CN109507872B - Novel auto-disturbance-rejection controller with embedded model - Google Patents
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Abstract
The invention discloses a novel auto-disturbance-rejection controller with an embedded model, which comprises an extended state observer module arranged in an inner ring and a controllerThe proportional differential feedback module is arranged on the outer ring; model information is embedded into the extended state observer module and used for observing total system disturbance outside a nominal model, and then a controlled object is modified into a standard type of a series integrator by compensating the total disturbance and known dynamics in real time in an inner ring; the proportional differential feedback module is based on the standard type of the series integrator and is based on the differential parameter k of the outer loop controllerdThe quantitative relation with a second-order system damping coefficient zeta realizes the control of the controlled object by adjusting the output control quantity through parameter setting; the system is a system of controlled objects. The invention can reduce the load of the extended state observer, achieve the aims of more accurate disturbance estimation and set value tracking and reducing the influence of noise on the output control quantity, and is convenient for parameter setting and adjustment in the actual control process.
Description
Technical Field
The invention relates to the field of automatic control, in particular to a novel auto-disturbance-rejection controller with an embedded model.
Background
The Active Disturbance Rejection Control (ADRC) is a novel control technology proposed by Mr. Han Jingqing, absorbs the thought essence of PID control of eliminating errors based on errors, attributes all uncertain factor effects acting on a controlled object to unknown disturbances, designs an Extended State Observer (ESO), observes the influence of the integration of unknown parts of a model and external unknown disturbances on a controlled object according to input-output data of the object, and then provides control quantity to compensate the disturbances, thereby greatly reducing the influence of the disturbances on the controlled quantity.
However, since no mathematical model of the controlled object is added in terms of making a proper estimation of the system, this presents considerable difficulties for the accuracy of the estimation and the subsequent tuning of the parameters in the control action. A large number of control simulations and practices show that the control effect of the model-free embedded active disturbance rejection controller is slightly better than that of a common PID controller, but the model-free embedded active disturbance rejection controller has a certain distance from the control effect of the expected active disturbance rejection controller in the aspects of set value tracking, output control quantity fluctuation and disturbance estimation.
Disclosure of Invention
The purpose of the invention is as follows: the invention aims to provide a novel model-embedded active disturbance rejection controller, which can reduce the burden of an extended state observer, achieve the aims of more accurately tracking disturbance estimation and set values and reducing the influence of noise on output control quantity, and facilitate the setting and adjustment of parameters in the actual control process.
The technical scheme is as follows: in order to achieve the purpose, the invention adopts the following technical scheme:
the model embedded novel active disturbance rejection controller comprises an extended state observer module arranged in an inner ring and a proportional differential feedback module arranged in an outer ring; model information is embedded into the extended state observer module and used for observing total system disturbance outside a nominal model, and then a controlled object is reconstructed into a standard type of a series integrator by compensating the total disturbance and known dynamic state of the part in real time in an inner ring; the proportional differential feedback module is based on the standard type of the series integrator and is based on the differential parameter k of the outer loop controllerdThe quantitative relation with a second-order system damping coefficient zeta realizes the control of the controlled object by adjusting the output control quantity through parameter setting; the system is a system of controlled objects.
Further, the parameters of the extended state observer module are defined as: beta is a1＝3ωo-a2、
Wherein, beta1To extend the first gain of the state observer module, β2To extend the second gain of the state observer module, β3To extend the third gain of the state observer module, a1And a2Are all controlled object parameters, omegaoTo extend the state observer module bandwidth.
Further, the parameters of the proportional-derivative feedback module are set as follows: proportional parameter of outer loop controller
Differential parameter k of outer loop controllerd＝2ωc,ωcIs the outer loop controller bandwidth.
Further, the differential parameter k according to the outer ring controllerdAnd second order system damping coefficient ζThe process of suppressing the response overshoot of the controlled object by the quantitative relation comprises the following steps: differentiating the outer loop controller by a parameter kdAnd if the damping coefficient zeta is increased, the second-order system damping coefficient zeta is correspondingly increased, so that the response overshoot of the controlled object is restrained.
Further, the outer loop controller differential parameter kdThe quantitative relation with the second-order system damping coefficient ζ is as follows:
Further, filtering processing is also performed after the control quantity is output through parameter setting adjustment.
