variables of the system under steady-state conditions Set as the state variable of the system , we get the optimal control equation, namely:

[0046] ;

[0047] S73. Calculate the control input of the system under steady-state conditions based on the optimal control equation ,Will Substitute it into the original controller to control the controlled object.

[0048] The present invention has the following beneficial effects:

[0049] The present invention proposes a system setting value tracking accuracy control method based on variable input. By analyzing the traditional controller, a negative slope function is introduced to set the system parameters in the traditional controller and the control input of the system under steady-state conditions to variable values, thereby greatly reducing the influence of the actual system parameters and improving the system's tracking accuracy of the set values. BRIEF DESCRIPTION OF THE DRAWINGS

[0050] Figure 1 This is a flow chart of a method for controlling the tracking accuracy of a system setting value based on variable input proposed by the present invention;

[0051] Figure 2 It is a schematic diagram of the intersection of the actual system parameters of the controlled object and the control input of the system under steady-state conditions;

[0052] Figure 3 It is a schematic diagram of the intersection of the actual system parameters and the control input under variable conditions;

[0053] Figure 4 Status for traditional controller and new controller Schematic diagram of the comparison;

[0054] Figure 5 Status for traditional controller and new controller Schematic diagram of the comparison;

[0055] Figure 6 Schematic diagram of the effect of different inherent frequency ranges on the set ratio value in the embodiment. DETAILED DESCRIPTION

[0056] The specific embodiments of the present invention are described below to facilitate understanding of the present invention by those skilled in the art. However, it should be clear that the present invention is not limited to the scope of the specific embodiments. For those skilled in the art, as long as various changes are within the spirit and scope of the present invention as defined and determined by the appended claims, these changes are obvious, and all inventions and creations utilizing the concepts of the present invention are protected.

[0057] like Figure 1 As shown, a system setting value tracking accuracy control method based on variable input includes the following steps S1-S7:

[0058] S1. Based on the system parameters of the controlled object, the control input and state variables of the system, a linear time-invariant system model is established.

[0059] In this embodiment, the system parameters of the controlled object (parameters of the controlled object), including mass, friction coefficient, capacitance and inductance, etc., vary depending on the specific controlled object and can be obtained through system identification. In addition, the system proposed in the present invention is a system of controlled objects. Since there are many types of controlled objects, they can be expressed using differential equations.

[0060] Specifically, the linear time-invariant system model in step S1 is:

[0061]

[0062] in, represents the output variable of the system, represents the state variables of the system, represents the first-order derivative of the system's state variables, 、 、 、 They represent the system parameters of the controlled object, represents the control input of the system, express dimensional real space, Represents the real number space.

[0063] S2. Based on the system parameters of the controlled object, when the system is in a steady-state condition, the steady-state equation of the system under steady-state conditions is established according to the state variables and control inputs of the system under steady-state conditions.

[0064] In this embodiment, the steady-state equation of the system under steady-state conditions is established and the difference is solved with the linear time-invariant system model established in the above steps to obtain the error equation of the state variables of the system and the state variables of the system under steady-state conditions.

[0065] Specifically, step S2 includes:

[0066] Based on the system parameters of the controlled object, if the system output setting value under steady-state conditions is , the state variables of the system under steady-state conditions are , the control input of the system under steady-state conditions is , then the steady-state equation of the system under steady-state conditions is established, namely:

[0067] .

[0068] S3. According to the linear time-invariant system model established in step S1 and the steady-state equation of the system under steady-state conditions established in step S2, the state variables of the system and the error equations of the state variables of the system under steady-state conditions are obtained.

[0069] Specifically, step S3 includes:

[0070] The linear time-invariant system model established in step S1 and the steady-state equation of the system under steady-state conditions established in step S2 are subjected to difference processing to obtain the error equation between the state variables of the system and the state variables of the system under steady-state conditions, namely:

[0071]

[0072] in, It represents the error between the state variables of the system and the state variables of the system under steady-state conditions, It represents the first derivative of the error between the state variable of the system and the state variable of the system under steady-state conditions.

[0073] S4. According to the control input of the system, the control input of the system under steady-state conditions, the error equation between the state variables of the system obtained in step S3 and the state variables of the system under steady-state conditions, the original controller is designed as proportional feedback of the error to obtain the original controller.

[0074] Specifically, the original controller obtained in step S4 is:

[0075]

[0076] in, Represents the proportional parameter of a conventional proportional controller.

