CN106054616A - Titanium tape reel continuous pickling loop sleeve height control method for fuzzy logic optimizing PID controller parameters - Google Patents

Abstract

The invention relates to a titanium tape reel continuous pickling loop sleeve height control method for fuzzy logic optimizing PID controller parameters, which belongs to the field of metallurgical engineering control. The control method comprises the following steps: firstly designing a PID controller for a titanium plate tape continuous pickling loop sleeve height; when the transient response curve of an object is stable within the control precision, obtaining the parameters of a fuzzy controller parameters according to the P, I, D parameter values at this time so as to design the fuzzy controller; when the loop height is within the allowable error accuracy range, keeping the the fuzzy PID controller parameters at the previous time unchanged; and when the loop height is out of the accuracy range, recalculating the fuzzy controller parameter values. According to the invention, it is possible to quickly design the parameters of a fuzzy logic optimizing PID controller and fully utilizes the mature parameter adjustment method of a traditional PID controller, which simplifies the complexity of the fuzzy logic optimizing PID controller design and can realize the accurate control of loop height during continuous pickling of a titanium plate.

Description

The titanium strip coil continuous acid-washing looper height control of fuzzy logic PID controller parameter Method processed

Technical field

The present invention relates to the titanium strip coil continuous acid-washing looper height control method of fuzzy logic PID controller parameter, Belong to metallurgical engineering and control technical field.

Background technology

Conventional PID controllers simple in construction, controls error and has robustness and the beneficially advantage such as realization, quilt process model It is widely used in the industrial process control field such as metallurgy, petrochemical industry, building materials, electric power.Along with process units complicates and product matter The raising that amount requires, the complexity of controlled process constantly deepens, particularly with seriality, time-varying, have noise unstable Complication system, traditional PID control cannot meet the requirement controlling target precision.Based on universal approximation property theory adaptive The self-adaptive fuzzy algorithm combined with fuzzy control should be controlled, there is any approximation capability to nonlinear function and self study Ability, it is possible to obtain the structure of system, parameter, uncertain and non-linear by the learning process of self, and obtain system institute The control law needed, is widely used at control field.Fuzzy controller is due to the non-linear of its essence and to mould Type not dependent, PID based on fuzzy self-adaption controls change for uncertain system and object parameters and have time lag Controlled system, all show the strongest adaptability and robustness.Conventional fuzzy controller is the most all dependent on expert Experience be designed, this brings much inconvenience to the application of fuzzy controller.The solution of further investigation fuzzy controller Analysis structure shows, this controller is the gamma controller of a kind of variable-gain, and has a lot of similarity with PID controller.Though So combine both and fuzzy has been carried out substantial amounts of research, but these researchs the most do not provide the adjustment of Fuzzy Controller Parameters Method.Propose the method for adjustment of Fuzzy Controller Parameters based on PID, it directly influence fuzzy control design efficiency, Design complexities, is one of the Industry Control problem most critical factor determined.The present invention proposes based on traditional PID control method, The method that can be adaptively adjusted fuzzy controller parameter.

Summary of the invention

The invention provides the titanium strip coil continuous acid-washing looper height control side of fuzzy logic PID controller parameter Method, cannot meet the state modulator precision requirement of complex object for conventional PID controllers, reduces fuzzy controller and sets The complexity of meter, and avoid expert's dependency of fuzzy controller parameter designing, it is achieved simple, the increasing of Industry Control upgrading Value.

The technical scheme is that the titanium strip coil continuous acid-washing looper height of fuzzy logic PID controller parameter Control method, uses traditional method to design the PID controller of titanium strip continuous acid-washing looper height, then adjusts according to a conventional method P, I, D control parameter；Secondly, when Object transition Process response curve stable in the range of control accuracy time, according to P now, I, D parameter value obtains the parameter value of fuzzy controller, thus designs fuzzy controller.Then, when looper height is in permission Within the scope of error precision, the value keeping previous moment fuzzy controller parameter is constant, and otherwise, looper height is at precision model Outside enclosing, recalculate the value of Fuzzy Controller Parameters.