Has the advantages that: the invention discloses a novel auto-disturbance-rejection controller with an embedded model, which has the following beneficial effects compared with the prior art:
1) compared with the traditional PI controller and the traditional active disturbance rejection controller, the method embeds the model information into the design of the active disturbance rejection controller, so that the novel active disturbance rejection controller has a better control effect, namely a better set value tracking effect;
2) compared with the traditional extended state observer module, the extended state observer module has the advantages that the model information is embedded into the extended state observer module, so that the estimation of the extended state observer module on the disturbance is more accurate, namely the estimated total disturbance fluctuation is reduced, the fluctuation of the output control quantity of the controller is reduced to a certain extent, and an execution mechanism is protected;
3) after the low-pass filter is introduced to correct the active disturbance rejection control output, the invention realizes that the fluctuation of the output control quantity is reduced while ensuring the good control effect, thereby protecting the actuating mechanism and prolonging the service life of the actuating mechanism.
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FIG. 1 is a diagram of a multi-tank experimental platform according to an embodiment of the present invention;
FIG. 2 is a diagram illustrating the result of the system transfer function model identification and the fitting effect of the experimental curve according to the embodiment of the present invention;
FIG. 3 is a diagram illustrating a comparison result of simulation experiments of a conventional ADRC, a novel ADRC, and a PI controller according to an embodiment of the present invention;
fig. 4 is a diagram illustrating a result of a set point tracking control experiment of a conventional active disturbance rejection controller according to an embodiment of the present invention;
FIG. 4(a) is a diagram illustrating system response and set values in a conventional ADRC experiment;
FIG. 4(b) is a diagram illustrating the output control amount of the system in the conventional active disturbance rejection control experiment;
FIG. 5 is a diagram illustrating the experimental results of tracking control of the setting values of the ADRC according to the embodiment of the present invention;
FIG. 5(a) is the system response and set point in the new active disturbance rejection control experiment;
FIG. 5(b) is the system output control in the novel auto-disturbance rejection control experiment;
FIG. 6 is a comparison graph of simulation experiments of the same noise influence degree of the conventional ADCs and the novel ADCs in the embodiment of the present invention;
fig. 6(a) shows the system output control amount in the conventional active disturbance rejection control simulation experiment;
fig. 6(b) shows the system output control amount in the new active disturbance rejection control simulation experiment;
FIG. 7 is a graph showing the result of tracking control experiments after adding a low pass filter and adjusting differential parameters of an outer loop controller in accordance with an embodiment of the present invention;
FIG. 7(a) shows the system response and set point in the filtering experiment;
FIG. 7(b) is a diagram showing the output control amount of the system in the filtering experiment;
fig. 8 is a system block diagram of the transfer function form of the active disturbance rejection controller according to the present invention.
Detailed Description
The technical solution of the present invention will be further described with reference to the following embodiments.
The specific embodiment discloses a novel model-embedded active disturbance rejection controller, which comprises an extended state observer module arranged in an inner ring and a proportional-derivative feedback module arranged in an outer ring; the extended state observer module is relativeIn an improvement of the prior art, the proportional-derivative feedback module is also referred to as an outer loop controller. Model information is embedded into the extended state observer module, the extended state observer module is used for observing total system disturbance outside a nominal model, and then the controlled object is modified into a standard type of a series integrator by compensating the total disturbance and the known dynamic state in real time in an inner ring; the proportional differential feedback module is based on the standard type of the series integrator and is based on the differential parameter k of the outer loop controllerdAnd the quantitative relation with the second-order system damping coefficient zeta realizes the control of the controlled object by adjusting the output control quantity through parameter setting.
Setting the transfer function of the controlled object to
The model information is substituted into the extended state observer module, and the model embedded extended state observer module is
In the formula (2), z is each estimated amount of the system.
The characteristic equation of the extended state observer module is obtained as follows: s3+(a2+β1)s2+(a2β1+β2+a1)s+β 30, wherein β1To extend the first gain of the state observer module, β2To extend the second gain of the state observer module, β3To extend the third gain of the state observer module, a1And a2Are all controlled object parameters. The parameters of the extended state observer are set as follows: beta is a1＝3ωo-a2、
Wherein, ω isoIs the observer bandwidth.
And (3) obtaining a state space format of the novel active disturbance rejection controller after the total disturbance of the compensation system:
in the formula (3), r is a set value, u2For the outer loop controller to output a control quantity, x1、x2Is the system state quantity.
The characteristic equation of the novel active disturbance rejection controller is as follows:
s2+kds+kp＝0(4)
the parameters of the outer loop controller are set as follows: proportional parameter of outer loop controller
Differential parameter k of outer loop controllerd＝2ωc,ωcIs the outer loop controller bandwidth. Differential parameter k of outer loop controllerdThe quantitative relation with the second-order system damping coefficient zeta is as follows:
ωnis the natural frequency.
According to the differential parameter k of the outer ring controllerdThe process of suppressing the response overshoot of the controlled object by the quantitative relation with the second-order system damping coefficient zeta is as follows: differentiating the outer loop controller by a parameter kdAnd if the damping coefficient zeta is increased, the second-order system damping coefficient zeta is correspondingly increased, so that the response overshoot of the controlled object is restrained.
