Molar water spray speed control optimization method for dental unitTechnical Field
The invention relates to the technical field of PID control, in particular to a molar water spray speed control optimization method for a dental treatment machine.
Background
Molar water sprays in dental treatment machines are commonly used in tooth cleaning and cooling processes. The water spraying system can provide necessary water flow in the tooth grinding operation process so as to ensure the smooth treatment process and reduce the damage to teeth caused by heat generated by the high-speed rotating tool. The water spraying mainly provides water pressure through the miniature liquid injection pump, and the device is usually required to have a precise control function, so that the pressure and the flow rate of the injected liquid can be precisely controlled, and the accuracy and the safety of a flushing effect are ensured.
The miniature infusion pump generally adopts a direct current motor as a driving source, and the rotating speed of the direct current motor is controlled, so that the liquid flow is controlled to flush the root canal of the tooth, and in the flushing process, the too high water flow pressure returns to cause the liquid in the root canal to permeate into surrounding tissues, so that pain or discomfort is caused, the root canal wall is damaged, and the shape of the root canal is changed or the root canal wall is broken. Thus, to precisely control the liquid injection rate of the molar surgical rinse, the robustness of the miniature infusion pump, i.e., the DC motor, must be controlled.
At present, the control of the miniature liquid injection pump mostly adopts open-loop control, the control signal (such as current, pulse and the like) of the motor is directly output by a control system without feedback or closed-loop control, the mode is simple, the cost is lower, but the actual state of the motor cannot be monitored and adjusted, and the control precision is relatively lower. Secondly, closed-loop PID control, proportional-integral-derivative (PID) control is a closed-loop control method, and the system error is regulated through three parts of proportion, integral and derivative to realize stable control, the PID control is commonly used for controlling the flow and the pressure of a miniature liquid injection pump to realize accurate control, but in practical application, the dynamic characteristic of the system can change along with time or be influenced by external environment, so that the regulation of PID parameters is difficult, the parameters are required to be optimized through trial and error or expert knowledge, and preferably, the PID control has slower reaction speed in the miniature liquid injection pump control and cannot meet the real-time requirement.
The Duck Swarm Algorithm (DSA) is an optimization method based on swarm intelligence, inspiration is derived from social behaviors of foraging behaviors of duck swarms, and exploration and development stages in the optimization process are guided by simulating food sources and foraging behaviors of ducks; compared with other known algorithms such as Particle Swarm Optimization (PSO), firefly algorithm, and gray wolf optimizer, the DSA shows superior performance on various multi-modal reference functions, and although DSA has better performance on multi-modal problems, in extreme cases, it is easy to fall into a local optimal solution, especially in a complex control system, initial parameter setting and population diversity have larger influence on a final result, and for micro-infusion pump control of a dental therapeutic machine with higher real-time requirements, the optimization process of DSA may take longer, cannot meet the requirement of quick response, and the optimal robustness is poor.
Disclosure of Invention
In order to overcome the defects in the prior art, the invention aims to provide a molar water spray speed control optimization method for a dental therapeutic machine, which is characterized in that a duck group optimization algorithm (DSA) is improved, an improved duck group optimization algorithm (IDSA) is utilized to optimize a position type PID control algorithm, an IDSA-PID control method is obtained, and a direct current motor of a miniature liquid injection pump is controlled by utilizing the IDSA-PID control algorithm, so that the control precision of the miniature liquid injection pump is improved, and the molar water spray speed of the dental therapeutic machine is precisely controlled.
In order to achieve the above purpose, the present invention adopts the following technical scheme: a molar water spray speed control optimization method for a dental treatment machine comprises a miniature liquid injection pump control system, wherein the system comprises a direct current motor driving source unit and a position type PID controller unit, and specifically comprises the following steps.
S1, converting the micro liquid injection pump control problem into a mathematical model to be optimized according to the relation between the rotation speed of the micro liquid injection pump driving source and the pump pressure of the micro liquid injection pump driving source.
