CN109946963A - A method of judging multiloop control system nargin - Google Patents
A method of judging multiloop control system nargin Download PDFInfo
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- CN109946963A CN109946963A CN201910330651.XA CN201910330651A CN109946963A CN 109946963 A CN109946963 A CN 109946963A CN 201910330651 A CN201910330651 A CN 201910330651A CN 109946963 A CN109946963 A CN 109946963A
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Abstract
A method of judging multiloop control system nargin, comprising the following steps: step 1 carries out equivalence transformation to multiloop control system, is transformed to the single loop control system of a non-unit feedback；Transformed open loop transfer function open (s) is calculated in step 2；Step 3 is calculated cutoff frequency according to open loop transfer function open (s) and isPhase margin isStep 4, computing relay nargin Dm judge the control nargin of multiloop control system according to delay nargin Dm.Method of the invention, which calculates acquisition control system delay nargin, can more illustrate the Control platform and robustness of multiloop control system for phase margin and magnitude margin, have versatility for multiloop control system.
Description
Technical field
The present invention relates to a kind of methods for judging multiloop control system nargin.
Background technique
For classical control system design, the Frequency Index of divided ring control loop is needed to be tested, that is, calculates and open
The phase and amplitude nargin of ring control loop and cutoff frequency etc., and then the Control platform of control loop is evaluated.But
Multiloop control system is designed and is analyzed, control theory and case history show: there are phase and amplitude nargin and
The case where cutoff frequency is all satisfied design objective, and Control platform and robustness are performed poor, illustrates abundant only in accordance with phase and amplitude
Spending the method for going the Control platform for judging multiloop control system and robustness has limitation.
Summary of the invention
Technology of the invention solves the problems, such as: overcome the deficiencies in the prior art, and the present invention proposes a kind of judgement multiloop control
The method of system margins processed, this control system margin definition are delay nargin, can be considered the absolute stability of multiloop control system
Nargin is suitable for multiloop control system and designs and analyze.
The technical solution of the invention is as follows: a method of judging multiloop control system nargin, comprising the following steps:
Step 1 carries out equivalence transformation to multiloop control system, is transformed to the unity loop control system an of non-unit feedback
System；
Multiloop control system is made of inner looping and external loop, and inner looping control is feedback controller Gc2(s), external loop
Control is through path controller Gc1(s)；
The forward path return transfer function G (s) of single loop control system is
G (s)=Gc1(s)S(s)P1(s)P2(s)；
Wherein, S (s) is executing agency, P1It (s) is controlled device, P2It (s) is the other controlling units of through path；
The feedback loop transfer function H (s) of single loop control system is represented by
Transformed open loop transfer function open (s) is calculated in step 2:
Step 3 is calculated cutoff frequency according to open loop transfer function open (s) and isPhase margin is
Computing relay nargin Dm on this basis:
The control nargin of multiloop control system is judged according to Dm.
Compared with the prior art, the invention has the beneficial effects that:
(1) it is based on control theory and case history, the multiloop control system with abundant phase and amplitude nargin exists
Control platform and the bad situation of robustness, the delay nargin concept of introducing can accurately measure the Control platform of control system
And robustness；
(2) method of the invention calculates the control system delay nargin explicit physical meaning obtained, it is only necessary to multiloop control
System processed can solve to obtain after carrying out equivalence transformation, be easy to apply in control loop design, designer can be according to this value
The absolute nargin of control loop is determined.
(3) it calculates by means of the present invention and obtains control system delay nargin, relative to phase margin and magnitude margin
For, it can more illustrate the Control platform and robustness of multiloop control system, there is versatility for multiloop control system, it can
It is considered as the absolute stability nargin of multiloop control system, is suitable for multiloop control system and designs and analyze.
Detailed description of the invention
Fig. 1 is multiloop control system equivalence transformation process；
Fig. 2 is Bode figure when former open loop corresponds to two groups of difference control parameters；
Fig. 3 is that Bode when open loop corresponds to two groups of difference control parameters after converting schemes；
Fig. 4 is unit-step response of two groups of difference control parameters when executing agency is not added and delay link is added.
Specific embodiment
The present invention provides a kind of method for judging multiloop control system nargin, this control system margin definition is that delay is abundant
Degree, can quantitatively be calculated the delay nargin of multiloop control system, and then determine the Control platform and robust of control system
Property, it can be used for multiloop control system design and analysis, comprising the following steps:
Step 1 carries out equivalence transformation to multiloop control system shown in FIG. 1, i.e., by the feedback output node of inner looping 3
The feed back input node 2 of inner looping is moved to the input node 1 of system by the output node 4 for moving to system, that is, be transformed to one it is non-
The single loop control system of unit feedback, forward path return transfer function are
G (s)=Gc1(s)S(s)P1(s)P2(s)
Feedback loop transmission function is represented by
Wherein, Gc1It (s) is through path controller, S (s) is executing agency, P1It (s) is controlled device, P2(s) for it is preceding to
The other controlling units of access, Gc2It (s) is the feedback controller of inner looping；
Multiloop control system is made of inner looping and external loop, and inner looping control is feedback control Gc2(s), external loop control
It is made as through path controller Gc1(s)；
Step 2, according to classical control theory, the open loop of non-unit feedback single loop control system transmits letter after transformation
Number is
Step 3 is calculated cutoff frequency according to open loop transfer function open (s) and isPhase margin is
Then postpone nargin Dm to be defined as follows
Different with magnitude margin from control system phase, the physical significance for postponing nargin can be regarded as control signal and execute
At mechanism when hysteresis delay nargin, system neutrality.On engineer application, delay nargin can be considered the absolute abundant of control system
Degree, when its value is larger, then characterization control system has more abundant nargin, and vice versa.