A block diagram of a system for embedding a novel form of the auto-disturbance rejection controller transfer function of model information is shown in fig. 8.
And filtering treatment is also carried out after the control quantity is output through parameter setting adjustment.
As shown in fig. 1, the invention is a multi-tank experimental platform constructed in the embodiment of the invention. The platform consists of three water tanks, a plurality of valves, a liquid level pressure sensor, a water pump, a reservoir and a control cabinet. Each water tank is provided with a water outlet and a pressure sensor for detecting liquid level, and a communicating pipe is arranged between the bottoms of the two upper water tanks. The water pump is used for supplying water to the water tank, the water discharged from the final-stage water tank directly flows into the reservoir, and the reservoir provides water for the water tank through regulation. The control cabinet comprises a communication device and a frequency converter, the communication device is used for reading signals of the pressure sensor and outputting control signals to the frequency converter, and the frequency converter changes the water yield of the water pump by adjusting the frequency of the water pump, so that the control of the water supply amount of the water tank is realized.
After the experimental platform is built, the on-off and the opening of each valve need to be adjusted. The regulation principle is that all water tanks are connected in series, the water storage capacity of the water tanks is fully utilized, and the whole system becomes a large-inertia system, so that a high-order system required for verifying the content of the right provided by the invention is constructed.
Fig. 2 is a diagram illustrating the effect of fitting the transfer function and the experimental data according to the embodiment of the present invention. Wherein, in order to obtain a transfer function model from a water pump frequency converter control signal (mV) to a final water tank liquid level (mm), a water pump step experiment is considered. In the steady-state ranges of the water pump rotating speed and the final water tank liquid level, the water pump rotating speed is stepped, and then model identification is carried out on a step result to obtain a transfer function model from a water pump frequency converter control signal (mV) to the final water tank liquid level (mm):
fig. 3 is a comparison graph of simulation experiments of two types of active disturbance rejection controllers and PID controllers according to the embodiment of the present invention. In order to observe the comparison of the tracking control simulation effects of two types of auto-disturbance rejection controllers more visually, the bandwidth of an observer is uniformly set to be omegao0.03 percent; controller bandwidth is set to omegac0.0035. As the identified transfer function model is a second-order model without time lag, an industrially common SIMC-PI controller is selected and set to obtain the PI controller parameter kp＝0.070715，Ti＝0.00008719。
The simulation result preliminarily verifies that the novel active disturbance rejection controller disclosed by the specific embodiment has a better control effect, namely a better set value tracking effect.
Fig. 4 is a diagram showing the experimental result of tracking control of the set value of the conventional active disturbance rejection controller according to the embodiment of the present invention. Wherein, the bandwidth omega of the state observer is expandedo0.03 percent; tracking error proportional term coefficient kp0.06914; setting the tracking error differential term coefficient as a segmented value according to the overshoot condition of the experimental curve: first step k d25; first step kd＝30。
FIG. 4(a) shows that there is some overshoot in the setpoint tracking experiment, but with kdThe increase overshoot of (2) is reduced; fig. 4(b) shows that there is a large fluctuation in the output control amount.
Fig. 5 is a diagram showing the experimental results of tracking and controlling the setting value of the novel active disturbance rejection controller according to the embodiment of the present invention. Wherein, the bandwidth omega of the state observer is expandedo0.03 percent; tracking error proportional term coefficient kp0.06914; setting the tracking error differential term coefficient as a segmented value according to the overshoot condition of the experimental curve: first step k d25; first step kd＝30。
In FIG. 5(a), although there is a certain overshoot in the set point tracking experiment, the overshoot is significantly reduced compared to FIG. 4(a), and the value of k is varieddThe increase overshoot of (d) is further reduced; fig. 4(b) shows that the fluctuation of the output control amount is significantly reduced compared to fig. 4(b), although it still exists.
By comparing the actual experiment results of fig. 4 and fig. 5, it is further verified that the novel active disturbance rejection controller has a better control effect than the conventional active disturbance rejection controller, and further, the correctness and validity of the content of the rights proposed by the present invention are verified.
Fig. 6 is a comparison graph of simulation experiments of the same noise influence degree of the conventional auto-disturbance-rejection controller and the novel auto-disturbance-rejection controller in the embodiment of the present invention. The same white noise is introduced into the output end in both simulation experiments so as to discuss whether the novel active disturbance rejection controller can reduce the influence of the noise on the output control quantity, namely reduce the fluctuation of the output control quantity compared with the traditional active disturbance rejection controller. The system output control quantity in the conventional active disturbance rejection control simulation experiment shown in fig. 6(a) and the system output control quantity in the novel active disturbance rejection control simulation experiment shown in fig. 6(b) are obtained.
