CN109946963B - Method for judging margin of multi-loop control system - Google Patents
Method for judging margin of multi-loop control system Download PDFInfo
- Publication number
- CN109946963B CN109946963B CN201910330651.XA CN201910330651A CN109946963B CN 109946963 B CN109946963 B CN 109946963B CN 201910330651 A CN201910330651 A CN 201910330651A CN 109946963 B CN109946963 B CN 109946963B
- Authority
- CN
- China
- Prior art keywords
- control system
- loop
- margin
- loop control
- transfer function
- Prior art date
- Legal status (The legal status is an assumption and is not a legal conclusion. Google has not performed a legal analysis and makes no representation as to the accuracy of the status listed.)
- Active
Links
Images
Landscapes
- Feedback Control In General (AREA)
Abstract
Judging margin of multi-loop control systemThe method comprises the following steps: step 1, carrying out equivalent transformation on a multi-loop control system to convert the multi-loop control system into a single-loop control system with non-unit feedback; step 2, calculating to obtain a transformed open loop transfer function open(s); step 3, calculating according to the open loop transfer function open(s) to obtain a cut-off frequency of
A phase margin of
And 4, calculating a delay margin Dm, and judging the control margin of the multi-loop control system according to the delay margin Dm. The method of the invention calculates and obtains the delay margin of the control system, can explain the control quality and robustness of the multi-loop control system relative to the phase margin and the amplitude margin, and has universality for the multi-loop control system.
Description
Technical Field
The invention relates to a method for judging the margin of a multi-loop control system.
Background
Based on the classical control system design, the frequency index of the open-loop control loop needs to be tested, that is, the phase and amplitude margin, the cut-off frequency and the like of the open-loop control loop are calculated, and then the control quality of the control loop is evaluated. However, for the design and analysis of the multi-loop control system, the control theory and the engineering example show that: the situation that both the phase and amplitude margins and the cut-off frequency meet the design index and the control quality and robustness are poor in performance exists, which shows that the method for judging the control quality and robustness of the multi-loop control system only according to the phase and amplitude margins is limited.
Disclosure of Invention
The technical problem to be solved by the invention is as follows: the invention provides a method for judging the margin of a multi-loop control system, which overcomes the defects of the prior art, wherein the margin of the control system is defined as a delay margin and can be regarded as an absolute stability margin of the multi-loop control system, and the method is suitable for designing and analyzing the multi-loop control system.
The technical solution of the invention is as follows: a method for judging the margin of a multi-loop control system comprises the following steps:
the multi-loop control system is composed of an inner loop and an outer loop, the inner loop is controlled by a feedback controller Gc2(s) outer loop control is a forward path controller Gc1(s)；
The forward channel loop transfer function G(s) of the single loop control system is
G(s)＝Gc1(s)S(s)P1(s)P2(s)；
Wherein S(s) is an actuator, P1(s) is the controlled object, P2(s) other control links of the forward path;
the feedback loop transfer function H(s) of a single loop control system can be expressed as
and judging the control margin of the multi-loop control system according to the Dm.
Compared with the prior art, the invention has the beneficial effects that:
(1) based on a control theory and an engineering example, the multi-loop control system with abundant phase and amplitude margins has the condition of poor control quality and robustness, and the introduced delay margin concept can accurately balance the control quality and robustness of the control system;
(2) the control system delay margin obtained by calculation of the method has definite physical significance, can be obtained by solving after equivalent transformation is carried out on the multi-loop control system, is easy to apply in control loop design, and a designer can judge the absolute margin of the control loop according to the value.
(3) The method can calculate and obtain the delay margin of the control system, can better explain the control quality and robustness of the multi-loop control system relative to the phase margin and the amplitude margin, has universality for the multi-loop control system, can be regarded as the absolute stability margin of the multi-loop control system, and is suitable for the design and analysis of the multi-loop control system.
Drawings
FIG. 1 is a diagram of an equivalent transformation process for a multi-loop control system;
FIG. 2 is a Bode diagram of an original open loop circuit corresponding to two sets of different control parameters;
FIG. 3 is a Bode diagram of the open loop after transformation corresponding to two different sets of control parameters;
FIG. 4 is a graph of the unit step response of two different sets of control parameters when the actuator is not engaged and when the delay loop is engaged.