The forward path return transfer function, the i.e. output node 4 from the input node 1 in circuit to system are included
The transmission function that is composed of links, transformed open loop and former open loop are in forward path transmission function
It is consistent.
The feedback loop transmission function, i.e., included from the output node 4 in circuit to system input node 1 is each
Link belongs to external loop negative-feedback, the control margin of error that negative-feedback is formed in the input node 1 in circuit and instruction.
The transformed open loop transfer function transmits letter by forward path return transfer function and feedback loop
Number product obtains.
Computer Simulation embodiment:
Certain multiloop control system control block diagram is as shown in Figure 1, executing agency's biography letter isControlled pair
As for pass letterInner looping feedback control coefficient is Gc2(s)=Kd, forward direction series connection ratio control
It is made as Gc(s)=Kp, two groups of control parameters are respectively sys1:Kd=0.9, Kp=4.0；Control parameter sys2:Kd=2.9, Kp=
12.0。
By classical control theory, the open loop that can obtain control system passes letter and is
System sys1 and sys2 open loop bode is as shown in Fig. 2, can solve to obtain the frequency-domain index of sys1 and sys2, sys1:
ωc=4.06rad/s, Gm=14.0dB, Pm=76.9 °；Sys2: ωc=4.04rad/s, Gm=14.8dB, Pm=85.7 °.
Phase and amplitude nargin according to system goes to judge the Control platform of control system, it may be concluded that the control of sys1 and sys2
Quality is suitable.
Method is introduced by the present invention and carries out equivalence transformation, and can obtain open loop biography letter is
By sys1 and sys2 control parameter substitute into above formula, solve obtain system sys1 and sys2 bode figure as shown in figure 3,
When control parameter is changed to sys2 by sys1, the open-loop cut-off frequency of control system after transformationIt is increased to by 14.9rad/s
31.4rad/s phase marginIt is reduced by 44.3 ° to 28.6 °, is solved delay nargin Dm and reduced by 51.8ms to 15.9ms,
That is the delay nargin of control system sys2 is substantially lower than system sys1.
The time domain specification of checking system sys1 and sys2 divide and increase 15.9ms at non-delay at executing agency and executing agency
Delay link two kinds of situations emulation sys1 and sys2 unit-step response, (left figure: nothing is prolonged executing agency at as shown in Figure 4
Late, right figure: postpone 15.9ms at executing agency), as seen from the figure, increase the delay of 15.9ms at executing agency, finds sys2
For neutrality, and sys1 has biggish control nargin.
Simulation result explanation:
(1) even if two systems control loop structure is as controlled device, and have similar cutoff frequency, amplitude abundant
Degree and phase margin, Control platform are also likely to be present very big difference；
(2) it for multiloop control system, goes to sentence only in accordance with the cutoff frequency of control system, phase and amplitude nargin
There are limitations for the Control platform and robustness of disconnected control system；
(3) the delay biggish system of nargin corresponds to preferable Control platform；
(4) cutoff frequency of open loop can not represent the rapidity of control system after equivalence transformation, cutoff frequency compared with
High person often corresponds to lower delay nargin, i.e. the nargin of control system is smaller.
Unspecified part of the present invention belongs to common sense well known to those skilled in the art.
Claims (6)
1. a kind of method for judging multiloop control system nargin, which comprises the following steps:
Step 1 carries out equivalence transformation to multiloop control system, is transformed to the single loop control system of a non-unit feedback；
Transformed open loop transfer function open (s) is calculated in step 2；
Step 3 is calculated cutoff frequency according to open loop transfer function open (s) and isPhase margin is
Step 4, computing relay nargin Dm judge the control nargin of multiloop control system according to delay nargin Dm.
2. a kind of method for judging multiloop control system nargin according to claim 1, it is characterised in that: described more times
Path control system includes inner looping and external loop, and inner looping control is feedback controller Gc2(s), external loop control is through path
Controller Gc1(s)。
3. a kind of method for judging multiloop control system nargin according to claim 1 or 2, it is characterised in that: described
The forward path return transfer function G (s) of single loop control system are as follows:
G (s)=Gc1(s)S(s)P1(s)P2(s)；
Wherein, S (s) is executing agency, P1It (s) is controlled device, P2It (s) is the other controlling units of through path.
4. a kind of method for judging multiloop control system nargin according to claim 3, it is characterised in that: described single time
The feedback loop transfer function H (s) of path control system indicates are as follows:
5. a kind of method for judging multiloop control system nargin according to claim 4, it is characterised in that: the open loop
Return transfer function open (s) are as follows:
6. a kind of method for judging multiloop control system nargin according to claim 5, it is characterised in that: the delay
Nargin
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| CN113467418A (en) * | 2021-06-25 | 2021-10-01 | 河北工业大学 | Method for measuring performance index of control loop |
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