Systematic steady state error can be eliminated respectively according to PI controller and PD controller, accelerate response speed, and avoid obscuring Controller complexity of the calculation.Use PI fuzzy controller and the PD Fuzzy Control of two input quantities (output error, error change) Two fuzzy sub-controller superpositions of device processed determine the control action of fuzzy controller.In conjunction with conventional PID controllers There is highly developed parameter regulation means, it is achieved that the self-adaptative adjustment of fuzzy controller；

The concrete step of the titanium strip coil continuous acid-washing looper height control method of described fuzzy logic PID controller parameter Rapid as follows:

Step1, first one titanium strip continuous acid-washing looper height PID controller of design, and use Ziegler-Nichols Method adjusts P, I, D parameter of PID controller, respectively obtains the proportional gain K of PID controller_p, storage gain K_iIncrease with differential Benefit K_d, then calculate each term coefficient of increment type discrete type PID controller

Wherein,It is the gain system of the current sample time of increment type discrete type PID controller respectively The gain coefficient of the 1st sampling instant several, front, the gain coefficient of front 2nd sampling instant；

Step2, set up Fuzzy Self-adaptive PID, obtain four parameters K of Fuzzy Self-adaptive PID_e、K_de、 K_PI、K_PDValue；This controller is made up of two parts: one is traditional PID controller, for directly bearing controlled device Feedback control, and realize the on-line tuning of tri-parameters of P, I, D；Two is fuzzy logic PID controller, and this fuzzy logic is excellent Changing PID controller to be made up of PI Fuzzy controller and PD Fuzzy controller respectively, both uses the two single outputs of input, often Individual input variable has " just " and " bearing " two fuzzy values, and output variable has " just ", " bearing " and " zero " three fuzzy values；

Wherein, K_e、K_de、K_PI、K_PDRepresent that kink output height adds with deviation variation rate, the change of error of expected value respectively Speed, the output gain of PI Fuzzy controller, the output gain of PI Fuzzy controller；

Step3, self adaptation, control in real time；After Step1 Yu Step2, obtain the fuzzy self-adaption under limit Four parameter values of PID controller, it is ensured that identical with PID controller performance, next further according to closed loop system during its stable state Response curve fine setting four parameters to reach desired performance；

Look first at the closed-loop response curve of Fuzzy Self-adaptive PID, estimate its overshoot, big according to overshoot Little the most rightIt is adjusted, such vernier control device parameter, until the response curve of closed loop system reaches Expected performance；If outside the range of error of looper height, circulation carries out step Step1～Step2, if in range of error In, the value keeping the Fuzzy Self-adaptive PID parameter of previous moment is constant.

Wherein,Represent three parameters of incremental fuzzy self-adaptive PID controller respectively, correspond to The K of conventional PID controllers_p、K_iAnd K_dThree coefficients, respectively represent incremental fuzzy self-adaptive PID controller proportional gain, Storage gain and the differential gain.

In described step Step1, PID controller is increment type discrete type PID controller, and its increment expression formula is:

${\mathrm{\ΔU}}_{PID}\left(k\right)=K_C^{0}e\left(k\right)+K_C^{1}e(k-1)+K_C^{2}e(k-2)---\left(1\right)$

In formula

$\left\{\begin{array}{c}{K}_C^0=K_p+K_i\·T_s/T_i+K_p\·K_d/T_s\\ K_C^1=-(K_p+2K_p\·K_d/T_s)\\ K_C^2=K_p\·K_d/T_s\end{array}\right.---\left(2\right)$

In formulaIt is the gain system of the current sample time of increment type discrete type PID controller respectively The gain coefficient of the 1st sampling instant several, front, the gain coefficient of front 2nd sampling instant；E (k) is the control deviation of PID controller； K_p、K_iAnd K_dIt is the proportional gain of PID controller, storage gain and the differential gain respectively；T_i、T_dAnd T_sBe respectively the time of integration, Derivative time and sampling；

In described step Step2, the increment expression formula of PI Fuzzy controller is:

${\mathrm{\ΔU}}_{F-PI}\left(k\right)=\frac{K_{PI}}{4-2x\left(k\right)}\[K_{e}e\left(k\right)+K_{de}\mathrm{\Δ}e\left(k\right)\]---\left(3\right)$

