A method for setting controller parameters of a MUDE control system

Abstract

This invention discloses a method for tuning controller parameters of a MUDE control system, comprising the following steps: establishing transfer function models for first-order stable, integral, and unstable time-delay processes of a thermal time-delay process; obtaining the two-degree-of-freedom equivalent control structure and its equivalent controller of the MUDE control system, and then scaling the transfer function model and the controller parameters of the MUDE control system; analyzing the nominal stability of the MUDE control system based on the dual-track method to obtain the nominal stability region of the MUDE controller parameters; and selecting controller parameters based on the nominal stability region, according to the tracking speed, disturbance rejection performance, and robust stability requirements of the MUDE closed-loop control system, according to a unified quantitative tuning rule. This method can directly obtain MUDE controller parameters based on easily obtainable transfer function models of time-delay systems, and the obtained controller parameters can guarantee nominal stability while possessing good robustness, tracking performance, and disturbance suppression performance, thus reducing the burden of MUDE controller parameter adjustment.

Description

Technical Field

[0001] This invention belongs to the field of industrial time-delay process control technology, and in particular, it is a method for tuning controller parameters for MUDE control systems for stable, integral and unstable time-delay processes. Background Technology

[0002] Thermal time-delay processes are prevalent in coal-fired power units, gas turbines, fuel cells, and new integrated energy systems, encompassing typical stages such as steady-state processes (e.g., various heat exchangers), integral processes (e.g., boiler drums), and unstable processes (e.g., combustion oscillation processes). Designing effective controls for various typical thermal time-delay processes is of paramount importance to the safety, economy, and stability of energy and power systems.

[0003] Current thermal time-delay process control commonly employs PID controllers. However, the performance of traditional PID controllers is unsatisfactory in many scenarios, especially in handling disturbances and uncertainties. For most industrial systems, a simple low-order model based on an open-loop step response or a reduced-order model is most readily available. On the other hand, various disturbances in real-world systems can lead to a deterioration in control performance, requiring the control system to have strong anti-interference capabilities.

[0004] Against this backdrop, Zhong Qingchang et al. proposed UDE (Uncertainty and Disturbance Estimator) control in the paper "Zhong QC, Kuperman A, Stobart R K. Design of UDE-based controllers from their two-degree-of-freedom nature[J]. International Journal of Robust and Nonlinear Control, 2011, 21(17): 1994-2008." This control considers modeling uncertainties and external disturbances in a lumped form, and its effectiveness has been proven and it has been widely studied. Building on this, Sun Li et al. further proposed an improved UDE control (MUDE) for time-delay processes in the paper "Sun L, Li D, Zhong QC, et al. Control of a class of industrial processes with time delay based on a modified uncertainty and disturbance estimator[J]. IEEE Transactions on Industrial Electronics, 2016, 63(11): 7018-7028." This improved UDE control inherits the advantages of the original UDE, namely simplicity (low order) and decoupling of tracking and disturbance rejection. It is a unified solution for open-loop stable, integral, and unstable time-delay processes.

[0005] However, like many disturbance observer-based controllers, the above studies only present the logical framework of the MUDE controller, without providing a quantitative tuning method for its parameters. Related controls require complex parameter tuning before deployment, which necessitates repeated trial and error by professionals. From a practical application perspective, although open-loop stable, integral, and unstable time-delay processes exhibit significant differences in characteristics, a unified controller design and parameter tuning method is still desired. Summary of the Invention

[0006] The purpose of this invention is to provide a method for tuning controller parameters in a MUDE (Improved Uncertainty and Disturbance Estimation) control system. This method allows for the direct acquisition of MUDE controller parameters based on readily available transfer function models of time-delay systems. The obtained controller parameters guarantee nominal stability and exhibit good robustness, tracking performance, and disturbance suppression performance, thereby reducing the burden of adjusting MUDE controller parameters.