[0077] In this embodiment, the original controller designed is a traditional controller, that is, the proportional feedback of the error is used as the set value of the traditional controller output under steady-state conditions. Perform tracking control. Among them, the control input of the system under steady-state conditions is By solving the equation You can get the set value of the system output under steady-state conditions However, when the system parameters of the controlled object are The actual system parameters of the controlled object If they are inconsistent, the system parameters of the controlled object will be determined according to the identified parameters. 、 、 、 The calculated control input of the system under steady-state conditions And the original controller equation established It is not possible to accurately track the set value output by the system under steady-state conditions The usual method to improve the tracking accuracy of the system is to identify the system parameters more accurately or to improve the processing accuracy, thereby reducing the system parameters of the controlled object. The actual system parameters of the controlled object However, the system parameter identification accuracy and processing accuracy are limited.

[0078] Therefore, in this embodiment, when the system parameter identification accuracy is limited or the processing accuracy is limited, the control equation of the system actual parameters of the controlled object is established to determine the system actual parameters of the controlled object. Control inputs that affect the system under steady-state conditions , which affects the tracking accuracy. Figure 2 As shown, Figure 2 It is a schematic diagram of the intersection of the actual system parameters of the controlled object and the control input of the system under steady-state conditions. Figure 2 When the control input of the system is in steady state condition and system parameters When the actual system parameters of the controlled object are constant, The change of the actual system parameters of the controlled object leads to the control equation The solution (i.e. Figure 2 Therefore, if the range of change can be reduced, the actual system parameters of the controlled object will also be reduced. The specific analysis is as follows:

[0079] S5. Analyze the original controller obtained in step S4. When the system parameters of the controlled object are inconsistent with the actual system parameters of the controlled object, establish control equations of the actual system parameters and control equations of the system parameters respectively.

[0080] Specifically, step S5 includes S51-S52:

[0081] S51. Calculate the state variables of the system under steady-state conditions, namely:

[0082] .

[0083] S52: Analyze the original controller obtained in step S4 based on the state variables of the system under steady-state conditions calculated in step S51. When the system parameters of the controlled object are inconsistent with the actual system parameters of the controlled object, establish the control equations of the system parameters and the control equations of the actual system parameters, respectively. Specifically,

[0084] based on , when the system parameters of the controlled object are inconsistent with the actual system parameters of the controlled object, then:

[0085]

[0086] in, Represents the actual system parameters of the controlled object.

[0087] when System parameters in is the identity matrix, the system parameters When is a zero matrix, the control equation of the system parameters is established, namely:

[0088] .

[0089] when System parameters in is the identity matrix, the system parameters When it is a zero matrix, the control equation of the actual parameters of the system is established, that is:

[0090] .

[0091] In this embodiment, in the subsequent steps S6-S7, the actual parameters of the system with the controlled object are The problem of low accuracy caused by changes is proposed by introducing a negative slope function to control the actual parameters of the system. Medium constant value Set to a variable value to establish a new control function after introducing a negative slope To evaluate variable values and The intersection of the actual system parameters of the controlled object and the variable system parameters is as follows: Figure 3 As shown, Figure 3 It is a schematic diagram of the intersection of the actual system parameters and the control input under variable conditions. Figure 3 It can be found that after introducing a negative slope function, the constant value It is a variable value, which can greatly reduce the actual system parameters of the controlled object. The influence of , and the new intersection point calculated satisfies the equation , even if the identified parameters are used Solving this equation, due to the negative slope function introduced in this embodiment Despite the existence of , good tracking accuracy can still be achieved.

[0092] S6. Perform steady-state analysis based on the control equations of the actual system parameters and the control equations of the system parameters established in step S5. By introducing a negative slope function, the system parameters of the controlled object and the state variables of the system under steady-state conditions are set to variable values, and a new control function after the negative slope is introduced is established.

[0093] Specifically, step S6 includes S61-S62:

[0094] S61, based on 、 ,draw Curve Curve and The system tracking accuracy diagram of the curve change is obtained respectively. Curve and The horizontal coordinate of the intersection point of the curve, Curve and The horizontal coordinate of the intersection point of the lines.

[0095] S62, based on the obtained Curve and The horizontal coordinate of the intersection point of the curve, Curve and The abscissa of the intersection of the curves is obtained by introducing a negative slope function, setting the system parameters of the controlled object and the state variables of the system under steady-state conditions to variable values, and establishing a new control function after the introduction of the negative slope, namely:

[0096]

[0097] in, Represents the new control function after the negative slope is introduced, represents a negative slope function, Indicates the intersection of curves.

