CN114019797B - Sewage treatment equipment ozone concentration sliding mode anti-interference control method under non-time-lag nominal model - Google Patents
Sewage treatment equipment ozone concentration sliding mode anti-interference control method under non-time-lag nominal model Download PDFInfo
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- CBENFWSGALASAD-UHFFFAOYSA-N Ozone Chemical compound [O-][O+]=O CBENFWSGALASAD-UHFFFAOYSA-N 0.000 title claims abstract description 45
- 238000000034 method Methods 0.000 title claims abstract description 33
- 239000010865 sewage Substances 0.000 title claims abstract description 25
- 238000013461 design Methods 0.000 claims description 19
- 230000000694 effects Effects 0.000 claims description 13
- 230000002411 adverse Effects 0.000 claims description 10
- 230000008569 process Effects 0.000 claims description 10
- 239000007788 liquid Substances 0.000 claims description 6
- 230000036039 immunity Effects 0.000 claims description 4
- 238000013459 approach Methods 0.000 claims description 3
- 230000003068 static effect Effects 0.000 claims description 3
- 230000001419 dependent effect Effects 0.000 claims description 2
- 230000002829 reductive effect Effects 0.000 description 9
- XLYOFNOQVPJJNP-UHFFFAOYSA-N water Substances O XLYOFNOQVPJJNP-UHFFFAOYSA-N 0.000 description 9
- 239000012071 phase Substances 0.000 description 6
- 230000004044 response Effects 0.000 description 6
- 238000010586 diagram Methods 0.000 description 5
- 239000012528 membrane Substances 0.000 description 4
- 238000007792 addition Methods 0.000 description 3
- QVGXLLKOCUKJST-UHFFFAOYSA-N atomic oxygen Chemical compound [O] QVGXLLKOCUKJST-UHFFFAOYSA-N 0.000 description 3
- 230000008859 change Effects 0.000 description 3
- 238000001914 filtration Methods 0.000 description 3
- 239000001301 oxygen Substances 0.000 description 3
- 229910052760 oxygen Inorganic materials 0.000 description 3
- 239000000645 desinfectant Substances 0.000 description 2
- 238000011161 development Methods 0.000 description 2
- 230000018109 developmental process Effects 0.000 description 2
- OSVXSBDYLRYLIG-UHFFFAOYSA-N dioxidochlorine(.) Chemical compound O=Cl=O OSVXSBDYLRYLIG-UHFFFAOYSA-N 0.000 description 2
- 238000005265 energy consumption Methods 0.000 description 2
- 239000003344 environmental pollutant Substances 0.000 description 2
- 230000000415 inactivating effect Effects 0.000 description 2
- 238000013178 mathematical model Methods 0.000 description 2
- 244000005700 microbiome Species 0.000 description 2
- 230000003647 oxidation Effects 0.000 description 2
- 238000007254 oxidation reaction Methods 0.000 description 2
- 230000036961 partial effect Effects 0.000 description 2
- 231100000719 pollutant Toxicity 0.000 description 2
- 239000002699 waste material Substances 0.000 description 2
- 241000894006 Bacteria Species 0.000 description 1
- QDHHCQZDFGDHMP-UHFFFAOYSA-N Chloramine Chemical compound ClN QDHHCQZDFGDHMP-UHFFFAOYSA-N 0.000 description 1
- KZBUYRJDOAKODT-UHFFFAOYSA-N Chlorine Chemical compound ClCl KZBUYRJDOAKODT-UHFFFAOYSA-N 0.000 description 1
- ZAMOUSCENKQFHK-UHFFFAOYSA-N Chlorine atom Chemical compound [Cl] ZAMOUSCENKQFHK-UHFFFAOYSA-N 0.000 description 1
- 239000004155 Chlorine dioxide Substances 0.000 description 1
- 239000005708 Sodium hypochlorite Substances 0.000 description 1
- 241000700605 Viruses Species 0.000 description 1
- XKMRRTOUMJRJIA-UHFFFAOYSA-N ammonia nh3 Chemical compound N.N XKMRRTOUMJRJIA-UHFFFAOYSA-N 0.000 description 1
- 239000000987 azo dye Substances 0.000 description 1
- 230000009286 beneficial effect Effects 0.000 description 1
- 230000033558 biomineral tissue development Effects 0.000 description 1
- 238000006243 chemical reaction Methods 0.000 description 1
- 239000000460 chlorine Substances 0.000 description 1
