阅读说明：本技术 基于稳定裕度和动态响应指标的pid控制参数整定方法 (PID control parameter setting method based on stability margin and dynamic response index ) 是由 王家栋 陆海琛 于 2020-05-27 设计创作，主要内容包括：本发明涉及PID控制领域,尤其涉及一种基于稳定裕度和动态响应指标的PID控制参数整定方法,包括：计算得到闭环回路控制系统的稳定裕度；根据闭环回路控制系统的稳定裕度计算得到PID控制参数；根据PID控制参数进行闭环控制系统阶跃响应仿真,通过阶跃响应曲线获取动态响应指标,以间接地关联稳定裕度和动态响应指标；基于稳定裕度和动态响应指标的关联方式,通过对稳定裕度进行搜索以获得优化问题的最优解,以对PID控制参数进行整定。通过使用本发明,可以实现以下效果：关联PID控制参数和动态响应性能指标,从而提高了用户友好度；使用的网格化搜索寻优可以直接给出满足用户对动态性能要求的最优解,从而提高了整定效率,避免了重复整定。(The invention relates to the field of PID control, in particular to a PID control parameter setting method based on stability margin and dynamic response indexes, which comprises the following steps: calculating to obtain the stability margin of the closed loop control system; calculating to obtain PID control parameters according to the stability margin of the closed loop control system; performing closed-loop control system step response simulation according to the PID control parameters, and acquiring a dynamic response index through a step response curve so as to indirectly associate the stability margin with the dynamic response index; based on the correlation mode of the stability margin and the dynamic response index, the stability margin is searched to obtain the optimal solution of the optimization problem, so that the PID control parameters are adjusted. By using the present invention, the following effects can be achieved: the PID control parameters and the dynamic response performance indexes are associated, so that the user friendliness is improved; the used gridding search optimization can directly provide the optimal solution meeting the requirements of the user on the dynamic performance, thereby improving the setting efficiency and avoiding repeated setting.)

1. A PID control parameter setting method based on stability margin and dynamic response index is applied to a closed loop control system and is characterized by comprising the following steps:

calculating to obtain the stability margin of the closed loop control system;

calculating to obtain PID control parameters according to the stability margin of the closed loop control system;

performing closed-loop control system step response simulation according to the PID control parameters, and acquiring a dynamic response index through a step response curve so as to indirectly associate the stability margin with the dynamic response index;

based on the correlation mode of the stability margin and the dynamic response index, the stability margin is searched to obtain the optimal solution of the optimization problem, so that the PID control parameters are adjusted.

2. The PID control parameter tuning method based on stability margin and dynamic response index as claimed in claim 1, wherein the stability margin comprises a gain margin and a phase margin.

3. The PID control parameter tuning method based on stability margin and dynamic response index as claimed in claim 2, wherein the calculating the stability margin of the closed loop control system comprises:

gain margin A_mAnd a phase margin phi_mThe calculation formula of (a) is as follows:

wherein, ω is_gAnd ω_pRespectively a gain crossing frequency and a phase crossing frequency of the closed loop control system, and satisfies:

4. the PID control parameter tuning method based on the stability margin and the dynamic response index as claimed in claim 3, wherein the calculating the PID control parameter according to the stability margin of the closed loop system comprises:

defining a controlled object model G(s) as a first-order time lag model:

wherein, K_pRepresents the gain, T_pRepresents a time constant, τ represents a time lag;

the mathematical form of a parallel PID controller defining a standard is:

wherein, K_c，T_i，T_dSequentially representing a first proportion, a first integration time and a first differentiation time;

let T_dIs equal to 0 and is according toGain margin A_mAnd a phase margin phi_mThe calculation formula and the relationship between the gain crossing frequency and the phase crossing frequency are used for obtaining the controller parameters:

T_d＝0，

wherein the content of the first and second substances,

5. the PID control parameter tuning method based on the stability margin and the dynamic response index as claimed in claim 3, wherein the calculating the PID control parameter according to the stability margin of the closed loop control system comprises:

defining the controlled object model G'(s) as a second-order time lag model:

wherein the content of the first and second substances,represents a newly added time constant and is less than or equal to T_p；

The mathematical form of a parallel PID controller defining a standard is:

wherein, K'_c，T′_i，T′_dSequentially representing a second proportion, a second integration time and a second differentiation time;

according to the gain margin A_mAnd a phase margin phi_mThe calculation formula and the relationship between the gain crossing frequency and the phase crossing frequency are used for obtaining the controller parameters:

6. the PID control parameter tuning method based on stability margin and dynamic response index as claimed in claim 1, wherein the dynamic response index comprises overshoot OS% and steady state time T_ss，

Wherein, y_peakA maximum value representing a sequence of closed loop step responses of the system; y is_finalRepresenting the final value of the closed loop step response sequence of the system;

steady state time T_ssDefined as the elapsed time to reach its 2% steady state value interval after the step response of the closed loop control system.