Detailed Description
The invention provides a method for judging the margin of a multi-loop control system, which defines the margin of the control system as a delay margin, can quantitatively calculate the delay margin of the multi-loop control system to further judge the control quality and robustness of the control system, can be used for designing and analyzing the multi-loop control system, and comprises the following steps:
G(s)＝Gc1(s)S(s)P1(s)P2(s)
The feedback loop transfer function may be expressed as
Wherein G isc1(s) is a forward path controller, S(s) is an actuator, P1(s) is the controlled object, P2(s) other control links for the forward path, Gc2(s) a feedback controller for the inner loop;
the multi-loop control system is composed of an inner loop and an outer loop, and the inner loop is controlled by feedback control Gc2(s) outer loop control is a forward path controller Gc1(s)；
Unlike control system phase and amplitude margins, the physical meaning of delay margins can be understood as the critical stability of the system when the control signal lags the delay margin at the actuator. In engineering applications, the delay margin may be regarded as an absolute margin of the control system, and when the value is larger, the control system is characterized to have a more abundant margin, and vice versa.
The forward channel loop transfer function, that is, the transfer function formed by combining all links from the input node 1 of the loop to the output node 4 of the system, is consistent with the original open loop on the forward channel transfer function.
The feedback loop transfer function, namely, each link from the output node 4 of the loop to the input node 1 of the system, belongs to the external loop negative feedback, and is negatively fed back to the input node 1 of the loop and the control error amount formed by the instruction.
The transformed open loop transfer function is obtained by the product of the forward channel loop transfer function and the feedback loop transfer function.
Computer simulation example:
the control block diagram of a multi-loop control system is shown in figure 1, and the executive mechanism has a transfer function of
The controlled object is a letter
Inner loop feedback control coefficient of Gc2(s)＝KdThe forward series ratio is controlled to Gc(s)＝KpTwo sets of control parameters are sys 1: kd＝0.9，Kp4.0 percent; control parameter sys 2: kd＝2.9，Kp＝12.0。
According to the classical control theory, the open-loop transfer function of the control system can be obtained as
The open loop bode of systems sys1 and sys2 is shown in fig. 2, and the frequency domain indexes of sys1 and sys2 can be obtained by solving, sys 1: omegac＝4.06rad/s，Gm＝14.0dB，Pm＝76.9°；sys2：ωc4.04rad/s, 14.8dB Gm, 85.7 ° Pm. The control quality of the control system is judged according to the phase and amplitude margin of the system, and a conclusion can be drawn: the control quality of sys1 and sys2 were comparable.
Performing equivalent transformation according to the introduction method of the invention to obtain an open-loop transfer function of
The bode graphs of the systems sys1 and sys2 obtained by substituting the control parameters sys1 and sys2 into the above formula are shown in fig. 3, and when the control parameters are changed from sys1 to sys2, the open-loop cut-off frequency of the control system is changed
Increasing from 14.9rad/s to 31.4rad/s, phase margin
The delay margin Dm is reduced from 51.8ms to 15.9ms, namely the delay margin of the control system sys2 is greatly lower than that of the system sys 1.
Examining the time domain characteristics of the systems sys1 and sys2, simulating the unit step response of sys1 and sys2 in two cases of no delay at the actuator and 15.9ms delay at the actuator, as shown in fig. 4 (left diagram: no delay at the actuator, right diagram: 15.9ms delay at the actuator), it can be seen that adding 15.9ms delay at the actuator finds that sys2 is critically stable, and sys1 has a larger control margin.
The simulation result shows that:
(1) even if the two system control loops have the same structure as the controlled object and have close cut-off frequency, amplitude margin and phase margin, the control quality of the two systems can be greatly different;
(2) for a multi-loop control system, the control quality and robustness of the control system are limited only by judging according to the cut-off frequency, the phase and the amplitude margin of the control system;
(3) systems with larger delay margins correspond to better control quality;
(4) the cut-off frequency of the open loop after the equivalence transformation cannot represent the rapidity of the control system, and the cut-off frequency higher is usually corresponding to the lower delay margin, that is, the margin of the control system is smaller.
The invention is not described in detail and is within the knowledge of a person skilled in the art.