S2, optimizing a mathematical model to be optimized by using an improved duck group optimization algorithm (IDSA), wherein the method comprises the following steps:
S21, improving the balance factor mu of a standard duck group optimization algorithm by utilizing the fitness value difference and the individual duck sequencing principle, and improving the position updating mathematical model of the duck group optimization algorithm;
s22, providing an environmental pressure strategy, and improving the optimizing strategy of the duck group optimizing algorithm based on the diversity of the environmental pressure and the adaptability;
S23, setting the control parameters of the proportional coefficient Kp, the integral coefficient Ki and the differential coefficient Kd of the position PID of the miniature liquid injection pump control system by using an improved duck group optimization algorithm (IDSA) to obtain the optimal control parameters.
S3, inputting the optimal control parameters of the position type PID obtained by setting in the step S22 and an error e (k) between the real-time pumping pressure and the target pumping pressure of the miniature liquid injection pump into a position type PID controller unit of the miniature liquid injection pump control system.
S4, outputting a control quantity u (k) by using a position type PID controller of the micro infusion pump control system in the step S3, controlling a direct current motor driving source of the micro infusion pump, and repeating the steps S2 to S4 to realize optimal robust control of the tooth grinding water spraying speed of the dental therapeutic machine.
Preferably, first, a relation model between the output pressure of the micro liquid injection pump and the rotation speed of a driving source of the micro liquid injection pump is established;
（1）；
In the formula (1), the components are as follows,Is the rotation speed of a driving source of the miniature liquid injection pump,Is a pump characteristic constant;
Further, the pressure control problem of the miniature injection pump is converted into a mathematical model to be optimizedNamely an objective function, and the mathematical formula is as follows:
（2）；
In the formula (2), the amino acid sequence of the compound,For the total control time it is possible to provide,For the kth second control time,For the miniature infusion pump target pump pressure, lambda is the weight coefficient of energy consumption,Pumping for the kth second of micro-priming,The drive source rotation speed of the micro infusion pump is k seconds.
Preferably, the balance factor mu of the standard duck group optimization algorithm is improved by utilizing the fitness value difference and the individual ordering principle, the maximum value of the improved balance factor is 1, the minimum value is 0.1, and the improved balance factor isThe mathematical model is:
（3）；
in the formula (3), the amino acid sequence of the compound,The balance factor value of the ith duck individual for the t-th iteration,The balance factor value of the ith duck individual in the t-1 th iteration,The minimum adaptation value of the duck group position for the t-th iteration,Is the minimum fitness value of the duck group position of the t-1 th iteration,For the maximum population size to be the largest,For the ordering of the ith duck individual in the current population,And the fitness value of the ith duck individual position of the t-th iteration is obtained.
Preferably, the balance factor mu is improved, the duck group optimization algorithm is improved, the balance factor is dynamically adjusted by utilizing the difference between the fitness value of the duck individuals and the current optimal duck individuals, so that the duck individuals can search more when the fitness change is large, search more finely when the fitness change is small, meanwhile, different adjustment amplitudes are given according to the fitness sequence of the individuals in the current population, so that the individuals ranked in front have larger search space, and the individuals ranked in back search more finely, more particularly, as shown in a formula (3),
Minimum fitness value for duck group position for the t-th iterationMinimum fitness value with t-1 th iteration duck group positionThe larger the absolute value of the differential value, the larger the change in fitness is, and the more the balance factor needs to be explored (smaller value); conversely, when the change is smaller, the balance factor performs a finer search (larger value);
wherein,The ratio of the current i-th individual fitness value to the current optimal fitness value reflects the fitness gap between the i-th duck individual and the optimal duck individual;
wherein,For the ratio of the sorting of the ith duck individuals in the current population to the maximum population scale, the smaller the ratio is, the higher the ranking of the ith duck individuals is, the larger the exploration space is needed; the larger the ratio, the finer the search should be after the ranking of individual ducks i.