Wherein,

$\left\{\begin{array}{c}e\left(k\right)=y_{sp}-y\left(k\right),\mathrm{\Δ}e\left(k\right)=e\left(k\right)-e(k-1)\\ 0\≤x\left(k\right)=\max (K_e\·|e\left(k\right)|,K_{de}\·|\mathrm{\Δ}e\left(k\right)\left|\right)\≤1.\end{array}\right.---\left(4\right)$

In like manner, the increment expression formula of PD Fuzzy controller is:

$\begin{array}{c}{\mathrm{\ΔU}}_{F-PD}\left(k\right)=\frac{K_{PD}}{4-2x\left(k\right)}\[K_{e}e\left(k\right)+K_{de}\mathrm{\Δ}e\left(k\right)\]-\\ \frac{K_{PD}}{4-2x\left(k\right)}\[K_{e}e(k-1)+K_{de}\mathrm{\Δ}e(k-1)\]\end{array}---\left(5\right)$

To sum up, the increment expression formula of fuzzy logic PID controller is:

$\begin{array}{c}{\mathrm{\ΔU}}_{F-PID}\left(k\right)={\mathrm{\ΔU}}_{F-PI}\left(k\right)+{\mathrm{\ΔU}}_{F-PD}\left(k\right)\\ =K_F^0\left(k\right)e\left(k\right)+K_F^1\left(k\right)e(k-1)+K_F^2\left(k\right)e(k-2)\end{array}---\left(6\right)$

In formula,

$K_F^0\left(k\right)=\frac{K_{PI}\·K_e+K_{PI}\·K_{de}+K_{PD}\·K_e+K_{PD}\·K_{de}}{4-2x\left(k\right)}---\left(7\right)$

$K_F^1\left(k\right)=-\[\frac{K_{PI}\·K_{de}+K_{PD}\·K_{de}}{4-2x\left(k\right)}+\frac{K_{PD}\·K_e+K_{PD}\·K_{de}}{4-2x(k-1)}\]---\left(8\right)$

$K_F^2\left(k\right)=\frac{K_{PD}\·K_{de}}{4-2x(k-1)}---\left(9\right)$

Make fuzzy logic PID controller equal with PID controller respective items coefficient, i.e. have fuzzy control during stable state Device parameter and pid parameter correspondent equal,

$\left\{\begin{array}{c}{K}_F^0\left(\mathrm{\∞}\right)=K_C^0\\ K_F^1\left(\mathrm{\∞}\right)=K_C^1\\ K_F^2\left(\mathrm{\∞}\right)=K_C^2\end{array}\right.---\left(10\right)$

Meanwhile, when membership function parameter L=1, consider further that input variable tries one's best in region [-1,1] × [-1,1], institute With, K_eSelection should meet

(y_sp-y₀)·K_e=1 (11)

By (10) and (11) formula, parameter K of fuzzy logic PID controller can be tried to achieve_e、K_de、K_PI、K_PD；

Wherein, Δ U_F-PIK () is the increment output of PI type Fuzzy type controller, Δ U_F-PDK () is the increasing of the fuzzy PD type controller Amount output, Δ U_F-PIDK () is the increment output of fuzzy logic PID controller, y_spIt is output high expectations value, y₀It is output Height value, other parameter implications are the same.

The invention has the beneficial effects as follows: the present invention can quickly design the parameter of fuzzy logic PID controller, fills Dividing utilizes conventional PID controllers to have highly developed parameter regulation means, simplifies fuzzy logic PID controller The complexity of design, can realize the accurate control of looper height during continuous acid-washing of titanium strip.

Accompanying drawing explanation

Fig. 1 is the Fuzzy Adaptive PID Control structure chart in the present invention；

Fig. 2 is the membership function figure of input/output variable of the present invention；

Fig. 3 is that the inventive method has the conventional PID controllers of noise time-dependent system to titanium strip acid cleaning loop height Control result figure；

Fig. 4 is that titanium strip acid cleaning loop height is had the fuzzy logic of noise factor to optimize PID control by the inventive method The control result figure of device；

Fig. 5 is the inventive method control result figure to the fuzzy logic PID controller of noise free system.