- 229910052801 chlorine Inorganic materials 0.000 description 1
- 235000019398 chlorine dioxide Nutrition 0.000 description 1
- 239000003599 detergent Substances 0.000 description 1
- 208000028659 discharge Diseases 0.000 description 1
- XWZDJOJCYUSIEY-UHFFFAOYSA-L disodium 5-[(4,6-dichloro-1,3,5-triazin-2-yl)amino]-4-hydroxy-3-phenyldiazenylnaphthalene-2,7-disulfonate Chemical compound [Na+].[Na+].Oc1c(N=Nc2ccccc2)c(cc2cc(cc(Nc3nc(Cl)nc(Cl)n3)c12)S([O-])(=O)=O)S([O-])(=O)=O XWZDJOJCYUSIEY-UHFFFAOYSA-L 0.000 description 1
- 238000004043 dyeing Methods 0.000 description 1
- 238000003912 environmental pollution Methods 0.000 description 1
- 239000012510 hollow fiber Substances 0.000 description 1
- 230000002209 hydrophobic effect Effects 0.000 description 1
- 230000005764 inhibitory process Effects 0.000 description 1
- 230000002147 killing effect Effects 0.000 description 1
- 239000007791 liquid phase Substances 0.000 description 1
- 238000004519 manufacturing process Methods 0.000 description 1
- 238000005259 measurement Methods 0.000 description 1
- 238000012986 modification Methods 0.000 description 1
- 230000004048 modification Effects 0.000 description 1
- 239000004810 polytetrafluoroethylene Substances 0.000 description 1
- 229920001343 polytetrafluoroethylene Polymers 0.000 description 1
- 230000001737 promoting effect Effects 0.000 description 1
- 230000036632 reaction speed Effects 0.000 description 1
- SUKJFIGYRHOWBL-UHFFFAOYSA-N sodium hypochlorite Chemical compound [Na+].Cl[O-] SUKJFIGYRHOWBL-UHFFFAOYSA-N 0.000 description 1
- 238000006467 substitution reaction Methods 0.000 description 1
- 238000012546 transfer Methods 0.000 description 1
- 239000002351 wastewater Substances 0.000 description 1
- 238000004065 wastewater treatment Methods 0.000 description 1
- 238000003911 water pollution Methods 0.000 description 1
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- G—PHYSICS
- G05—CONTROLLING; REGULATING
- G05B—CONTROL OR REGULATING SYSTEMS IN GENERAL; FUNCTIONAL ELEMENTS OF SUCH SYSTEMS; MONITORING OR TESTING ARRANGEMENTS FOR SUCH SYSTEMS OR ELEMENTS
- G05B13/00—Adaptive control systems, i.e. systems automatically adjusting themselves to have a performance which is optimum according to some preassigned criterion
- G05B13/02—Adaptive control systems, i.e. systems automatically adjusting themselves to have a performance which is optimum according to some preassigned criterion electric
- G05B13/04—Adaptive control systems, i.e. systems automatically adjusting themselves to have a performance which is optimum according to some preassigned criterion electric involving the use of models or simulators
- G05B13/042—Adaptive control systems, i.e. systems automatically adjusting themselves to have a performance which is optimum according to some preassigned criterion electric involving the use of models or simulators in which a parameter or coefficient is automatically adjusted to optimise the performance
-
- C—CHEMISTRY; METALLURGY
- C02—TREATMENT OF WATER, WASTE WATER, SEWAGE, OR SLUDGE
- C02F—TREATMENT OF WATER, WASTE WATER, SEWAGE, OR SLUDGE
- C02F1/00—Treatment of water, waste water, or sewage
- C02F1/72—Treatment of water, waste water, or sewage by oxidation
- C02F1/78—Treatment of water, waste water, or sewage by oxidation with ozone
-
- C—CHEMISTRY; METALLURGY
- C02—TREATMENT OF WATER, WASTE WATER, SEWAGE, OR SLUDGE
- C02F—TREATMENT OF WATER, WASTE WATER, SEWAGE, OR SLUDGE
- C02F2103/00—Nature of the water, waste water, sewage or sludge to be treated
- C02F2103/06—Contaminated groundwater or leachate
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Abstract
The invention belongs to the field of automatic control, and discloses an ozone concentration sliding mode anti-interference control method of sewage treatment equipment under a non-time-lag nominal model.