Preferably, the standard duck group optimization algorithm (DSA) optimizing strategy only comprises food searching (global searching stage) and group foraging (local developing stage), and the optimizing strategy is easy to fall into local optimization when the algorithm optimizes the PID controller controlled by the micro liquid injection pump pressure, and influences the setting precision of parameters of the PID controller, thereby influencing the control performance of the system; the environment pressure strategy is provided, the optimizing strategy of the duck group optimizing algorithm is improved based on the diversity of the environment pressure and the adaptability, and the environment pressure strategy comprises the following specific methods:
s221, introducing an environmental pressure factor, simulating the influence of different environmental conditions on foraging of the ducks, wherein the environmental pressure factor changes randomly, and the mathematical model is as follows:
（4）；
In the formula (4), the amino acid sequence of the compound,For the ambient pressure value of the t-th iteration,As an initial value of the ambient pressure,For the current number of iterations,The maximum iteration number is the maximum iteration number, and beta is a fluctuation amplitude factor;
s222, calculating the adaptability of each duck individual to the environmental pressure in the current iteration, wherein the higher the adaptability is, the higher the survival rate is, and the mathematical model is as follows:
（5）；
in the formula (5), the amino acid sequence of the compound,The fitness value of the ith duck individual position of the t-th iteration,In order to adapt the parameters to be adjusted,Adaptability to the environmental pressure of the ith duck individual;
S223, dynamically adjusting the mutation rate according to the overall adaptability of the duck population, increasing the mutation rate to improve diversity when the overall adaptability is reduced, and reducing the mutation rate to keep stable when the overall adaptability is increased;
（6）；
In the formula (6), the amino acid sequence of the compound,For the variation rate of the ith duck individual in the t-th iteration,For the initial rate of variation, the average value of the variation,In order to adjust the coefficient of the coefficient,For the difference between the adaptability of the current iteration and the adaptability of the previous generation,Is the average adaptability of the current population.
Preferably, by introducing a periodic function to simulate the environmental pressure, the searching behavior of the duck group is changed along with time, the premature convergence of the algorithm can be effectively avoided, the capability of the algorithm for exploring an unknown area is increased, the strategy is favorable for balancing the algorithm between global searching and local fine searching, the robustness and efficiency of the algorithm are improved, secondly, the behavior of the individual is dynamically adjusted by calculating the adaptability difference between the duck individual and the current optimal solution, the method enables the algorithm to adjust the searching strategy according to the environmental change and the performance difference between the individuals, the capability of the algorithm for adapting to a complex searching environment is improved, finally, the variability rate is dynamically adjusted according to the environmental pressure, the dynamic adjustment strategy is favorable for increasing the diversity in the global searching stage of the algorithm, the variability is reduced in the local stage requiring fine searching, and the searching efficiency and the quality of the algorithm are improved.