[0007] To achieve the above objectives, the solution of the present invention is:

[0008] A method for tuning controller parameters in a MUDE control system includes the following steps:

[0009] Step 1: Establish transfer function models for the first-order stable, integral, and unstable time-delay processes of the thermal time-delay process, respectively;

[0010] Step 2: Obtain the two-degree-of-freedom equivalent control structure and its equivalent controller of the MUDE control system, and then scale the transfer function model and controller parameters of the MUDE control system established in Step 1.

[0011] Step 3: Analyze the nominal stability of the MUDE control system based on the dual-track method and obtain the nominal stability domain of the MUDE controller parameters;

[0012] Step 4: Based on the nominal stability region obtained in Step 3, and according to the tracking speed, disturbance rejection performance and robust stability requirements of the MUDE closed-loop control system, select the controller parameters according to the unified quantitative tuning rules.

[0013] In step 1 above, transfer function models for the first-order stable, integral, and unstable time-delay processes of the thermal time-delay process are established, including:

[0014] The transfer function model for a first-order steady-state time-delay process is as follows: Where T > 0;

[0015] The transfer function model for a first-order integral time-delay process is as follows:

[0016] The transfer function model for a first-order unstable time-delay process is as follows: Where T < 0

[0017] Where K is the steady-state gain; T is the time constant, which is T > 0 for a first-order steady-state time delay process and T < 0 for a first-order unstable time delay process; L is the time delay.

[0018] In step 2 above, obtaining the two-degree-of-freedom equivalent control structure and its equivalent controller of the MUDE control system includes, among other things, the equivalent controller including a feedforward controller G. F (s) and equivalent feedback controller G E1 (s), G E2 (s);

[0019] For first-order stable and unstable processes with thermal time delay, the two-degree-of-freedom equivalent controller of the MUDE control system is:

[0020]

[0021] For a first-order integral time-delay process involving thermal time delay, the two-degree-of-freedom equivalent controller of the MUDE control system is:

[0022]

[0023] Among them, P n For a no-delay nominal model; L0 is the nominal delay of a first-order stable, unstable, or integral process; G m =1 / (1+T) m s) is the reference model, T m Q is the time constant of the reference model; e =B -1 K e For error feedback controller, K e For feedback gain, B = K / T for first-order stable and first-order unstable time-delay processes, and B = K for first-order integral time-delay processes, where K is the steady-state gain; T is the time constant, where T > 0 for first-order stable time-delay processes and T < 0 for first-order unstable time-delay processes; G f =1 / (1+T) f s) is a low-pass filter, T f This is the time constant of the low-pass filter.

[0024] In step 2 above, the transfer function model and controller parameters of the MUDE control system established in step 1 are scaled, including:

[0025] For first-order stable and first-order unstable time-delay processes in thermal processes, we have:

[0026] χ:=K e T

[0027] For a first-order integral time-delay process of thermal time-delay, we have:

[0028] χ:=K e L

[0029] Where L is the time delay; T is the time constant, where T > 0 for a first-order steady-state time delay process and T < 0 for a first-order unstable time delay process; T f K is the time constant of the low-pass filter; e For feedback gain;

[0030] Here, τ is the normalized Labrador operator, λ is the characteristic parameter of the normalization process, λ is the time constant of the normalized filter, and χ is the scaling feedback gain.

[0031] In step 3 above, the nominal stability of the MUDE control system is analyzed based on the dual-track method to obtain the nominal stability region of the MUDE controller parameters, including:

[0032] For open-loop stable and unstable MUDE control systems, the scaled closed-loop characteristic equation is:

[0033]

[0034] in, Here, τ is the normalized Labrador operator, χ is the characteristic parameter of the normalization process, and χ is the scaling feedback gain.