Claims (5)
1. A method for judging the margin of a multi-loop control system is characterized by comprising the following steps:
step 1, carrying out equivalent transformation on a multi-loop control system to convert the multi-loop control system into a single-loop control system with non-unit feedback;
step 2, calculating to obtain a transformed open loop transfer function open(s);
step 3, calculating according to the open loop transfer function open(s) to obtain a cut-off frequency of
A phase margin of
Step 4, calculating a delay margin Dm, and judging a control margin of the multi-loop control system according to the delay margin Dm; the delay margin
2. The method of claim 1, wherein the method further comprises: the multi-loop control system comprises an inner loop and an outer loop, wherein the inner loop is controlled by a feedback controller Gc2(s) outer loop control is a forward path controller Gc1(s)。
3. The method for determining multi-loop control system margin according to claim 1 or 2, wherein: the forward channel loop transfer function G(s) of the single-loop control system is as follows:
G(s)＝Gc1(s)S(s)P1(s)P2(s)；
wherein S(s) is an actuator, P1(s) is the controlled object, P2And(s) is other control links of the forward path.
4. The method of claim 3, wherein the method further comprises: the feedback loop transfer function h(s) of the single loop control system is expressed as:
5. the method of claim 4, wherein the method further comprises: the open loop transfer function open(s) is:
Priority Applications (1)
| Application Number | Priority Date | Filing Date | Title |
|---|---|---|---|
| CN201910330651.XA CN109946963B (en) | 2019-04-23 | 2019-04-23 | Method for judging margin of multi-loop control system |
Applications Claiming Priority (1)
| Application Number | Priority Date | Filing Date | Title |
|---|---|---|---|
| CN201910330651.XA CN109946963B (en) | 2019-04-23 | 2019-04-23 | Method for judging margin of multi-loop control system |
Publications (2)
| Publication Number | Publication Date |
|---|---|
| CN109946963A CN109946963A (en) | 2019-06-28 |
| CN109946963B true CN109946963B (en) | 2021-10-15 |
Family
ID=67016002
Family Applications (1)
| Application Number | Title | Priority Date | Filing Date |
|---|---|---|---|
| CN201910330651.XA Active CN109946963B (en) | 2019-04-23 | 2019-04-23 | Method for judging margin of multi-loop control system |
Country Status (1)
| Country | Link |
|---|---|
| CN (1) | CN109946963B (en) |
Families Citing this family (1)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN113467418B (en) * | 2021-06-25 | 2022-06-28 | 河北工业大学 | Method for measuring performance index of control loop |
Citations (7)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN102081355A (en) * | 2011-01-27 | 2011-06-01 | 西北工业大学 | Flight test robust determination method for equivalent stability margin of statically unstable aircraft |
| RU2011111991A (en) * | 2011-03-30 | 2012-10-10 | Федеральное государственное унитарное предприятие "Центральный аэрогидродинамический институт имени профессора Н.Е. Жуковского" (ФГУП | METHOD FOR DETERMINING STABILITY STABILITY RESERVES AND DEVICE FOR ITS IMPLEMENTATION |
| CN106507989B (en) * | 2010-05-20 | 2013-07-24 | 西北工业大学 | The flight test of quiet unstable flight device multiloop stability margin directly determines method |
| CN103777523A (en) * | 2014-02-28 | 2014-05-07 | 西安费斯达自动化工程有限公司 | Aircraft multi-loop model cluster composite PID (proportion integration differentiation) robust controller design method |
| CN103809442A (en) * | 2014-02-28 | 2014-05-21 | 西安费斯达自动化工程有限公司 | Method for designing composite frequency robust controller for multi-loop model cluster of aircraft |
| CN106338913A (en) * | 2016-11-04 | 2017-01-18 | 河北省科学院应用数学研究所 | Fractional-order PID control design method based on phase margin and cutoff frequency |
| CN107294085A (en) * | 2017-06-16 | 2017-10-24 | 东南大学 | The micro-capacitance sensor delay margin calculation method tracked based on critical characteristic root |
-
2019
- 2019-04-23 CN CN201910330651.XA patent/CN109946963B/en active Active
Patent Citations (7)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN106507989B (en) * | 2010-05-20 | 2013-07-24 | 西北工业大学 | The flight test of quiet unstable flight device multiloop stability margin directly determines method |