7. The PID control parameter tuning method based on stability margin and dynamic response index as claimed in claim 2, wherein the optimal solution of the optimization problem is obtained by performing gridding search in two dimensions of gain margin and phase margin.

8. The PID control parameter tuning method based on stability margin and dynamic response index as claimed in claim 7, wherein the obtaining the optimal solution of the optimization problem by performing a gridding search in two dimensions of gain margin and phase margin comprises:

definition of

setting optimization problems as follows:

according to the search grids of two dimensions of the gain margin and the phase margin, the optimal solution T of the optimization problem is obtained by searching from small to large or from large to small in sequence_ss ^min。

9. The PID control parameter tuning method based on the stability margin and the dynamic response index as claimed in claim 1, wherein the tuning the PID control parameter comprises:

and obtaining an optimal PID control parameter corresponding to the optimal solution, and setting the current PID control parameter through the optimal PID control parameter.

10. The PID control parameter tuning method based on stability margin and dynamic response index as claimed in claim 8, further comprising:

and obtaining the gain margin and the phase margin in the search grid corresponding to the optimal solution so as to measure the robustness of the closed loop control system.

Technical Field

The invention relates to the field of PID control, in particular to a PID control parameter setting method based on stability margin and dynamic response indexes.

Background

Proportional Integral Derivative (PID) control is currently one of the most common and effective control methods in the field of industrial process control. According to statistics, more than 90% of automatic control loops adopt PID control strategies. The PID control has the advantages that: simple structure, good stability, safety, reliability and convenient adjustment.

At present, the widely applied PID parameter setting method mainly comprises a data-driven setting method and a model-based setting method. For a data-driven parameter setting method, the closed-loop control performance generally cannot be estimated accurately in advance, so that a setting strategy cannot be adjusted according to actual dynamic response requirements; secondly, it is often necessary to make the process reach a specific state and perform feature extraction of the curve during the tuning process, for example: a Z-N method, a critical ratio method, an attenuation curve method, and the like. In addition, more human-computer interaction generally exists in the setting process; if the process response time is long, setting will take much time. For model-based tuning methods, for example: the Lambda method, the setting method based on internal model control and the like have the advantages that a large number of loops can be set in batch by utilizing loop historical data; meanwhile, if the model is accurate, the closed-loop control performance can be adjusted according to the experience of a user. However, these methods listed above do not correlate the tuning parameters to a specific closed loop dynamic response index, and thus the user is not expecting closed loop control performance during parameter tuning. Although a user can adjust the parameters after setting, the stability of the closed-loop control system cannot be sufficiently ensured in the adjustment process. Particularly, when a large number of PID loops need to be adjusted, for example, during the driving stage of the device or after the operating conditions change, technicians have difficulty in having time to finely adjust the parameters of each loop until better control performance occurs, and once the adjustment range is too large, the control system may be unstable.

Disclosure of Invention

In order to solve the problems, the invention provides a PID control parameter setting method based on a stability margin and a dynamic response index so as to meet the robust stability of a closed-loop control system.

A PID control parameter setting method based on stability margin and dynamic response index is applied to a closed loop control system and comprises the following steps:

calculating to obtain the stability margin of the closed loop control system;

calculating to obtain PID control parameters according to the stability margin of the closed loop control system;

performing closed-loop control system step response simulation according to the PID control parameters, and acquiring a dynamic response index through a step response curve so as to indirectly associate the stability margin with the dynamic response index;

based on the correlation mode of the stability margin and the dynamic response index, the stability margin is searched to obtain the optimal solution of the optimization problem, so that the PID control parameters are adjusted.

Preferably, the stability margin includes a gain margin and a phase margin.

Preferably, the calculating the stability margin of the closed loop control system includes:

gain margin A_mAnd a phase margin phi_mThe calculation formula of (a) is as follows:

wherein, ω is_gAnd ω_pRespectively a gain crossing frequency and a phase crossing frequency of the closed loop control system, and satisfies:

preferably, the calculating the PID control parameter according to the stability margin of the closed loop system includes:

defining a controlled object model G(s) as a first-order time lag model:

wherein, K_pRepresents the gain, T_pRepresents a time constant, τ represents a time lag;

the mathematical form of a parallel PID controller defining a standard is:

wherein, K_c，T_i，T_dSequentially representing a first proportion, a first integration time and a first differentiation time;

let T _d0 and according to the gain margin A_mAnd a phase margin phi_mThe calculation formula and the relationship between the gain crossing frequency and the phase crossing frequency are used for obtaining the controller parameters:

wherein the content of the first and second substances,

preferably, the calculating the PID control parameter according to the stability margin of the closed loop control system includes:

defining the controlled object model G'(s) as a second-order time lag model:

wherein the content of the first and second substances,

represents a newly added time constant and is less than or equal to T_p；

The mathematical form of a parallel PID controller defining a standard is:

wherein, K'_c，T’_i，T’_dSequentially representing a second proportion, a second integration time and a second differentiation time;

according to the gain margin A_mAnd a phase margin phi_mThe calculation formula and the relationship between the gain crossing frequency and the phase crossing frequency are used for obtaining the controller parameters:

preferably, the dynamic response indicator includes overshoot OS% and steady state time T_ss，