[0035] For an integral process MUDE control system, its scaled closed-loop characteristic equation is:

[0036]

[0037] Therefore, the nominal stability region of the MUDE controller parameters is obtained based on the dual-track method:

[0038] The nominal stability region of the MUDE controller parameters for a steady-state time-delay process is:

[0039]

[0040] Where θ is the solution of the equation θ=-τtan(θ) on (0,π);

[0041] The nominal stability region of the MUDE controller parameters for an integral time-delay process is:

[0042] 0 < χ < π / 2

[0043] The nominal stability region of the MUDE controller parameters for an unstable time-delay process is:

[0044]

[0045] Where α is the solution of the equation α=-τtan(α) on (0,π / 2).

[0046] In step 4 above, based on the nominal stability region obtained in step 3, and according to the tracking response, disturbance rejection response, and robust stability requirements of the MUDE control system, controller parameters are selected according to the unified quantitative tuning rules, including:

[0047] Step 41, for a first-order steady-state time-delay process, an integral time-delay process, and an unstable time-delay process, the nominal tracking transfer function is:

[0048]

[0049] Therefore, by selecting σ = T m / L to obtain the expected tracking response;

[0050] Among them, T mL is the reference model time constant; L is the time delay;

[0051] Step 42, within the nominal stability region described in step 3, combining root locus analysis and Pad approximation of the disturbance rejection response of the MUDE control system,

[0052] Within the nominal stability region in step 3, combining root locus analysis and Pad approximation of the disturbance rejection response of the MUDE control system, we obtain:

[0053] The quantitative tuning rule for χ in a steady-state time-delay process is as follows:

[0054]

[0055] The quantitative tuning rule for χ in a first-order integral time-delay process is:

[0056]

[0057] The quantitative tuning rule for χ in an unstable time-delay process is as follows:

[0058]

[0059] Where τ is the normalization process characteristic parameter, and χ is the scaling feedback gain; ξ d The desired damping of the system;

[0060] Step 43: Combine the disturbance rejection response and robust stability analysis of the MUDE control system to obtain unified quantitative tuning rules for stable, integral and unstable time-delay processes.

[0061] In step 43 above, the unified quantitative tuning rule is as follows:

[0062] σ=1,χ=χ d ,λ=0.3.

[0063] After adopting the above scheme, this invention is applicable to stable, integral, and unstable thermal time-delay processes. First, the two-degree-of-freedom equivalent control structure and its equivalent controller for the MUDE are derived, and the controller parameters of the stable, integral, and unstable time-delay process models and the MUDE control system are scaled. The nominal stability of the MUDE control system is analyzed based on the dual-track method. Based on the expected tracking dynamics of the MUDE control system, quantitative tuning rules for the reference model parameter σ in the MUDE are established. Within the stability domain of the MUDE controller parameters, quantitative tuning rules for the feedback controller parameter χ in the MUDE are established based on the root locus analysis of the closed-loop system's disturbance rejection transfer function and the Pad approximation. Based on the trade-off between the robustness and control performance of the MUDE control system, quantitative tuning rules for the low-pass filter parameter λ in the MUDE are established. Finally, a unified quantitative tuning method for the MUDE controller for a class of time-delay processes is obtained. This invention, based on appropriate parameter scaling, provides unified quantitative tuning of MUDE controller parameters for various types of thermal time-delay processes. This invention only requires obtaining the transfer function model of the time-delay system to directly calculate the controller parameters, and can guarantee the nominal stability, robustness, tracking performance, and disturbance suppression performance of the closed-loop control system. This invention eliminates the cumbersome parameter tuning and trial-and-error work required for MUDE controllers in various types of thermal time-delay processes, and has significant theoretical and applied research value.

[0064] This invention uses a parameter scaling method to uniformly and quantitatively tune the controller parameters of a MUDE control system. By simply obtaining the transfer function model of the time-delay system, the controller parameters can be directly obtained based on the proposed uniform quantitative tuning rules. The obtained controller parameters can guarantee nominal stability and have good robustness, tracking performance, and disturbance suppression performance. This reduces the burden of adjusting the MUDE controller parameters and has good theoretical and applied research value. Attached Figure Description

[0065] Figure 1 This is a structural diagram of the MUDE control system in this invention;

[0066] Figure 2 This is the equivalent control structure diagram of the MUDE two-degree-of-freedom in this invention;

[0067] Figure 3 This is the root locus diagram of χ variation when τ = 0.5 provided by the present invention;

[0068] Figure 4 This is a graph showing the trend of gain margin as a function of λ in the MUDE control system for a first-order open-loop steady-state time-delay process provided by the present invention.