Preferably, the control parameters of the proportional coefficient Kp, the integral coefficient Ki and the differential coefficient Kd of the position PID of the miniature liquid injection pump control system are set by utilizing an improved duck group optimization algorithm (IDSA), so as to obtain the optimal control parameters, and the specific steps are as follows:
step 1, coding a proportional coefficient Kp, an integral coefficient Ki and a differential coefficient Kd of a PID control algorithm of a miniature injection pump of a dental therapeutic instrument into a three-dimensional space vector form, and dividing the three-dimensional space vector form into M groups of three-dimensional space vectors;
Step 2, setting a maximum population scale N of the improved duck group optimization algorithm, a problem dimension D, an upper bound ub and a lower bound lb of solution values of the improved duck group optimization algorithm and a maximum iteration numberInitial value of ambient pressureInitial mutation rate；
Step 3, randomly initializing individual duck positions for improving duck group optimization algorithmWherein i=1, 2,3,; j=1, 2, D, positioning individual ducksEstablishing real number mapping with M groups of three-dimensional space vectors, wherein N=M and D=3;
Step 4, calculating the fitness value of each current duck individual position by using an objective function, and reserving the minimum fitness value of the current duck group positionTaking the duck individual position corresponding to the minimum fitness value as an optimal position;
Step 5, if the current iteration number t is smaller than the maximum iteration number Max_iter, executing step 6, otherwise, exiting the setting loop, outputting the optimal duck individual position of the improved duck group optimization algorithm corresponding to the minimum fitness value, and decoding the optimal individual position into a proportional coefficient Kp, an integral coefficient Ki and a differential coefficient Kd of a miniature infusion pump PID of the dental therapeutic instrument;
Step 6, utilizing the improved balance factor balance algorithm global search and local development strategy, and establishing a duck individual position updating mathematical model in the global search and local development stage of the improved duck group optimization algorithm to form a new algorithm optimizing strategy; updating the parameter values of Kp, ki and Kd of a PID control algorithm of a miniature injection pump of the dental therapeutic instrument through a new algorithm optimizing strategy;
step 7, limiting the boundary of each updated individual duck position so that the solution value of the improved duck group optimization algorithm is between an upper boundary ub and a lower boundary lb;
Step 8, calculating a new fitness value of each current duck individual position by using an objective function, comparing the fitness values of each duck individual position before updating, and taking the new fitness value as the current fitness value and taking the duck individual position corresponding to the new fitness value as the current duck individual position if the new fitness value is smaller than the fitness value before updating; otherwise, the current fitness value is unchanged from the current duck individual position;
Step 9, introducing an environmental pressure strategy, establishing a population position variation mathematical model for improving the duck group optimization algorithm according to a formula (7), updating the duck group position, executing t=t+1 for the current iteration times, and then returning to execute the step 5;
（7）；
In the formula (7), the amino acid sequence of the compound,The value of the j-th dimension of the ith duck individual position is iterated for the t+1th time,For the value of the j-th dimension of the position updated for the ith individual duck of the t-th iteration,The j-th dimensional value of the post-position is updated for the t-th iteration worst-position individual,The minimum fitness value of the updated position of the duck group for the t-th iteration,The adaptation value with the largest position after the updating of the duck group for the t-th iteration,Is a minimum value, takes a value of 0.1,The variation rate of the ith duck individual is the t iteration.
Preferably, the specific steps of introducing an environmental pressure strategy and establishing a duck individual position updating mathematical model of the global searching and local development stage of the improved duck group optimization algorithm are as follows:
s61, updating the improved balance factor mu by using a formula (3) to obtain a balance factor value of an ith duck individual in the t-th iteration；
S62, if the balance factor value of the ith duck individual of the t-th iterationIf the value is greater than 0.5, executing step S63, otherwise, executing step S64;
S63, in the global searching stage, the ducks with strong simulated searching capability are close to the center of the food source, other individuals are attracted to be close to the center, a duck individual position updating mathematical model in the global searching stage is established according to a formula (8), and a duck individual position value is updated;
（8）；
in the formula (8), the amino acid sequence of the compound,The value of the j-th dimension of the ith duck individual position is iterated for the t+1th time,The value of the j-th dimension of the ith duck individual position for the t-th iteration,For the j-th dimension value of the individual position of the optimal position for the t-th iteration,Is a sign function, influences the process of seeking food for duck individuals,In order to search for the transition probabilities,A uniform random number within 0 to 1; The ith iteration is the ith around the ith duck individualThe j-th dimensional value of the individual position of the individual duck,Is a random number within the range of 0 to 1,AndThe cooperation and competition coefficients among the ducks in the searching stage are calculated;
s64, in a local development stage, simulating foraging of a duck group, wherein all duck individuals approach food, the next position is influenced by the adjacent individuals and the food position or the pilot duck, a duck individual position updating mathematical model in the local development stage is established according to a formula (8), and a duck individual position value is updated;
（9）；
In the formula (9), the amino acid sequence of the compound,、、Is explained in the same manner as in the formula (8),The fitness value of the ith duck individual position of the t-th iteration,Is the fitness value of the ith duck individual position of the t+1th iteration,AndTo develop the cooperation and competition coefficients between ducks individuals; AndThe ith iteration is the ith around the ith duck individualAndAnd (5) a j-th dimensional value of the individual position of the individual ducks.