Detailed description of the invention

Embodiment 1: as Figure 1-4, the titanium strip coil continuous acid-washing looper height of fuzzy logic PID controller parameter Control method, specifically comprising the following steps that of described method

Step1, first one titanium strip continuous acid-washing looper height PID controller of design, and use Ziegler-Nichols Method adjusts P, I, D parameter of PID controller, respectively obtains the proportional gain K of PID controller_p, storage gain K_iIncrease with differential Benefit K_d, then calculate each term coefficient of increment type discrete type PID controller

Wherein,It is the gain system of the current sample time of increment type discrete type PID controller respectively The gain coefficient of the 1st sampling instant several, front, the gain coefficient of front 2nd sampling instant；

Step2, set up Fuzzy Self-adaptive PID, obtain four parameters K of Fuzzy Self-adaptive PID_e、K_de、 K_PI、K_PDValue；This controller is made up of two parts: one is traditional PID controller, for directly bearing controlled device Feedback control, and realize the on-line tuning of tri-parameters of P, I, D；Two is fuzzy logic PID controller, and this fuzzy logic is excellent Changing PID controller to be made up of PI Fuzzy controller and PD Fuzzy controller respectively, both uses the two single outputs of input, often Individual input variable has " just " and " bearing " two fuzzy values, and output variable has " just ", " bearing " and " zero " three fuzzy values；

Wherein, K_e、K_de、K_PI、K_PDRepresent that kink output height adds with deviation variation rate, the change of error of expected value respectively Speed, the output gain of PI Fuzzy controller, the output gain of PI Fuzzy controller；

Step3, self adaptation, control in real time；After Step1 Yu Step2, obtain the fuzzy self-adaption under limit Four parameter values of PID controller, it is ensured that identical with PID controller performance, next further according to closed loop system during its stable state Response curve fine setting four parameters to reach desired performance；

Look first at the closed-loop response curve of Fuzzy Self-adaptive PID, estimate its overshoot, big according to overshoot Little the most rightIt is adjusted, such vernier control device parameter, until the response curve of closed loop system reaches Expected performance；If outside the range of error of looper height, circulation carries out step Step1～Step2, if in range of error In, the value keeping the Fuzzy Self-adaptive PID parameter of previous moment is constant.

Wherein,Represent three parameters of incremental fuzzy self-adaptive PID controller respectively, correspond to The K of conventional PID controllers_p、K_iAnd K_dThree coefficients；

In described step Step1, PID controller is increment type discrete type PID controller, and its increment expression formula is:

${\mathrm{\ΔU}}_{PID}\left(k\right)=K_C^{0}e\left(k\right)+K_C^{1}e(k-1)+K_C^{2}e(k-2)---\left(1\right)$

In formula

$\left\{\begin{array}{c}{K}_C^0=K_p+K_i\·T_s/T_i+K_p\·K_d/T_s\\ K_C^1=-(K_p+2K_p\·K_d/T_s)\\ K_C^2=K_p\·K_d/T_s\end{array}\right.---\left(2\right)$

In formulaIt is the gain system of the current sample time of increment type discrete type PID controller respectively The gain coefficient of the 1st sampling instant several, front, the gain coefficient of front 2nd sampling instant；E (k) is the control deviation of PID controller； K_p、K_iAnd K_dIt is the proportional gain of PID controller, storage gain and the differential gain respectively；T_i、T_dAnd T_sBe respectively the time of integration, Derivative time and sampling；

In described step Step2, the increment expression formula of PI Fuzzy controller is:

${\mathrm{\ΔU}}_{F-PI}\left(k\right)=\frac{K_{PI}}{4-2x\left(k\right)}\[K_{e}e\left(k\right)+K_{de}\mathrm{\Δ}e\left(k\right)\]---\left(3\right)$

Wherein,

$\left\{\begin{array}{c}e\left(k\right)=y_{sp}-y\left(k\right),\mathrm{\Δ}e\left(k\right)=e\left(k\right)-e(k-1)\\ 0\≤x\left(k\right)=\max (K_e\·|e\left(k\right)|,K_{de}\·|\mathrm{\Δ}e\left(k\right)\left|\right)\≤1.\end{array}\right.---\left(4\right)$