| CN102081355A (en) * | 2011-01-27 | 2011-06-01 | 西北工业大学 | Flight test robust determination method for equivalent stability margin of statically unstable aircraft |
| RU2011111991A (en) * | 2011-03-30 | 2012-10-10 | Федеральное государственное унитарное предприятие "Центральный аэрогидродинамический институт имени профессора Н.Е. Жуковского" (ФГУП | METHOD FOR DETERMINING STABILITY STABILITY RESERVES AND DEVICE FOR ITS IMPLEMENTATION |
| CN103777523A (en) * | 2014-02-28 | 2014-05-07 | 西安费斯达自动化工程有限公司 | Aircraft multi-loop model cluster composite PID (proportion integration differentiation) robust controller design method |
| CN103809442A (en) * | 2014-02-28 | 2014-05-21 | 西安费斯达自动化工程有限公司 | Method for designing composite frequency robust controller for multi-loop model cluster of aircraft |
| CN106338913A (en) * | 2016-11-04 | 2017-01-18 | 河北省科学院应用数学研究所 | Fractional-order PID control design method based on phase margin and cutoff frequency |
| CN107294085A (en) * | 2017-06-16 | 2017-10-24 | 东南大学 | The micro-capacitance sensor delay margin calculation method tracked based on critical characteristic root |
Also Published As
| Publication number | Publication date |
|---|---|
| CN109946963A (en) | 2019-06-28 |
Similar Documents
| Publication | Publication Date | Title |
|---|---|---|
| Moreno | Lyapunov function for levant's second order differentiator | |
| Huang et al. | Design of adaptive finite-time controllers for nonlinear uncertain systems based on given transient specifications | |
| Berger et al. | Funnel control for nonlinear systems with known strict relative degree | |
| Wang et al. | Adaptive neural network finite-time output feedback control of quantized nonlinear systems | |
| Ma et al. | Decentralized adaptive fault-tolerant control for a class of strong interconnected nonlinear systems via graph theory | |
| Su | Cooperative global output regulation of second-order nonlinear multi-agent systems with unknown control direction | |
| Biegler et al. | Large-scale nonlinear programming using IPOPT: An integrating framework for enterprise-wide dynamic optimization | |
| Liu et al. | Event-triggered cooperative robust practical output regulation for a class of linear multi-agent systems | |
| Zhang et al. | Adaptive neural tracking control of pure-feedback nonlinear systems with unknown gain signs and unmodeled dynamics | |
| CN104698842B (en) | A kind of LPV model nonlinear forecast Control Algorithms based on interior point method | |
| Wang et al. | L1 adaptive controller for nonlinear time-varying reference systems | |
| WO2005019949A1 (en) | Pid parameter adjustment device | |
| Wang et al. | Prescribed performance adaptive fault-tolerant tracking control for nonlinear time-delay systems with input quantization and unknown control directions | |
| CN109946963B (en) | Method for judging margin of multi-loop control system | |
| Ranjan et al. | Fractional filter IMC-TDD controller design for integrating processes | |
| CN103324093A (en) | Multi-model adaptive control system and control method thereof | |
| Dong et al. | Fixed-time synchronization of networked uncertain Euler–Lagrange systems | |
| WO2009067952A1 (en) | An art control method and a device thereof | |
| CN103558761B (en) | A kind of control method with the saturated nonlinear chemical reaction circulation Uncertain time-delayed systems of controller input | |
| Zhmud et al. | Numerical optimization of PID-regulator for object with distributed parameters | |
| CN106019934A (en) | Controller and control method | |
| Li et al. | Control design for arbitrary complex nonlinear discrete-time systems based on direct NNMRAC strategy | |
| Yu et al. | Robust state-estimator-based control of uncertain semi-Markovian jump systems subject to actuator failures and time-varying delay | |
| JP2014191736A (en) | Control parameter determination device, method, and program, and controller, and optimization control system | |
| CN115236990A (en) | Generalized estimator, generalized interference rejection controller and design method |
Legal Events
| Date | Code | Title | Description |
|---|---|---|---|
| PB01 | Publication | ||
| PB01 | Publication | ||
| SE01 | Entry into force of request for substantive examination | ||
| SE01 | Entry into force of request for substantive examination | ||
| GR01 | Patent grant | ||
| GR01 | Patent grant |