More specifically, the miniature injection pump control system comprises a position type PID controller unit, an error calculation unit for the real-time pumping pressure and the target pumping pressure of the miniature injection pump, an objective function unit, an improved duck group optimization algorithm unit, a control signal output unit and a driving source direct current motor rotating speed real-time acquisition unit; wherein, the error value e (t) of the real-time pumping pressure and the target pumping pressure of the miniature injection pump is optimized by the improved duck group optimization algorithmCalculating a PID control output value u (T) of a miniature liquid injection pump of the dental therapeutic machine, driving a direct current motor to move by using the output value u (T), calculating the real-time rotating speed of the direct current motor by using an encoder, converting the real-time pumping pressure of the miniature liquid injection pump by using a formula (1), namely controlling the water spraying speed by the pumping pressure until the item reaches the control maximum time T, and realizing the closed-loop control of the miniature liquid injection pump of the dental therapeutic machine.
Compared with the prior art, the invention has the beneficial effects that: the invention realizes the accurate control of the direct current motor driving source of the miniature liquid injection pump by improving the duck group optimization algorithm (IDSA) to optimize the position PID control algorithm, thereby improving the control precision of the miniature liquid injection pump, and simultaneously, the invention adopts the environmental pressure strategy and the searching and developing strategy of the adaptive adjustment dynamic adjustment algorithm, so that the algorithm can be adjusted according to the environmental change in the global searching and local development stages, the real-time response capability of the control system is obviously improved, the improved algorithm can better adapt to the complex control environment by dynamically adjusting the variation rate and the adaptive adjustment parameter, and the adaptability and the control performance of the miniature liquid injection pump control system are improved.
Drawings
Fig. 1 is a diagram of the steps of the method for optimal robust control of the water jet rate of the teeth grinding of a dental unit.
Fig. 2 is a flowchart of a method for adjusting control parameters of a proportional coefficient Kp, an integral coefficient Ki and a differential coefficient Kd of a position type PID of a miniature liquid injection pump control system by improving a duck group optimization algorithm.
Fig. 3 is a flow chart for establishing a mathematical model for updating individual duck position during the global search and local development phases of an improved duck group optimization algorithm.
Fig. 4 is a graph comparing the results of the improved duck group optimization algorithm to the Kp, ki, kd settings of the PID algorithm of the miniature infusion pump control system.
Fig. 5 is a graph comparing the change in objective function value of the IDSA-PID method with other methods for molar water jet rate control of a dental treatment machine.
Figure 6 is a graph comparing the effects of the IDSA-PID method with other methods for dental treatment machine micro infusion pump pressure control.
Detailed Description
The technical solutions of the embodiments of the present invention will be clearly and completely described with reference to the drawings in the embodiments of the present invention, and it is apparent that the described embodiments are only some embodiments of the present invention, not all embodiments; all other embodiments, which can be made by those skilled in the art based on the embodiments of the invention without making any inventive effort, are intended to be within the scope of the invention.
The invention provides a technical scheme that: a molar water spray speed control optimization method for a dental treatment machine comprises a miniature liquid injection pump control system, wherein the system comprises a direct current motor driving source unit and a position type PID controller unit, and specifically comprises the following steps as shown in figure 1.
S1, converting the micro liquid injection pump control problem into a mathematical model to be optimized according to the relation between the rotation speed of the micro liquid injection pump driving source and the pump pressure of the micro liquid injection pump driving source.