In like manner, the increment expression formula of PD Fuzzy controller is:

$\begin{array}{c}{\mathrm{\ΔU}}_{F-PD}\left(k\right)=\frac{K_{PD}}{4-2x\left(k\right)}\[K_{e}e\left(k\right)+K_{de}\mathrm{\Δ}e\left(k\right)\]-\\ \frac{K_{PD}}{4-2x\left(k\right)}\[K_{e}e(k-1)+K_{de}\mathrm{\Δ}e(k-1)\]\end{array}---\left(5\right)$

To sum up, the increment expression formula of fuzzy logic PID controller is:

$\begin{array}{c}{\mathrm{\ΔU}}_{F-PID}\left(k\right)={\mathrm{\ΔU}}_{F-PI}\left(k\right)+{\mathrm{\ΔU}}_{F-PD}\left(k\right)\\ =K_F^0\left(k\right)e\left(k\right)+K_F^1\left(k\right)e(k-1)+K_F^2\left(k\right)e(k-2)\end{array}---\left(6\right)$

In formula,

$K_F^0\left(k\right)=\frac{K_{PI}\·K_e+K_{PI}\·K_{de}+K_{PD}\·K_e+K_{PD}\·K_{de}}{4-2x\left(k\right)}---\left(7\right)$

$K_F^1\left(k\right)=-\[\frac{K_{PI}\·K_{de}+K_{PD}\·K_{de}}{4-2x\left(k\right)}+\frac{K_{PD}\·K_e+K_{PD}\·K_{de}}{4-2x(k-1)}\]---\left(8\right)$

$K_F^2\left(k\right)=\frac{K_{PD}\·K_{de}}{4-2x(k-1)}---\left(9\right)$

Make fuzzy logic PID controller equal with PID controller respective items coefficient, i.e. have fuzzy control during stable state Device parameter and pid parameter correspondent equal,

$\left\{\begin{array}{c}{K}_F^0\left(\mathrm{\∞}\right)=K_C^0\\ K_F^1\left(\mathrm{\∞}\right)=K_C^1\\ K_F^2\left(\mathrm{\∞}\right)=K_C^2\end{array}\right.---\left(10\right)$

Meanwhile, when membership function parameter L=1, consider further that input variable tries one's best in region [-1,1] × [-1,1], institute With, K_eSelection should meet

(y_sp-y₀)·K_e=1 (11)

By (10) and (11) formula, parameter K of fuzzy logic PID controller can be tried to achieve_e、K_de、K_PI、K_PD；

Wherein, Δ U_F-PIK () is the increment output of PI type Fuzzy type controller, Δ U_F-PDK () is the increasing of the fuzzy PD type controller Amount output, Δ U_F-PIDK () is the increment output of fuzzy logic PID controller, y_spIt is output high expectations value, y₀It is output Height value, other parameter implications are the same.

In fuzzy logic PID controller, two sub-controllers all use two input list outputs, it is assumed that each of which is defeated Entering variable and have two fuzzy values " just " and " bearing ", its output variable has three fuzzy values " just ", " bearing " and " zero ", inputs, exports Variable membership degree function is as shown in Figure 2.

The present invention utilizes MATLAB environment, with the titanium strip continuous acid-washing looper height control system of Yunnan Tai Ye company Actual parameter, the transmission function deriving controlled device is G (s)=0.58/ (0.04s × 0.036s+1).It practice, this system It is time-dependent system, meanwhile, in acid cleaning process, often along with various interference.Utilize Fuzzy Logic Toolbox workbox Devise fuzzy controller, use step signal that looper height control system has been carried out regulatory PID control and fuzzy self-adaption The emulation experiment of Tuning PID Controller compares.Initial value y₀=0, looper height setting value y_sp=1.With traditional PI D method for designing, control Making its parameter value is: K_p0=5.46, the T time of integration_i0=86 and T derivative time_d0=4.And then the parameter of (10) formula can be calculated It is made to be respectively equal to each parameter of (6) formula fuzzy controller during stable state (the sampling instant k in (6) formula takes infinite, i.e. arrives stable state), in conjunction with (11) formula, can obtain each parameter of fuzzy control respectively Value is K_e=1, K_de=0.5975, K_PI=1.3509, K_PD=24.015.Sampling time is 1ms, some companion of each sampling time With this system add amplitude be δ=± 3.0 within random noise disturbance, PID controls to ring with fuzzy control simulation closed loop Should result as shown in Figure 3-Figure 5.