Wherein, y_peakA maximum value representing a sequence of closed loop step responses of the system; y is_finalRepresenting the final value of the closed loop step response sequence of the system;

steady state time T_ssDefined as the elapsed time to reach its 2% steady state value interval after the step response of the closed loop control system.

Preferably, the optimal solution of the optimization problem is obtained by performing a gridding search in two dimensions, namely gain margin and phase margin.

Preferably, the obtaining an optimal solution of the optimization problem by performing a gridding search in two dimensions of the gain margin and the phase margin includes:

definition of

Respectively forming two dimensionality search grids of the gain margin and the phase margin for the value ranges of the gain margin and the phase margin and the corresponding search step length;

setting optimization problems as follows:

wherein the OS^*% is the desired overshoot;

according toSearching grids of two dimensions of gain margin and phase margin from small to large or from large to small in sequence respectively to obtain the optimal solution T of the optimization problem_ss ^min。

Preferably, the tuning the PID control parameter includes:

and obtaining an optimal PID control parameter corresponding to the optimal solution, and setting the current PID control parameter through the optimal PID control parameter.

Preferably, the method further comprises the following steps:

and obtaining the gain margin and the phase margin in the search grid corresponding to the optimal solution so as to measure the robustness of the closed loop control system.

By using the present invention, the following effects can be achieved:

1. the invention relates PID control parameters and dynamic response performance indexes, thereby improving the user friendliness;

2. the gridding search optimization used by the invention can directly provide the optimal solution meeting the requirements of users on the dynamic performance, thereby improving the setting efficiency and avoiding repeated setting;

3. the invention ensures the robust stability of the closed loop control system through the correlation of the stability margin and the dynamic response index, and can provide the measurement of the stability margin of the closed loop system under the expected dynamic response index.

Drawings

The present invention will be described in further detail with reference to the accompanying drawings and specific embodiments.

FIG. 1 is a schematic block diagram of a closed loop control system in an embodiment of the present invention;

FIG. 2 is a schematic flow chart diagram of an embodiment of the present invention;

FIG. 3 is a graph of a step response in an embodiment of the present invention;

fig. 4 is a schematic flowchart of step S4 according to the embodiment of the present invention.

Detailed Description

The technical solutions of the present invention will be further described below with reference to the accompanying drawings, but the present invention is not limited to these embodiments.

The basic idea of the invention is to associate the stability margin, the PID control parameters and their dynamic response performance indicators and to calculate the optimal PID control parameters. Three parameters for a PID controller in a closed loop control system, namely the ratio K_cIntegration time T_iDifferential time T_dAnd meanwhile, setting is carried out, so that the control performance of the whole closed loop control system after the controller is put into operation meets the control requirement of a user on the dynamic response performance index.

Based on the above inventive concept, the present embodiment provides a PID control parameter tuning method based on stability margin and dynamic response index, which is applied to a closed loop control system, as shown in fig. 1. Wherein r (t), u (t), y (t), e (t), n (t) respectively represent a closed loop control system G_clReference signal, process input measurement, process output measurement, tracking error, and measurement noise. G(s) is a model of the controlled object, a process model commonly used in the process industry is the first-order time-lapse model (FOPDT), i.e.:

wherein, K_pIs the gain, T_pIs the time constant and τ is the time lag. C(s) is a standard parallel PID controller, which is common in industrial fields, and its mathematical form can be expressed as:

wherein, K_c，T_i，T_dThe first proportion, the first integration time, and the first differentiation time are sequentially indicated.

As shown in fig. 2, a PID control parameter tuning method based on stability margin and dynamic response index in this embodiment includes the following steps:

s1: and calculating to obtain the stability margin of the closed loop control system.

The stability margin is one of the standards for measuring the robustness of the closed loop control system, and the gain margin A can be used specifically_mAnd a phase margin phi_mTo calculate, its formula is written as:

in the formula (3), ω_gAnd ω_pRespectively a gain crossing frequency and a phase crossing frequency of the closed loop control system, and satisfies:

s2: and calculating to obtain PID control parameters according to the stability margin of the closed loop control system.