[0069] Figure 5 This is a graph showing the variation of the stability margin of the first-order open-loop steady-state time-delay MUDE control system with λ, provided by the present invention.

[0070] Figure 6 This is a graph showing the trend of relative time delay margin as a function of λ in the MUDE control system for a first-order open-loop steady-state time-delay process provided by the present invention. Detailed Implementation

[0071] To make the objectives, technical solutions, and advantages of this invention clearer, the invention will be described in detail below with reference to the accompanying drawings and specific embodiments.

[0072] This invention provides a unified quantitative tuning method for a MUDE controller, comprising the following steps:

[0073] S1. Establish transfer function models for first-order stable, integral, and unstable time-delay processes of various types of thermal time-delay processes;

[0074] The MUDE control system used in this invention can be referenced. Figure 1 As shown, the transfer function models of the controlled time-delay processes include those for first-order stable, integral, and unstable time-delay processes, as detailed below:

[0075] Transfer function model of a first-order steady-state time-delay process. Where K is the steady-state gain, T is the time constant (T > 0 for steady-state time-delay processes), and L is the time delay;

[0076] Transfer function model of a first-order integral time-delay process.

[0077] Transfer function model of a first-order unstable time-delay process. Where T is the time constant (for unstable time-delay processes, T < 0);

[0078] S2, obtain the two-degree-of-freedom equivalent control structure of MUDE and its equivalent controller, and then scale the transfer function model and the controller parameters of the MUDE control system.

[0079] Will Figure 1 The equivalent transformation of the MUDE control structure shown is as follows: Figure 2 The two-degree-of-freedom control structure is shown. Where G... F (s), G E1 (s) and G E2 (s) represent the feedforward controller and two equivalent feedback controllers, respectively. Specifically:

[0080] For first-order stable and unstable processes, the MUDE two-degree-of-freedom equivalent controller is:

[0081]

[0082] Among them, P n For the transfer function model G p(s) is the no-delay nominal model that does not include a time delay component, where the superscript -1 indicates the inverse; L0 is the nominal time delay of a first-order stable, unstable, or integral process. For a first-order integral process, the MUDE two-degree-of-freedom equivalent controller is:

[0083]

[0084] Among them, G m =1 / (1+T) m s) is the reference model, T m Q is the time constant of the reference model; e =B -1 K e For error feedback controller, K e For feedback gain, B = K / T for both steady and unstable time-delay processes, and B = K for integral time-delay processes; G f =1 / (1+T) f s) is a low-pass filter, T f The filter time constant;

[0085] Then, the transfer function model and the controller parameters of the MUDE control system are scaled down, specifically:

[0086] For first-order stable and unstable processes, we have:

[0087] χ:=K e T,

[0088] For the first-order integral process, we have:

[0089] χ:=K e L.

[0090] in, Here, τ is the normalized Labrador operator, λ is the normalized process characteristic parameter (only for stable and unstable time-delay processes), λ is the normalized filter time constant, and χ is the scaling feedback gain.

[0091] S3. The nominal stability of the MUDE control system is analyzed based on the dual-track method to obtain the nominal stability domain of the MUDE controller parameters;

[0092] For open-loop stable and unstable process MUDE control systems, the scaled open-loop transfer function is:

[0093]

[0094] Furthermore, based on its closed-loop characteristic equation It can be converted into:

[0095]

[0096] For the integral process MUDE control system, its scaled open-loop transfer function is:

[0097]

[0098] Furthermore, based on its closed-loop characteristic equation It can be converted into:

[0099]

[0100] Therefore, the nominal stability region of the MUDE controller parameters can be obtained based on the dual-track method:

[0101] The nominal stability region of the MUDE controller parameters for a steady-state time-delay process is:

[0102]

[0103] Where θ is the solution of the equation θ=-τtan(θ) on (0,π);

[0104] The nominal stability region of the MUDE controller parameters for an integral time-delay process is:

[0105] 0 < χ < π / 2.