Further, firstly, establishing a relation model between the output pressure of the micro liquid injection pump and the rotation speed of a driving source of the micro liquid injection pump;
（1）；
In the formula (1), the components are as follows,Is the rotation speed of a driving source of the miniature liquid injection pump,Is a pump characteristic constant;
Further, the pressure control problem of the miniature injection pump is converted into a mathematical model to be optimizedNamely an objective function, and the mathematical formula is as follows:
（2）；
In the formula (2), the amino acid sequence of the compound,For the total control time it is possible to provide,For the kth second control time,For the miniature infusion pump target pump pressure, lambda is the weight coefficient of energy consumption,Pumping for the kth second of micro-priming,The drive source rotation speed of the micro infusion pump is k seconds.
S2, optimizing a mathematical model to be optimized by using an improved duck group optimization algorithm (IDSA), wherein the method comprises the following steps:
S21, improving the balance factor mu of a standard duck group optimization algorithm by utilizing the fitness value difference and the individual duck sequencing principle, and improving a position updating mathematical model of a global searching stage of the duck group optimization algorithm; the specific method comprises the following steps: the balance factor mu of the standard duck group optimization algorithm is improved by utilizing the fitness value difference and the individual sequencing principle, the maximum value of the improved balance factor is 1, the minimum value is 0.1, and the improved balance factor isThe mathematical model is:
（3）；
in the formula (3), the amino acid sequence of the compound,The balance factor value of the ith duck individual for the t-th iteration,The balance factor value of the ith duck individual in the t-1 th iteration,The minimum adaptation value of the duck group position for the t-th iteration,Is the minimum fitness value of the duck group position of the t-1 th iteration,For the maximum population size to be the largest,For the ordering of the ith duck individual in the current population,And the fitness value of the ith duck individual position of the t-th iteration is obtained.
Further, by improving the balance factor mu and improving the duck group optimization algorithm, the balance factor is dynamically adjusted by utilizing the difference between the fitness value of the duck individuals and the current optimal duck individuals, so that the duck group optimization algorithm can perform more exploration when the fitness change is large, perform finer searching when the fitness change is small, and simultaneously, give different adjustment amplitudes according to the fitness order of the individuals in the current group, so that the individuals ranked in front have larger exploration space, and the individuals ranked in back perform finer searching, more specifically, as shown in a formula (3),
Minimum fitness value for duck group position for the t-th iterationMinimum fitness value with t-1 th iteration duck group positionThe larger the absolute value of the differential value, the larger the change in fitness is, and the more the balance factor needs to be explored (smaller value); conversely, when the change is smaller, the balance factor performs a finer search (larger value);
wherein,The ratio of the current i-th individual fitness value to the current optimal fitness value reflects the fitness gap between the i-th duck individual and the optimal duck individual;
wherein,For the ratio of the sorting of the ith duck individuals in the current population to the maximum population scale, the smaller the ratio is, the higher the ranking of the ith duck individuals is, the larger the exploration space is needed; the larger the ratio, the finer the search should be after the ranking of individual ducks i.