Description
Technical Field
The invention belongs to the technical field of automatic control, and provides a control method of a large-inertia large-time-lag system based on ozone concentration control of garbage residual liquid sewage treatment equipment.
Background
For the present time, environmental pollution is a problem that needs to be strongly paid attention to all country regions of the world, but for the advanced country, the industry is advanced at a high speed for the last decades, many pollutions are emerging in the process of rapidly advancing industry, and the population of China is huge, so how to treat the garbage residue and sewage is necessary for the development of the country, not only the emission of water pollution can be reduced, but also the renewable development of water sources can be promoted.
Ozone oxidation treatment of wastewater is currently widely used in wastewater treatment systems
(1) Effectively removes COD, anionic detergent and ammonia nitrogen in the sewage, and reduces the ozone into oxygen after about 30min at normal temperature, so that no residue and secondary pollution exist.
(2) Ozone can be manufactured on the production site, compared with liquid chlorine and sodium hypochlorite, the ozone does not need storage and transportation links, and the operation danger is reduced.
(3) Ozone has strong oxidation and high reaction speed. Ozone has good inactivating and killing effects on microorganisms, bacteria and viruses, and the effect of inactivating microorganisms is better than that of disinfectants such as chlorine, chloramine, chlorine dioxide and the like. And can also oxidize and degrade other pollutants in the water.
(4) The residual ozone in the water can be quickly and naturally decomposed into oxygen, the yielding water contains higher dissolved oxygen, the burden of the water body is not increased after the yielding water is discharged to the receiving water body, the water quality of the water body can be improved, and the disinfectant is the cleanest.
However, in the sewage treatment process, the concentration of ozone also has an influence on the sewage treatment efficiency and the energy consumption. Increasing ozone concentration is beneficial to promoting ozone mass transfer, and the decoloring rate and COD removal rate are increased, but mineralization efficiency (delta COD/delta O) is increased 3 ) And the ozone utilization rate is reduced. Excessive ozone addition does not result in a proportional increase in the concentration of ozone on the liquid phase side and can result in ozone remaining.
Currently, in the actual control process of ozone concentration, mainly on-off control, PID control and fuzzy control are focused. The switch control is the simplest control mode, but the control precision is extremely low, the fluctuation is large, and the energy consumption is high; the fuzzy control needs a great deal of field practical experience and has no self-learning capability, so that the actual characteristics of the reaction process cannot be very good, and the stability of the ozone concentration cannot be well maintained.
Aiming at the problems, the application provides a sliding mode anti-interference control method, which reduces the overshoot of the output of the system, improves the response speed, anti-interference capability and robustness of the system.
Disclosure of Invention
The invention mainly solves the technical problems existing in the prior art; the method for controlling the anti-interference of the ozone concentration sliding mode of the sewage treatment equipment under the non-time-lag nominal model is provided.
A method for controlling the noise immunity of an ozone concentration sliding mode of sewage treatment equipment under a time-lag-free nominal model is characterized by comprising the following steps:
step 1, a sliding mode controller takes the difference value between the actual concentration of ozone and a design value as an input quantity, and outputs a non-time-lag nominal model after error removal to a disturbance observer;
step 2, estimating system disturbance by a disturbance observer through controlled variables and system output, and feeding the observed system disturbance forward to a forward channel so as to inhibit the disturbance;
and 3, effectively filtering high-frequency noise by a low-pass filter, compensating low-frequency interference, and converting an inverse model of g(s) into a true partial formula.
The specific method of step 1 is that the sliding mode controller is designed according to the system non-time-lag nominal model and the feedback of the model, and the specific method is that:
step 1.1: controlling the concentration of ozone in the garbage residual liquid sewage treatment system, and introducing integral design sliding mode function, namely
Wherein c is the sliding mode surface coefficient, and the tracking error isy d Is the ozone concentration set value;
step 1.2: defining Lyapunov function as
Then
In the control principle, the Lyapunov function is used for judging the stability of the system, and the system equation is used for judging the stability of the system
It can be seen that for the equilibrium point s, if there is a continuous function V that satisfies
And->
Then the system will equilibrate at an equilibrium point s=0, i.e
Step 1.3: order theThen both the first condition and the second condition of Lyapunov's second law are satisfied>When the condition of Lyapunov second law is satisfied, s=0, and s finally stabilizes the sliding mode surface;
step 1.4: in general, there are three options for the sliding mode control law:
selecting a second sliding mode control law
Wherein k and delta are the band design parameters and sgn s is the switching function of s;
Then
step 1.5: thereby making it
Inequality equationSolution to (1)
It can be seen that the V (t) index converges to 0, therebyAnd e (t) is dependent on k; the exponential term-ks can ensure that when s is larger, the system state can approach the sliding mode at a greater speed.