[0106] The nominal stability region of the MUDE controller parameters for an unstable time-delay process is:

[0107]

[0108] Where α is the solution of the equation α=-τtan(α) on (0,π / 2).

[0109] S4. Based on the tracking speed, nominal stability, disturbance rejection response and robust stability requirements of the MUDE control system, the controller parameters are selected according to the unified quantitative tuning rules proposed in this invention, and the design and parameter tuning of the MUDE control system are completed.

[0110] Considering the tracking speed of the MUDE control system, for the above three types of time-delay processes, the nominal tracking transfer function (i.e., the transfer function from r to y) is:

[0111]

[0112] This can be achieved by selecting σ = T m / L is used to obtain the desired tracking response, and it is generally recommended to set σ = 1;

[0113] Under nominal conditions, for both open-loop stable and unstable MUDE control systems, the scaled disturbance response (i.e., the transfer function from d to y) is:

[0114]

[0115] It can be seen that the disturbance rejection response can be accelerated by choosing a smaller λ; on the other hand, the disturbance rejection response of MUDE can also be accelerated by increasing χ. Furthermore, it can be seen that the second root of the above equation is independent of λ (determined by τ and χ). Therefore, we can determine χ and λ separately, first determining χ based on the disturbance rejection response requirements of the industrial process.

[0116] Generally, increasing the χ² value can accelerate the disturbance rejection response, but an excessively large χ² value may also cause the system to diverge. This can be addressed through analysis. We can analyze this transformation process by finding the root of the second part of the denominator. Let... The roots of the following equation are:

[0117]

[0118] Substituting, we get:

[0119]

[0120] For any first-order open-loop stable time-delay system (i.e., with a fixed τ > 0), the roots of the above equations can be obtained by solving them with a fixed χ; by changing χ, the root locus under the corresponding χ variation can be obtained.

[0121] Taking a time delay of τ = 0.5 as an example, the stability region of the MUDE parameters can be obtained from step S3 as (-1, 3.8). By varying χ within this range, its root locus can be obtained as follows: Figure 3 As shown. When χ = 0, the root can be obtained as As χ gradually increases, the root will shift along the negative direction of the imaginary axis, thus accelerating the disturbance rejection response. However, when χ increases to χ... * At approximately 0.45, a virtual root appears, indicating that the disturbance rejection response will exhibit oscillations or overshoot. As χ increases further, the oscillations gradually intensify until the system reaches critical oscillation at χ = ​​3.8.

[0122] To simplify parameter tuning and retuning of χ, the following Pad approximation is introduced:

[0123]

[0124] Therefore, we can obtain

[0125]

[0126] The corresponding system damping is

[0127]

[0128] Therefore, given the desired damping ξ of the system dThus, the corresponding feedback gain is:

[0129]

[0130] For first-order integrals and open-loop unstable time-delay processes, χ d Similarly, it can be obtained through the Pad approximation, expressed as follows:

[0131]

[0132]

[0133] It is generally recommended to take ξ. d =0.9. Furthermore, the above parameter tuning rules also facilitate parameter retuning, such as by selecting a smaller ξ. d This can accelerate the system's disturbance rejection response, but at the same time, the system's disturbance rejection response may experience overshoot or oscillation.

[0134] By combining the system's disturbance rejection response and robust stability analysis, a unified quantitative tuning rule for the time delay λ of stable, integral, and unstable time delay processes is obtained. Taking a first-order open-loop stable time delay system as an example, the phase margin, stability margin, and relative delay margin of the MUDE control system for different time delay processes (different τ) are as follows: Figure 4 , Figure 5 and Figure 6 As shown.