Comparing two groups of experimental control quantity fluctuation situations in fig. 6, it can be seen that under the same noise influence, compared with the conventional active disturbance rejection controller, the output control quantity fluctuation of the novel active disturbance rejection controller is obviously smaller, and further calculating the average value of the fluctuation amplitude of the output control quantity of the two types of active disturbance rejection controllers compared with the noise-free situation can obtain: the average value of the control quantity fluctuation amplitude of the traditional active disturbance rejection controller is as follows: 0.112477, respectively; the average value of the fluctuation amplitude of the control quantity of the novel active disturbance rejection controller is as follows: 0.055759. this shows that the new type of auto-disturbance-rejection controller can reduce the influence of noise on the output control amount, i.e., reduce the fluctuation of the output control amount.
FIG. 7 shows an additional filter and parameter adjustment experiment according to an embodiment of the present invention. Wherein, on the basis of the above experiment, a low pass filter is added to the output control quantity of the novel active disturbance rejection controller, and the filter transfer function is as follows:
setting the tracking error differential term coefficient as a segmented value according to the overshoot condition of the experimental curve, wherein the values are respectively kd＝25、kd＝30、kd＝39。
Shown in FIG. 7(a), with kdThe overshoot can be continuously reduced by increasing; fig. 7(b) shows that the output control amount fluctuation is reduced after the low-pass filter is added, so that the output control amount fluctuation can be reduced on the basis of ensuring the control effect, and the two are complementary to each other, so that the good control effect is ensured, the execution mechanism is protected, and the content of the rights proposed by the present invention is verified.
Claims (5)
1. A novel auto-disturbance-rejection controller with embedded model is characterized in that: the system comprises an extended state observer module arranged in an inner ring and a proportional-derivative feedback module arranged in an outer ring; model information is embedded in the extended state observer module forObserving the total system disturbance outside the nominal model, and then compensating the total disturbance and the known dynamic state in real time through an inner ring to modify the controlled object into a standard type of a series integrator; the proportional differential feedback module is based on the standard type of the series integrator and is based on the differential parameter k of the outer loop controllerdThe quantitative relation with a second-order system damping coefficient zeta realizes the control of the controlled object by adjusting the output control quantity through parameter setting; the system is a system of a controlled object; the parameters of the extended state observer module are defined as: beta is a1＝3ωo-a2、
Wherein, beta1To extend the first gain of the state observer module, β2To extend the second gain of the state observer module, β3To extend the third gain of the state observer module, a1And a2Are all controlled object parameters, omegaoTo extend the state observer module bandwidth.
2. The model-embedded new auto-disturbance-rejection controller according to claim 1, wherein: the parameters of the proportional-derivative feedback module are set as follows: proportional parameter of outer loop controller
Differential parameter k of outer loop controllerd＝2ωc,ωcIs the outer loop controller bandwidth.
3. The model-embedded new auto-disturbance-rejection controller according to claim 1, wherein: the differential parameter k according to the outer ring controllerdThe process of suppressing the response overshoot of the controlled object by the quantitative relation with the second-order system damping coefficient zeta is as follows: differentiating the outer loop controller by a parameter kdWhen the damping coefficient zeta of the second-order system is increased, the damping coefficient zeta of the second-order system is correspondingly increasedThereby suppressing the overshoot of the controlled object response.
4. The model-embedded new auto-disturbance-rejection controller according to claim 1, wherein: the outer loop controller differential parameter kdThe quantitative relation with the second-order system damping coefficient zeta is as follows:
ωnis the natural frequency.
5. The model-embedded new auto-disturbance-rejection controller according to claim 1, wherein: and filtering after the control quantity is output through parameter setting adjustment.
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| CN110209055B (en) * | 2019-06-12 | 2022-02-08 | 洛阳师范学院 | Second-order system controller and control method based on reference model and disturbance observation |
| CN110460035B (en) * | 2019-08-30 | 2021-03-09 | 北方工业大学 | DC-DC converter dynamic compensation method and system based on robust disturbance observer |
| CN111416524A (en) * | 2020-04-27 | 2020-07-14 | 山东大学 | High-disturbance-rejection fast-response control system and method for resonant DC-DC converter |
| CN112578670B (en) * | 2020-12-01 | 2022-05-24 | 东南大学 | Parameter setting method of active disturbance rejection time-lag controller in thermal process and controller |
| CN113700563B (en) * | 2021-08-13 | 2023-01-03 | 哈尔滨工程大学 | Cascade gas turbine power control method based on active disturbance rejection control |
| CN113669163B (en) * | 2021-08-13 | 2023-01-03 | 哈尔滨工程大学 | Cascade gas turbine rotating speed control method based on active disturbance rejection control |
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