From figure 3, it can be seen that conventional PID controller to having noise, time-dependent system is uncontrollable.Can from Fig. 4 Going out, fuzzy logic optimizes PID and controls constantly adjusting systematic error, makes Control performance standard optimization, and fuzzy logic optimizes PID control Device processed for the titanium this time-dependent system with random noise of strip continuous acid-washing looper height, looper height error energy Control below 5%, it is possible to reach preferably to control effect.As can be seen from Figure 5, if system is noise free system, obscures and patrol The Control performance standard collecting PID controller is more excellent, controls effect more preferable.

Above in conjunction with accompanying drawing, the detailed description of the invention of the present invention is explained in detail, but the present invention is not limited to above-mentioned Embodiment, in the ken that those of ordinary skill in the art are possessed, it is also possible to before without departing from present inventive concept Put that various changes can be made.

Claims (2)

1. the titanium strip coil continuous acid-washing looper height control method of fuzzy logic PID controller parameter, it is characterised in that: institute State specifically comprising the following steps that of method

Step1, first one titanium strip continuous acid-washing looper height PID controller of design, and use Ziegler-Nichols method Adjust P, I, D parameter of PID controller, respectively obtain the proportional gain K of PID controller_p, storage gain K_iWith differential gain K_d, Calculate each term coefficient of increment type discrete type PID controller again

Wherein,It is the gain coefficient of the current sample time of increment type discrete type PID controller, front respectively The gain coefficient of the 1st sampling instant, the gain coefficient of front 2nd sampling instant；

Step2, set up Fuzzy Self-adaptive PID, obtain four parameters K of Fuzzy Self-adaptive PID_e、K_de、K_PI、 K_PDValue；This controller is made up of two parts: one is traditional PID controller, for directly controlled device being carried out negative feedback Control, and realize the on-line tuning of tri-parameters of P, I, D；Two is fuzzy logic PID controller, and this fuzzy logic optimizes PID controller is made up of PI Fuzzy controller and PD Fuzzy controller respectively, and both uses the two single outputs of input, each Input variable has " just " and " bearing " two fuzzy values, and output variable has " just ", " bearing " and " zero " three fuzzy values；

Wherein, K_e、K_de、K_PI、K_PDRepresent respectively kink output height and the deviation variation rate of expected value, change of error acceleration, The output gain of PI Fuzzy controller, the output gain of PI Fuzzy controller；

Step3, self adaptation, control in real time；After Step1 Yu Step2, obtain the Fuzzy Adaptive PID control under limit Four parameter values of device processed, it is ensured that identical with PID controller performance during its stable state, next further according to the response of closed loop system Curve four parameters of fine setting are to reach desired performance；

Looking first at the closed-loop response curve of Fuzzy Self-adaptive PID, estimate its overshoot, the size according to overshoot is anti- Multiple rightIt is adjusted, such vernier control device parameter, until the response curve of closed loop system reaches expectation Performance；If outside the range of error of looper height, circulation carries out step Step1～Step2, if in range of error, The value keeping the Fuzzy Self-adaptive PID parameter of previous moment is constant；

Wherein,Respectively represent the proportional gain of incremental fuzzy self-adaptive PID controller, storage gain and The differential gain.

The titanium strip coil continuous acid-washing looper height control of fuzzy logic PID controller parameter the most according to claim 1 Method processed, it is characterised in that: in described step Step1, PID controller is increment type discrete type PID controller, and its increment is expressed Formula is:

${\mathrm{\ΔU}}_{PID}\left(k\right)=K_C^{0}e\left(k\right)+K_C^{1}e(k-1)+K_C^{2}e(k-2)---\left(1\right)$

In formula

$\left\{\begin{array}{c}{K}_C^0=K_p+K_i\·T_s/T_i+K_p\·K_d/T_s\\ K_C^1=-(K_p+2K_p\·K_d/T_s)\\ K_C^2=K_p\·K_d/T_s\end{array}\right.---\left(2\right)$