[0135] Therefore, to ensure the robust stability of the MUDE control system (appropriate robustness margin), λ = 0.3 is selected.

[0136] In summary, the unified quantitative tuning rule for MUDE of stable, integral, and unstable time-delay processes can be obtained as follows:

[0137] σ=1,χ=χ d ,λ=0.3

[0138] The above embodiments provide a unified quantitative tuning method for MUDE control of stable, integral, and unstable time-delay processes. First, the two-degree-of-freedom equivalent control structure and its equivalent controller of the MUDE are derived. Then, the controller parameters of the stable, integral, and unstable time-delay process models and the MUDE control system are scaled. The nominal stability of the MUDE control system is analyzed based on the dual-track method. Quantitative tuning rules for the reference model parameters in the MUDE are established based on the expected tracking dynamics of the MUDE control system. Within the stability domain of the MUDE controller parameters, quantitative tuning rules for the feedback controller parameters in the MUDE are established based on the root locus analysis of the closed-loop system's disturbance rejection transfer function and the Pad approximation. Quantitative tuning rules for the low-pass filter parameters in the MUDE are established based on the trade-off between the robustness and control performance of the MUDE control system. Finally, a unified quantitative tuning method for the MUDE controller of a class of time-delay processes is obtained. This invention uses a parameter scaling method to uniformly and quantitatively tune the controller parameters of a MUDE control system. By simply obtaining the transfer function model of the time-delay system, the controller parameters can be directly obtained based on the proposed uniform quantitative tuning rules. The obtained controller parameters can guarantee nominal stability and have good robustness, tracking performance, and disturbance suppression performance. This reduces the burden of adjusting the MUDE controller parameters and has good theoretical and applied research value.

[0139] The system embodiments described in this specification are basically similar to the method embodiments, so they are described in a relatively simple manner. For relevant details, please refer to the descriptions of the method embodiments. Those skilled in the art can understand and implement these embodiments without any creative effort.

[0140] It should be noted that in this invention, relational terms such as "first" and "second" are used merely to distinguish one entity or operation from another, and do not necessarily require or imply any such actual relationship or order between these entities or operations. Furthermore, the terms "comprising," "including," or any other variations thereof are intended to cover non-exclusive inclusion, such that a process, method, article, or apparatus that comprises a list of elements includes not only those elements but also other elements not expressly listed, or elements inherent to such a process, method, article, or apparatus. Without further limitations, an element defined by the phrase "comprising one..." does not exclude the presence of other identical elements in the process, method, article, or apparatus that includes said element.

[0141] The above description is merely a specific embodiment of the present invention, but the scope of protection of the present invention is not limited thereto. Any variations or substitutions that can be easily conceived by those skilled in the art within the scope of the technology disclosed in the present invention should be included within the scope of protection of the present invention.

Claims

1. A method of tuning controller parameters of a MUDE control system, characterized by Includes the following steps: Step 1: Establish transfer function models for the first-order stable, integral, and unstable time-delay processes of the thermal time-delay process, respectively; Step 2: Obtain the two-degree-of-freedom equivalent control structure and its equivalent controller of the MUDE control system, and then scale the transfer function model and controller parameters of the MUDE control system established in Step 1. Step 3: Analyze the nominal stability of the MUDE control system based on the dual-track method and obtain the nominal stability domain of the MUDE controller parameters; Step 4: Based on the nominal stability region obtained in Step 3, and according to the tracking speed, disturbance rejection performance and robust stability requirements of the MUDE closed-loop control system, select the controller parameters according to the unified quantitative tuning rules. In step 3, the nominal stability of the MUDE control system is analyzed based on the dual-trajectory method to obtain the nominal stability region of the MUDE controller parameters, including: For open-loop stable and unstable MUDE control systems, the scaled closed-loop characteristic equation is: ， in, To normalize the Labras operator, These are the characteristic parameters of the normalization process. For scaling feedback gain; For an integral process MUDE control system, its scaled closed-loop characteristic equation is: ， Therefore, the nominal stability region of the MUDE controller parameters is obtained based on the dual-track method: The nominal stability region of the MUDE controller parameters for a steady-state time-delay process is: ， in For the equation exist The solution above; The nominal stability region of the MUDE controller parameters for an integral time-delay process is: ， The nominal stability region of the MUDE controller parameters for an unstable time-delay process is: ， in For the equation exist The solution above.