According to the method for controlling the anti-interference of the ozone concentration sliding mode of the sewage treatment equipment under the non-time-lag nominal model, the disturbance observer estimates system disturbance through the controlled variable and the system output, and the observed system disturbance is fed forward to the forward channel so as to inhibit interference, and the adverse effect of the interference on the controlled process is reduced; as shown in a dashed line box 1 of a system block diagram of the control method of the application, r(s) is a system set value, and u 0 (s) is output by a sliding mode controller, y(s) is output by an actual system, and G p (s) is the actual controlled process,e is the inverse of the model of the minimum phase part of the system -τ The time lag link of the actual system; within the dashed box 1 is a disturbance observer, d(s) is the actual disturbance in the system, +.>Is a disturbance estimation value of the disturbance observer.
The method for controlling the anti-interference of the ozone concentration sliding mode of the sewage treatment equipment under the non-time-lag nominal model comprises the following steps of:
step 3.1: the order k of the low pass filter typically takes G because of the adverse effect of an excessively high order phase lag on the system p (s) relative order; the system is more stable along with the increase of the time constant eta of the low-pass filter, but the disturbance rejection capability of the system is reduced, so that the design of a disturbance observer should comprehensively consider the disturbance rejection performance and the robustness of the system;
step 3.2: q(s) is usually a low-pass filter, and the external noise interference brought in the actual system operation can be filtered by adding the low-pass filter, and the minimum phase inverse model of the control object can be converted into a true component formula;
wherein eta is the time constant of the filter and k is the order of the filter;
step 3.3: when the Q(s) static gain is 1, the disturbance estimation value of the disturbance observer can be calculated
Drawings
FIG. 1 is a system block diagram of a slip-form disturbance rejection control of the ozone concentration of the waste residue sewage under a time-lapse-free model of the present invention.
FIG. 2 is a simulated output diagram of the control method of the present application and a conventional PID control.
FIG. 3 is a waste residue sewage treatment plant.
Detailed Description
The technical scheme of the invention is further specifically described below through examples and with reference to the accompanying drawings.
Examples:
the invention provides a non-time-lag nominal model system for controlling the ozone concentration sliding mode immunity of sewage treatment equipment, which is shown in a control block diagram of a system in fig. 1, wherein the non-time-lag nominal model can simplify the design of a sliding mode controller, and the sliding mode controller designed by the non-time-lag nominal model is used for controlling an original system, so that adverse effects of time lag on the system can be reduced, overshoot of the system can be reduced, and response speed and control precision can be improved; when disturbance is added in an actual system, a disturbance observer is designed to estimate and compensate the disturbance, so that the anti-interference capability and the robustness of the ozone concentration system are improved, and the method specifically comprises the following steps:
(1) On the premise that a membrane contact assembly manufactured by a self-made PTFE hollow fiber hydrophobic membrane is coupled with UV to form a new membrane contact ozone oxidation-UV process, ozone is transmitted through the membrane to greatly improve efficiency, and the reactive brilliant red X-3B of azo dye commonly used in the printing and dyeing industry is taken as a target pollutant to carry out sewage pollution discharge treatment:
(2) The original system mathematical model is a first-order large-inertia large-time-lag system, and in order to simplify the design of the sliding mode controller and reduce the adverse effect of time lag on the system, the sliding mode controller is designed according to the nominal model of the time-lag-free system and the feedback thereof. Comprising the following steps:
and the sliding mode controller is used for: the sliding mode control is also called variable structure control, is a nonlinear controller, can ensure that the sliding mode controller can continuously change in a system according to the state of the system, can respond more quickly, solves the problems of unobvious parameter change and disturbance and the like, and can reach a sliding mode, namely a stable state more quickly.
Disturbance observer: the difference between the actual model and the ideal model output caused by external interference and model parameter change can be equivalent to the equivalent input, namely the equivalent interference can be observed, the observed interference is introduced into equivalent compensation, and the complete inhibition of the interference is realized
A low pass filter: because the disturbance observer is not obvious to the measurement noise, but can realize the effective filtering to the high-frequency noise, the addition of the low-pass filter can realize the effective compensation to the low-frequency interference and the effective filtering to the high-frequency noise, and the inverse model of g(s) can be converted into a true partial formula, so that the control design is simplified.