In formulaBe respectively the gain coefficient of the current sample time of increment type discrete type PID controller, front The gain coefficient of 1 sampling instant, the gain coefficient of front 2nd sampling instant；E (k) is the control deviation of PID controller；K_p、K_iWith K_dIt is the proportional gain of PID controller, storage gain and the differential gain respectively；T_i、T_dAnd T_sWhen being the time of integration, differential respectively Between and sampling；

In described step Step2, the increment expression formula of PI Fuzzy controller is:

${\mathrm{\ΔU}}_{F-PI}\left(k\right)=\frac{K_{PI}}{4-2x\left(k\right)}\[K_{e}e\left(k\right)+K_{de}\mathrm{\Δ}e\left(k\right)\]---\left(3\right)$

Wherein,

$\left\{\begin{array}{c}e\left(k\right)=y_{sp}-y\left(k\right),\mathrm{\Δ}e\left(k\right)=e\left(k\right)-e(k-1)\\ 0\≤x\left(k\right)=max(K_e\·|e\left(k\right)|,K_{de}\·|\mathrm{\Δ}e\left(k\right)\left|\right)\≤1.\end{array}\right.---\left(4\right)$

In like manner, the increment expression formula of PD Fuzzy controller is:

$\begin{array}{c}{\mathrm{\ΔU}}_{F-PD}\left(k\right)=\frac{K_{PD}}{4-2x\left(k\right)}\[K_{e}e\left(k\right)+K_{de}\mathrm{\Δ}e\left(k\right)\]-\\ \frac{K_{PD}}{4-2x\left(k\right)}\[K_{e}e\left(k-1\right)+K_{de}\mathrm{\Δ}e\left(k-1\right)\]\end{array}---\left(5\right)$

To sum up, the increment expression formula of fuzzy logic PID controller is:

$\begin{array}{c}{\mathrm{\ΔU}}_{F-PID}\left(k\right)={\mathrm{\ΔU}}_{F-PI}\left(k\right)+{\mathrm{\ΔU}}_{F-PD}\left(k\right)\\ =K_F^0\left(k\right)e\left(k\right)+K_F^1\left(k\right)e\left(k-1\right)+K_F^2\left(k\right)e\left(k-2\right)\end{array}---\left(6\right)$

In formula,

$K_F^0\left(k\right)=\frac{K_{PI}\·K_e+K_{PI}\·K_{de}+K_{PD}\·K_e+K_{PD}\·K_{de}}{4-2x\left(k\right)}---\left(7\right)$

$K_F^1\left(k\right)=-\[\frac{K_{PI}\·K_{de}+K_{PD}\·K_{de}}{4-2x\left(k\right)}+\frac{K_{PD}\·K_e+K_{PD}\·K_{de}}{4-2x(k-1)}\]---\left(8\right)$

$K_F^2\left(k\right)=\frac{K_{PD}\·K_{de}}{4-2x(k-1)}---\left(9\right)$

Make fuzzy logic PID controller equal with PID controller respective items coefficient, i.e. have fuzzy controller ginseng during stable state Number and pid parameter correspondent equal,

$\left\{\begin{array}{c}{K}_F^0\left(\mathrm{\∞}\right)=K_C^0\\ K_F^1\left(\mathrm{\∞}\right)=K_C^1\\ K_F^2\left(\mathrm{\∞}\right)=K_C^2\end{array}\right.---\left(10\right)$

Meanwhile, when membership function parameter L=1, consider further that input variable tries one's best in region [-1,1] × [-1,1], so, K_e Selection should meet

(y_sp-y₀)·K_e=1 (11)

By (10) and (11) formula, parameter K of fuzzy logic PID controller can be tried to achieve_e、K_de、K_PI、K_PD；

Wherein, Δ U_F-PIK () is the increment output of PI type Fuzzy type controller, Δ U_F-PDK () is that the increment of the fuzzy PD type controller is defeated Go out, Δ U_F-PIDK () is the increment output of fuzzy logic PID controller, y_spIt is output high expectations value, y⁰It it is output height Value, other parameter implications are the same.