2. The method as described in claim 1, characterized in that: In step 1, transfer function models for the first-order stable, integral, and unstable time-delay processes of the thermal time-delay process are established, including: The transfer function model for a first-order steady-state time-delay process is as follows: ,in ; The transfer function model for a first-order integral time-delay process is as follows: ; The transfer function model for a first-order unstable time-delay process is as follows: ,in , Where K is the steady-state gain; T is the time constant, and in a first-order steady-state time-delay process we have In a first-order unstable time-delay process, there is L represents the time delay.

3. The method as described in claim 1, characterized in that: In step 2, obtaining the two-degree-of-freedom equivalent control structure and its equivalent controller of the MUDE control system includes, among other things, a feedforward controller. and equivalent feedback controller , ; For first-order stable and unstable processes with thermal time delay, the two-degree-of-freedom equivalent controller of the MUDE control system is: ， For a first-order integral time-delay process involving thermal time delay, the two-degree-of-freedom equivalent controller of the MUDE control system is: ， Among them, P n For a no-delay nominal model; L0 is the nominal delay of a first-order stable, unstable, or integral process; As a reference model, The reference model time constant; For error feedback controller, For feedback gain, for first-order stable and first-order unstable time-delay processes For a first-order integral time delay process Where K is the steady-state gain; T is the time constant, and in a first-order steady-state time-delay process we have In a first-order unstable time-delay process, there is ; It is a low-pass filter. This is the time constant of the low-pass filter.

4. The method as described in claim 1, characterized in that: In step 2, the transfer function model and controller parameters of the MUDE control system established in step 1 are scaled, including: For first-order stable and first-order unstable time-delay processes in thermal processes, we have: ， For a first-order integral time-delay process of thermal time-delay, we have: ， Where L is the time delay; T is the time constant, and in a first-order steady-state time-delay process we have In a first-order unstable time-delay process, there is ; This represents the time constant of the low-pass filter. For feedback gain; To normalize the Labras operator, These are the characteristic parameters of the normalization process. This is the normalized filter time constant. This is for scaling feedback gain.

5. The method as described in claim 1, characterized in that: In step 4, based on the nominal stability region obtained in step 3, and according to the tracking response, disturbance rejection response, and robust stability requirements of the MUDE control system, controller parameters are selected according to a unified quantitative tuning rule, including: Step 41, for a first-order steady-state time-delay process, an integral time-delay process, and an unstable time-delay process, the nominal tracking transfer function is: ， Thus by selecting To obtain the expected tracking response; in, L is the reference model time constant; L is the time delay; Step 42, within the nominal stability region described in step 3, combining root locus analysis and Pad approximation of the disturbance rejection response of the MUDE control system, Within the nominal stability region in step 3, combining root locus analysis and Pad approximation of the disturbance rejection response of the MUDE control system, we obtain: steady-state time-delay process The quantitative tuning rule is as follows: ， First-order integral time delay process The quantitative tuning rule is as follows: ， Unstable time-delay processes The quantitative tuning rule is as follows: ， in, These are the characteristic parameters of the normalization process. For scaling feedback gain; The desired damping of the system; Step 43: Combine the disturbance rejection response and robust stability analysis of the MUDE control system to obtain unified quantitative tuning rules for stable, integral and unstable time-delay processes.

6. The method as described in claim 5, characterized in that: In step 43, the unified quantitative tuning rule is as follows: 。

Images