An ozone concentration slip form disturbance rejection control of a sewage treatment device under a time-lapse-free nominal model, comprising:
and step 1, the sliding mode controller takes the difference value between the actual concentration of ozone and the design value as input quantity, and outputs the nominal model without time lag after the error is removed to a disturbance observer.
And 2, estimating system disturbance by using a disturbance observer through controlled variables and system output, and feeding the observed system disturbance forward to a forward channel so as to inhibit the disturbance and reduce the adverse effect of the disturbance on the controlled process.
And 3, the low-pass filter can effectively filter high-frequency noise, the low-pass filter is added to effectively compensate low-frequency interference and effectively filter high-frequency noise, the inverse model of g(s) can be converted into true components, and the first-order low-pass filter can reduce cost and simplify control design under the condition of not reducing the effect.
The specific method of the step 1 is that the sliding mode controller designs according to the system non-time lag nominal model and the feedback of the model, and specifically comprises the following steps:
step 1.1: controlling the concentration of ozone in the garbage residual liquid sewage treatment system, and introducing integral design sliding mode function, namely
Wherein c is the sliding mode surface coefficient, and the tracking error isy d Is the ozone concentration set value.
Step 1.2: defining Lyapunov function as
Then
In the control principle, the Lyapunov function is used for judging the stability of the system, and the system equation is used for judging the stability of the system
It can be seen that for the equilibrium point s, if there is a continuous function V that satisfies
And->
Then the system will equilibrate at an equilibrium point s=0, i.e
Step 1.3: order theThen both the first condition and the second condition of Lyapunov's second law are satisfied>When the condition of Lyapunov second law is satisfied, s=0, s will eventually stabilize the sliding surface.
Step 1.4: in general, there are three options for the sliding mode control law:
selecting a second sliding mode control law
Where k and δ are the band design parameters and sgn s is the switching function of s.
Then
Step 1.4: thereby making it
Inequality equationSolution to (1)
It can be seen that the V (t) index converges to 0, therebyAnd the exponential convergence speed of e (t) depends on k. The exponential term-ks can ensure that when s is larger, the system state can approach the sliding mode at a greater speed.
Step 2: a disturbance observer is designed.
The disturbance observer estimates the system disturbance through the controlled variable and the system output, and feeds the observed system disturbance forward to the forward channel to inhibit the disturbance and reduce the adverse effect of the disturbance on the controlled process. As shown in a dashed line box 1 of a system block diagram of the control method of the application, r(s) is a system set value, and u 0 (s) is output by a sliding mode controller, y(s) is output by an actual system, and G p (s) is the actual controlled process,is the inverse of the model of the minimum phase portion of the system,e -τ is a time lag link of an actual system. Within the dashed box 1 is a disturbance observer, d(s) is the actual disturbance in the system, +.>As a disturbance estimate for a disturbance observer,
step 3: a low pass filter in the disturbance observer is designed.
Step 3.1: in the design of disturbance observers, the design of the low-pass filter has a significant impact on the dynamic characteristics of the observer and the robustness of the system. The response speed of the disturbance observer and the ability to suppress the disturbance will vary with the order of the low-pass filter, the higher the order of the low-pass filter, the faster the response speed of the disturbance observer, the more robust the system will be,
step 3.2: the order k of the low pass filter is typically G due to the adverse effect of the underdamping on the system caused by the excessive phase lag p (s) relative order. The system is more stable along with the increase of the time constant of the low-pass filter, but the disturbance rejection capability of the system is reduced, so that the disturbance observer is designed by comprehensively considering the disturbance rejection performance and the robustness of the system.
Step 3.3: q(s) is usually a low-pass filter, and the low-pass filter can be added to filter external noise interference caused in the actual system operation, and can convert the minimum phase inverse model of the control object into a true component formula.
Where η is the time constant of the filter and k is the order of the filter.
Step 3.3: when the Q(s) static gain is 1, the disturbance estimation value of the disturbance observer can be calculated
The method for controlling the concentration of ozone in the garbage residual sewage treatment as described in claim 1, wherein the sliding mode controller is a sliding mode surface designed according to the expected dynamic characteristics of the system, the sliding mode controller is used for converging the outside of the sliding mode surface in the state of the system to the sliding mode surface, and once the effect of the sliding mode control is reached, the system can ensure that the system reaches the origin of the system along the sliding mode surface, so that the accurate control of a mathematical model is realized, the accuracy and the anti-interference capability are improved, and the overshoot and the adjustment time are reduced.