[0098] S7. Based on the new control function after introducing the negative slope established in step S6 and the control equation of the actual system parameters, a new controller equation is established, and the actual system parameters of the controlled object and the state variables of the system under steady-state conditions are replaced to obtain the optimal control equation and solve the control input of the system under steady-state conditions and substitute it into the original controller to realize control of the controlled object.

[0099] Specifically, step S7 includes S71-S73:

[0100] S71, according to the control equation of the new control function after introducing the negative slope established in step S6 and the actual parameters of the system, by setting and Equal, establish a new control equation, namely:

[0101] .

[0102] S72. According to the new control equation, the actual system parameters of the controlled object are Replaced with the system parameters of the controlled object , the state variables of the system under steady-state conditions Set as the state variable of the system , we get the optimal control equation, namely:

[0103] .

[0104] S73. Calculate the control input of the system under steady-state conditions based on the optimal control equation ,Will Substitute it into the original controller to control the controlled object.

[0105] In this embodiment, due to Plays a negative feedback role, so the calculated Under the condition of ensuring the stability of the system, the value can directly act on the controlled object and be used to track the system setting value accurately; in addition, Substitute the value into the controller The controlled object is controlled in order to track the system setting value accurately.

[0106] In this embodiment, the effectiveness of the system setting value tracking accuracy control method based on variable input proposed by the present invention is verified through experiments. Specifically, an undamped simple pendulum system is selected, and the state space of the simple pendulum system is: , ,in Indicates the swing angle, represents the first derivative of the swing angle, represents the angular velocity of the swing, represents the first derivative of the angular velocity of the swing, represents the force applied to the pendulum, represents the natural frequency of the simple pendulum system, Indicates the output of the simple pendulum system, that is, the swing angle. In order to achieve a certain set value angle , according to the traditional controller design method, the traditional controller equation can be obtained as , and the variable input-based system setting value tracking accuracy control method proposed by the present invention is used to design the variable input, so that the negative slope function A simple proportional function is , the new controller equation is , let the set value angle , set the ratio value , when the natural frequency of the simple pendulum system When the range of is [0.5, 1.5] Hz, the error of the traditional controller equation and the error of the new controller equation are as follows: Figure 4-5 As shown, Figure 4 Status for traditional controller and new controller A comparison diagram of Figure 5 Status for traditional controller and new controller Schematic diagram of the comparison; Figure 4 When the natural frequency of the simple pendulum system When the range of variation is [0.5, 1.5] Hz, its natural frequency The natural frequency is 0.5Hz The narrowband fluctuation range formed by 1.5Hz is larger, and Figure 5 When the natural frequency of the simple pendulum system When the range of variation is [0.5, 1.5] Hz, its natural frequency The natural frequency is 0.5Hz The narrowband fluctuation range formed by 1.5 Hz is relatively small. Therefore, the system setting value tracking accuracy control method based on variable input proposed by the present invention has a higher tracking accuracy for the setting value.

[0107] In addition, to test the setting of the ratio value The influence of the two inherent frequency ranges is selected respectively. Hz and Hz, for different set ratio values The final steady-state error is Figure 6 As shown, from Figure 6 It can be found that as the ratio value is set As the value of the proportional value increases, the steady-state error quickly approaches 0, so the tracking accuracy can be high enough. Just big enough.

[0108] Specific embodiments are used in the present invention to illustrate the principles and implementation methods of the present invention. The description of the above embodiments is only used to help understand the method of the present invention and its core ideas. At the same time, for those skilled in the art, according to the ideas of the present invention, there may be changes in the specific implementation methods and application scopes. In summary, the contents of this specification should not be understood as limiting the present invention.

[0109] Those skilled in the art will appreciate that the embodiments described herein are intended to help readers understand the principles of the present invention, and it should be understood that the scope of protection of the present invention is not limited to such specific descriptions and embodiments. Those skilled in the art can make various other specific variations and combinations based on the technical teachings disclosed in the present invention without departing from the essence of the present invention, and such variations and combinations are still within the scope of protection of the present invention.

