CN110032171B - Control loop design method based on cut-off frequency - Google Patents
Control loop design method based on cut-off frequency Download PDFInfo
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- CN110032171B CN110032171B CN201910329820.8A CN201910329820A CN110032171B CN 110032171 B CN110032171 B CN 110032171B CN 201910329820 A CN201910329820 A CN 201910329820A CN 110032171 B CN110032171 B CN 110032171B
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Abstract
The invention discloses a cut-off frequency control loop design method, which is suitable for single loop or multi-loop control loop design of forward series proportional control, integral control or proportional-integral control. According to the method, other control links except a forward access controller are equivalent to a generalized controlled object, the cut-off frequency is determined according to the rapidity requirement of a control system, and the controller parameters are quantitatively calculated and determined on the basis of the cut-off frequency and the generalized controlled object. Theoretical analysis and simulation verification show that the designed control loop meets the rapidity design index and has good control quality.
Description
Technical Field
The invention relates to a control loop design method, belonging to the field of control system design.
Background
The traditional control loop design mostly adopts a 'trial and error' method to determine controller parameters, designers need to carry out a large amount of complicated and repeated work, firstly, the structure of a control loop is determined, on the basis, a group of controller parameters are selected to carry out numerical simulation, time domain index parameters and frequency domain index parameters of the control loop are calculated, when the design index is not met, the structure of another control loop is determined or a group of controller parameters are selected to carry out calculation of each index of the control loop, and iteration is carried out until the design index of the control loop is met. When the controller parameters are more than three or more than three, the control loop design workload is huge, the efficiency is low, the control quality of the designed control loop also depends on the experience and level of a designer to a large extent, and in addition, the traditional control loop design method belongs to a trial and error method, is difficult to obtain theoretical support and is inconvenient for the improvement of the design level of the designer.
Disclosure of Invention
The technical problem to be solved by the invention is as follows: the invention overcomes the defects of the prior art, provides a cut-off frequency control loop design method, can quantitatively calculate and determine the parameters of a controller, and the designed control loop has better control quality and robustness.
The technical solution adopted by the invention is as follows: a design method based on a cut-off frequency control loop comprises the following steps:
(1) according to the characteristics of the controlled object and the actuator and the requirement of rapidity of the control system, the cut-off frequency omega of the open-loop control loop is determinedc；
(2) Will divide forward path controller GcOther control links except for(s) are equivalent to a generalized controlled object P(s); if the system is a multi-loop control system, the controlled object p is included1The inner loop equivalence including(s) is transformed into a generalized controlled object P(s);
(3) determining a forward path controller G according to the type of the generalized controlled object P(s)c(s) is proportional control, integral control or proportional-integral control: if the generalized controlled object P(s) is a zero-type controlled object, PI control or integral control with integral control as the main and proportional control as the auxiliary is adopted; if the generalized controlled object P(s) is a type or more than one type of controlled object, PI control or proportional control with integral control as auxiliary and proportional control as main is adopted;
(4) calculating to obtain a forward path controller G according to the amplitude value of the open loop at the cut-off frequency as 1c(s) gain, and calculating to obtain the forward path controller GcA proportionality coefficient and an integral coefficient of(s);
for zero-type controlled object, the integral coefficient K of the controlleriCan be determined by:
wherein j is an imaginary number;
coefficient of proportionality KpThe determination method of (2) is as follows:
the method comprises the following steps: taking the proportionality coefficient as one twentieth-one tenth of the integral coefficient;
the method 2 comprises the following steps: the relationship between the proportionality coefficient and the integral coefficient is determined according to the following equation:
for one type or more than one type of controlled objects, the proportional coefficient K of the controllerpCan be determined by:
and taking the integral coefficient as one twentieth to one tenth of the proportional coefficient or taking the integral coefficient as 0.
Compared with the prior art, the invention has the beneficial effects that:
(1) the method of the invention equates other control links except the forward path controller to a generalized controlled object, determines the cut-off frequency according to the rapidity requirement of the control system, quantitatively calculates and determines the controller parameter according to the cut-off frequency and the generalized controlled object, and is suitable for the design of a single-loop or multi-loop control loop of forward series proportional control, integral control or proportional-integral control.
(2) The method of the invention can quantitatively calculate the parameters of the controller, thoroughly changes the traditional method of designing the parameters of the controller by a trial and error method, greatly improves the design efficiency, and ensures that the designed control loop has better control quality and robustness.
Drawings
FIG. 1 is a block diagram of a single loop control circuit of the present invention;
FIG. 2 is a block diagram of a multi-loop control circuit of the present invention;
FIG. 3 is a bode diagram of a control loop after the controller is designed;
fig. 4 is a unit step response of the control loop after the controller is designed.
Detailed Description
The invention provides a cut-off frequency control loop design method, which is suitable for the design of a single loop or a multi-loop control loop of forward series proportional control, integral control or proportional-integral control, and comprises the following steps:
(1) according to the characteristics of the controlled object and the actuator and the requirement of rapidity of the control system, the cut-off frequency omega of the open-loop control loop is determinedcω iscIs an important design index of the control loop, and can be regarded as the bandwidth of the control loop.