3. The method for controlling the concentration of ozone in the garbage residual sewage treatment as described in claim 1, wherein the disturbance observer estimates the disturbance of the system through the controlled variable and the system output and feeds back the disturbance to the forward channel for compensation, thereby improving the anti-interference capability and the robustness of the system.
Compared with the prior art, the invention has the following advantages:
(1) The anti-interference capability is strong, the control precision is high, and the control effect is good. Compared with the traditional PID control, the system controller adopts a sliding mode controller and a disturbance observer, and improves the control precision, the response speed and the anti-interference capability of the system.
(2) The sliding mode controller is constructed by adopting the nominal model without time lag and the output feedback thereof, so that the design of the sliding mode controller is simplified, and the adverse effect of time lag on the system is eliminated.
(4) The whole control method is simple, the working reliability is high, the sliding mode is adopted as a controller, the control precision and the response speed for ozone can be improved, and a disturbance observer is added, so that the control requirement of the system can be met under different working conditions.
The specific embodiments described in this application are merely illustrative of the spirit of the invention. Those skilled in the art may make various modifications or additions to the described embodiments or substitutions thereof without departing from the spirit of the invention or exceeding the scope of the invention as defined in the accompanying claims.
Claims (3)
1. A method for controlling the noise immunity of an ozone concentration slip form of a garbage residual liquid sewage treatment device based on a time-lag-free nominal model is characterized by comprising the following steps:
step 1, a sliding mode controller takes the difference value between the actual concentration of ozone and a design value as an input quantity, and outputs a non-time-lag nominal model after error removal to a disturbance observer;
step 2, estimating system disturbance by a disturbance observer through controlled variables and system output, and feeding the observed system disturbance forward to a forward channel so as to inhibit the disturbance;
step 3, the low-pass filter effectively filters high-frequency noise, compensates low-frequency interference and converts an inverse model of g(s) into true components;
the specific method of the step 1 is that the sliding mode controller designs according to the nominal model without time lag of the system and the feedback of the model, and specifically comprises the following steps:
step 1.1: controlling the concentration of ozone in the garbage residual liquid sewage treatment system, and introducing integral design sliding mode function, namely
Wherein c is the sliding mode surface coefficient, and the tracking error isy d Is the ozone concentration set value;
step 1.2: defining Lyapunov function as
Then
In the control principle, the Lyapunov function is used for judging the stability of the system, and the system equation is used for judging the stability of the system
It can be seen that for the equilibrium point s, if there is a continuous function V that satisfies
And->
Then the system will equilibrate at an equilibrium point s=0, i.e
Step 1.3: order the
Step 1.4: slip form control law:
is available in the form of
Wherein k and delta are the band design parameters and sgn s is the switching function of s;
Then
step 1.5: thereby making it
Inequality equationSolution to (1)
It can be seen that the V (t) index converges to 0, therebyAnd e (t) is dependent on k; the exponential term-ks can ensure that when s is larger, the system state can approach the sliding mode at a greater speed.
2. The method for controlling the anti-interference of the ozone concentration sliding mode of the garbage residual liquid sewage treatment equipment based on the non-time-lag nominal model according to claim 1, wherein the disturbance observer estimates the system disturbance through the controlled variable and the system output, and the observed system disturbance is fed forward to the forward channel so as to inhibit the interference and reduce the adverse effect of the interference on the controlled process.
3. The method for controlling the noise immunity of the ozone concentration sliding mode of the garbage residual sewage treatment equipment based on the non-time-lag nominal model according to claim 1, wherein a low-pass filter in a disturbance observer is specifically implemented by:
step 3.1: the order κ of the low pass filter typically takes G because too high a phase lag can adversely affect the system due to underdamping p (s) relative order;
step 3.2: q(s) is usually a low-pass filter, and external noise interference brought by the actual system operation can be filtered by adding the low-pass filter, and the minimum phase inverse model of the control object can be converted into a true component type;
where η is the time constant of the filter and κ is the order of the filter;
step 3.3: when the Q(s) static gain is 1, the disturbance estimation value of the disturbance observer can be calculated
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