Claims

1. A system setting value tracking accuracy control method based on variable input, characterized in that: The following steps are involved: S1. Based on the system parameters of the controlled object, the control input and state variables of the system, a linear time-invariant system model is established; Among them, the linear time-invariant system model is: in, represents the output variable of the system, represents the state variables of the system, represents the first-order derivative of the system's state variables, 、 、 、 They represent the system parameters of the controlled object, represents the control input of the system, express dimensional real space, represents the real number space; S2. Based on the system parameters of the controlled object, when the system is in steady-state conditions, the steady-state equation of the system under steady-state conditions is established according to the state variables and control inputs of the system under steady-state conditions. Specifically: Based on the system parameters of the controlled object, if the system output setting value under steady-state conditions is , the state variables of the system under steady-state conditions are , the control input of the system under steady-state conditions is , then the steady-state equation of the system under steady-state conditions is established, namely: ； S3. According to the linear time-invariant system model established in step S1 and the steady-state equation of the system under steady-state conditions established in step S2, the error equation of the state variables of the system and the state variables of the system under steady-state conditions are obtained, specifically: The linear time-invariant system model established in step S1 and the steady-state equation of the system under steady-state conditions established in step S2 are subjected to difference processing to obtain the error equation between the state variables of the system and the state variables of the system under steady-state conditions, namely: in, It represents the error between the state variables of the system and the state variables of the system under steady-state conditions, It represents the first derivative of the error between the state variable of the system and the state variable of the system under steady-state conditions; S4. Designing the original controller as proportional feedback of the error based on the control input of the system, the control input of the system under steady-state conditions, the state variable of the system obtained in step S3, and the error equation of the state variable of the system under steady-state conditions to obtain the original controller; Among them, the original controller is: in, represents the proportional parameter of a conventional proportional controller; S5. Analyze the original controller obtained in step S4. When the system parameters of the controlled object are inconsistent with the actual system parameters of the controlled object, establish the control equations of the actual system parameters and the control equations of the system parameters, respectively. Specifically, S51. Calculate the state variables of the system under steady-state conditions, namely: ； S52: Analyze the original controller obtained in step S4 based on the state variables of the system under steady-state conditions calculated in step S51. When the system parameters of the controlled object are inconsistent with the actual system parameters of the controlled object, establish the control equations of the system parameters and the control equations of the actual system parameters, respectively. Specifically, based on , when the system parameters of the controlled object are inconsistent with the actual system parameters of the controlled object, then: in, Represents the actual system parameters of the controlled object; when System parameters in is the identity matrix, the system parameters When is a zero matrix, the control equation of the system parameters is established, namely: ； when System parameters in is the identity matrix, the system parameters When it is a zero matrix, the control equation of the actual parameters of the system is established, that is: ； S6. Based on the control equations of the actual system parameters and the control equations of the system parameters established in step S5, a steady-state analysis is performed. By introducing a negative slope function, the system parameters of the controlled object and the state variables of the system under steady-state conditions are set to variable values, and a new control function after the negative slope is introduced is established. Specifically, S61, based on 、 ,draw Curve Curve and The system tracking accuracy diagram of the curve change is obtained respectively. Curve and The horizontal coordinate of the intersection point of the curve, Curve and The horizontal coordinates of the intersection points of the lines; S62, based on the obtained Curve and The horizontal coordinate of the intersection point of the curve, Curve and The abscissa of the intersection of the curves is obtained by introducing a negative slope function, setting the system parameters of the controlled object and the state variables of the system under steady-state conditions to variable values, and establishing a new control function after the introduction of the negative slope, namely: in, Represents the new control function after the negative slope is introduced, represents a negative slope function, Indicates the intersection of curves; S7. Based on the new control function after introducing the negative slope established in step S6 and the control equation of the actual system parameters, a new controller equation is established, and the actual system parameters of the controlled object and the state variables of the system under steady-state conditions are replaced to obtain the optimal control equation and solve the control input of the system under steady-state conditions and substitute it into the original controller to realize control of the controlled object. Specifically, S71, according to the control equation of the new control function after introducing the negative slope established in step S6 and the actual parameters of the system, by setting and Equal, establish a new control equation, namely: ； S72. According to the new control equation, the actual system parameters of the controlled object are Replaced with the system parameters of the controlled object , the state variables of the system under steady-state conditions Set as the state variable of the system , we get the optimal control equation, namely: ； S73. Calculate the control input of the system under steady-state conditions based on the optimal control equation ,Will Substitute it into the original controller to control the controlled object.

Images