(2) As shown in fig. 1, will divide forward path controller GcOther control links except(s) are equivalent to the generalized controlled object p(s), and as shown in fig. 2, if the control loop is a multi-control loop, the inner loop including the controlled object needs to be equivalent to the generalized controlled object p(s).
(3) Determining a forward path controller G according to the type of the generalized controlled object P(s)c(s) is proportional control, integral control or proportional-integral control: if the generalized controlled object P(s) is a zero-type controlled object, PI control or integral control with integral control as the main and proportional control as the auxiliary is adopted; if the generalized controlled object p(s) is a type or more than one type of controlled object, PI control or proportional control with integral control as auxiliary and proportional control as main is adopted.
(4) Calculating to obtain the G increase of the controller according to the amplitude value of the open loop at the cut-off frequency as 1c(s) benefit and calculating to obtain the forward path controller GcThe proportionality coefficient and the integral coefficient of(s).
For a zero-type controlled object, the magnitude of the controller's integral coefficient can be determined by:
wherein j is an imaginary number; s is a complex variable;
coefficient of proportionality KpThe determination method of (2) is as follows:
the method comprises the following steps: taking the proportionality coefficient as one twentieth-one tenth of the integral coefficient;
the method 2 comprises the following steps: the relationship between the proportionality coefficient and the integral coefficient is determined according to the following equation:
for one type or more than one type of controlled objects, the proportional coefficient K of the controllerpCan be determined by
An integral coefficient determination method comprises the following steps: the method 1) determines the integral coefficient as a small amount of the proportional coefficient, for example, the integral coefficient is one twentieth to one tenth of the integral coefficient; method 2) alternatively takes the integration coefficient to be 0.
Computer simulation example:
in the multi-loop control system shown in FIG. 2, the feedback of the inner loop is proportional control with a coefficient of K, and the forward path is connected in series with a controller Gc(s) is a PI controller, and the PI controller is a power amplifier,
getting K ═ 0.1239, can obtain
Then the generalized controlled object p(s) can be obtained as
According to the requirement of rapidity of a control loop, the open loop cut-off frequency of the system is designed to be omegac2.0rad/s, the cut-off frequency is substituted into the above formulaObtaining the amplitude of the generalized controlled object at the cut-off frequency
As the generalized controlled object is 0 type, the control strategy that integral control is main and proportional control is auxiliary can be determined, namely the controller is controlled at omegacThe gain of the amplitude is-48.32 dB, namely
|Ki|＝0.0077，
The proportionality coefficient is mainly configured with the zero point of the controller, and can take a smaller value, this embodiment Kp＝0.0556KiThe gain of the controlled object is negative, so that the transfer function of the controller can be obtained
After the controller is determined, the open loop transfer function is
The bode diagram of the open-loop control loop is shown in fig. 3, and the unit step response is shown in fig. 4, from which it can be seen that:
1) the control system is stable, and the steady-state error is 0;
2) the amplitude margin of the open-loop control loop is 17.47dB, the phase margin is 70.4 degrees, the cut-off frequency is 2.01rad/s, the amplitude slope at the cut-off position is-20 dB/dec, and the cut-off frequency is far away from two front and back connection frequencies, so that the 'staggering principle' in engineering is met;
3) the control system has better dynamic response characteristics.
The present invention has not been described in detail, partly as is known to the person skilled in the art.
Claims (1)
1. A design method based on a cut-off frequency control loop is characterized by comprising the following steps:
(1) according to the characteristics of controlled object and actuator and control systemRapidity requirement, determining cut-off frequency omega of open-loop control loopc；
(2) Will divide forward path controller GcOther control links except for(s) are equivalent to a generalized controlled object P(s); if the system is a multi-loop control system, the controlled object p is included1The inner loop equivalence including(s) is transformed into a generalized controlled object P(s);
(3) determining a forward path controller G according to the type of the generalized controlled object P(s)c(s) proportional control, integral control or proportional-integral control;
(4) calculating to obtain a forward path controller G according to the amplitude value of the open loop at the cut-off frequency as 1c(s) gain, and calculating to obtain the forward path controller GcA proportionality coefficient and an integral coefficient of(s);
in the step (3): if the generalized controlled object P(s) is a zero-type controlled object, PI control or integral control with integral control as the main and proportional control as the auxiliary is adopted; if the generalized controlled object P(s) is a type or more than one type of controlled object, PI control or proportional control with integral control as auxiliary and proportional control as main is adopted;
in the step (4), for the zero-type controlled object, the integral coefficient K of the controlleriIs determined by the following formula:
wherein j is an imaginary number;
taking a proportionality coefficient KpIs an integral coefficient KiOne twentieth to one tenth of the above, or the proportionality coefficient K is determined according to the following formulapAnd integral coefficient KiThe relationship between:
in the step (4), for one type or more than one type of controlled objects, the controller proportionality coefficient KpIs determined by the following formula:
taking integral coefficient KiIs a proportionality coefficient KpOne twentieth to one tenth of the above or an integral coefficient KiIs 0.
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