According to the total of four equations (3) and (4), if the controlled object model parameters are known and let T be_d0, the unknown parameter is not greater than four, then the controller parameter can be calculated. The derivation process is as follows:

in a first step, substituting formulae (1) and (2) into formulae (3) and (4) yields:

and secondly, approximating an arctan function:

and simplifying processing equation (5) to obtain:

thirdly, solving the formula (7) to obtain PID control parameters:

wherein the content of the first and second substances,

in general, PI controllers achieve better control performance for most loop types in the process control field, such as level, pressure, flow loops, etc. For temperature loops, we often need to use a PID controller. If a PID controller is used, the number of unknowns is already greater than the number of equations and a solution to the equations cannot generally be calculated. Looking at equations (3) and (4), where the transfer functions C(s) G(s) of the feed-forward channels are used, it is contemplated that a second order lag model may be used:

wherein the content of the first and second substances,

represents a newly added time constant and is less than or equal to T_p。

The newly added unknown parameter T can be obtained by taking the PID control parameter as the following value_dAndone term cancels out:

wherein, K'_c，T’_i，T’_dSequentially representing a second proportion, a second integration time and a second differentiation time;

the PID parameter formula derived above is calculated according to a given stability margin, and is suitable for the parallel PID controller shown in (2). In practical applications, since the concept of the stability margin is generally unknown to users, it is necessary to correlate the stability margin with the performance index of the closed-loop control system from the perspective of the users.

S3: and performing step response simulation of the closed-loop control system according to the PID control parameters, and acquiring a dynamic response index through a step response curve so as to indirectly associate the stability margin with the dynamic response index.

The following provides an indication of the performance of a closed loop control system that is relatively easy to understand and accept in the industrial field, and then indicates its correlation with the steady state margin. According to the classical control theory, the performance indexes of the closed loop control system are various, and the performance indexes which are easily understood and accepted by users are considered by the invention to be two: overshoot and steady state time; and the two indexes can be respectively used for measuring the smoothness and the response speed of the dynamic response of the closed-loop control system.

Overshoot (Overshoot):

wherein, y_peakA maximum value representing a sequence of closed loop step responses of the system; y is_finalRepresenting the final value of the sequence of the closed loop step response of the system.

Steady-state Time (setting Time): t for steady time_ssExpressed as the elapsed time to reach its 2% steady state value interval after the step response of the closed loop control system.

The invention adopts the step response curve output by simulating the closed loop control system, as shown in figure 3, the overshoot OS% and the steady state time T are calculated according to the step response curve_ssThereby indirectly correlating the stability margin and the dynamic response index.

According to the invention, the PID parameters are bound, and the overshoot and the steady-state time are taken as dynamic response performance indexes, so that the user friendliness is improved, and a bridge between the process requirement and the PID parameters is established.

S4: based on the correlation mode of the stability margin and the dynamic response index, the stability margin is searched to obtain the optimal solution of the optimization problem, so that the PID control parameters are adjusted.

Based on the above correlation method, the optimal solution of the following optimization problem can be approximately obtained by parameter search in two dimensions of the gain margin and the phase margin.

Among the above problems, OS^*% is the desired overshoot value, specified by the user.

Preferably, in the embodiment, the optimal solution of the optimization problem is obtained by performing a gridding search on two dimensions of the gain margin and the phase margin, which specifically includes the following steps as shown in fig. 4:

s41: definition of

Respectively forming two dimensionality search grids of the gain margin and the phase margin for the value ranges of the gain margin and the phase margin and the corresponding search step length;

the denser the grid, the higher the complexity, but the closer the searched optimal solution is to the optimal solution of the optimization problem. The gain margin and the phase margin are considered separately, so that the performance of the closed loop control system is more in line with the actual requirement although the solving complexity is increased to a certain degree.

Regarding the reasonable value ranges of the gain margin and the phase margin, according to the rule of thumb, the following can be taken:

s42: setting an optimization problem:

wherein the OS^*% is the desired overshoot.

S43: according to the search grids of two dimensions of the gain margin and the phase margin, the optimal solution T of the optimization problem is obtained by searching from small to large or from large to small in sequence_ss ^min。

At the time of obtaining the optimal solution T_ss ^minAfter that time, the user can use the device,obtaining an optimal solution T_ss ^minAnd the corresponding optimal PID control parameter is used for tuning the current PID control parameter.

In the embodiment, the optimal solution of the optimization problem is obtained by carrying out gridding search on two dimensions of the gain margin and the phase margin, so that the setting efficiency is improved, and repeated setting is avoided.

When the stability margin is associated, the gain margin and the phase margin can be bound to obtain the gain margin and the phase margin in the search grid corresponding to the optimal solution so as to measure the robustness of the closed-loop control system, and therefore the robustness of the control system can be adjusted by using a single parameter.

Various modifications or additions may be made to the described embodiments or alternatives may be employed by those skilled in the art without departing from the spirit or ambit of the invention as defined in the appended claims.