S22, providing an environmental pressure strategy, and improving the optimizing strategy of the duck group optimizing algorithm based on the diversity of the environmental pressure and the adaptability; the specific method comprises the following steps: the standard duck group optimizing algorithm (DSA) optimizing strategy only comprises food searching (global searching stage) and group foraging (local developing stage), and when the algorithm optimizes the PID controller controlled by the micro liquid injection pump pressure, the optimizing strategy is easy to sink into local optimization, and the setting precision of the parameters of the PID controller is influenced, so that the control performance of the system is influenced; the environment pressure strategy is provided, the optimizing strategy of the duck group optimizing algorithm is improved based on the diversity of the environment pressure and the adaptability, and the environment pressure strategy comprises the following specific methods:
s221, introducing an environmental pressure factor, simulating the influence of different environmental conditions on foraging of the ducks, wherein the environmental pressure factor changes randomly, and the mathematical model is as follows:
（4）；
In the formula (4), the amino acid sequence of the compound,For the ambient pressure value of the t-th iteration,As an initial value of the ambient pressure,For the current number of iterations,The maximum iteration number is the maximum iteration number, and beta is a fluctuation amplitude factor;
s222, calculating the adaptability of each duck individual to the environmental pressure in the current iteration, wherein the higher the adaptability is, the higher the survival rate is, and the mathematical model is as follows:
（5）；
in the formula (5), the amino acid sequence of the compound,The fitness value of the ith duck individual position of the t-th iteration,In order to adapt the parameters to be adjusted,Adaptability to the environmental pressure of the ith duck individual;
S223, dynamically adjusting the mutation rate according to the overall adaptability of the duck population, increasing the mutation rate to improve diversity when the overall adaptability is reduced, and reducing the mutation rate to keep stable when the overall adaptability is increased;
（6）；
In the formula (6), the amino acid sequence of the compound,For the variation rate of the ith duck individual in the t-th iteration,For the initial rate of variation, the average value of the variation,In order to adjust the coefficient of the coefficient,For the difference between the adaptability of the current iteration and the adaptability of the previous generation,Is the average adaptability of the current population.
S23, setting control parameters of a proportion coefficient Kp, an integral coefficient Ki and a differential coefficient Kd of a position PID of the miniature liquid injection pump control system by using an improved duck group optimization algorithm (IDSA), and obtaining optimal control parameters, wherein the method specifically comprises the following steps of:
step 1, coding a proportional coefficient Kp, an integral coefficient Ki and a differential coefficient Kd of a PID control algorithm of a miniature injection pump of a dental therapeutic instrument into a three-dimensional space vector form, and dividing the three-dimensional space vector form into M groups of three-dimensional space vectors;
Step 2, setting a maximum population scale N of the improved duck group optimization algorithm, a problem dimension D, an upper bound ub and a lower bound lb of solution values of the improved duck group optimization algorithm and a maximum iteration numberInitial value of ambient pressureInitial mutation rate；
Step 3, randomly initializing individual duck positions for improving duck group optimization algorithmWherein i=1, 2,3,; j=1, 2, D, positioning individual ducksEstablishing real number mapping with M groups of three-dimensional space vectors, wherein N=M and D=3;
Step 4, calculating the fitness value of each current duck individual position by using an objective function, and reserving the minimum fitness value of the current duck group positionTaking the duck individual position corresponding to the minimum fitness value as an optimal position;
Step 5, if the current iteration number t is smaller than the maximum iteration number Max_iter, executing step 6, otherwise, exiting the setting loop, outputting the optimal duck individual position of the improved duck group optimization algorithm corresponding to the minimum fitness value, and decoding the optimal individual position into a proportional coefficient Kp, an integral coefficient Ki and a differential coefficient Kd of a miniature infusion pump PID of the dental therapeutic instrument;
Step 6, utilizing the improved balance factor balance algorithm global search and local development strategy, and establishing a duck individual position updating mathematical model in the global search and local development stage of the improved duck group optimization algorithm to form a new algorithm optimizing strategy; updating the parameter values of Kp, ki and Kd of a PID control algorithm of a miniature injection pump of the dental therapeutic instrument through a new algorithm optimizing strategy;
step 7, limiting the boundary of each updated individual duck position so that the solution value of the improved duck group optimization algorithm is between an upper boundary ub and a lower boundary lb;
Step 8, calculating a new fitness value of each current duck individual position by using an objective function, comparing the fitness values of each duck individual position before updating, and taking the new fitness value as the current fitness value and taking the duck individual position corresponding to the new fitness value as the current duck individual position if the new fitness value is smaller than the fitness value before updating; otherwise, the current fitness value is unchanged from the current duck individual position;
Step 9, introducing an environmental pressure strategy, establishing a population position variation mathematical model for improving the duck group optimization algorithm according to a formula (7), updating the duck group position, executing t=t+1 for the current iteration times, and then returning to execute the step 5;
（7）；
In the formula (7), the amino acid sequence of the compound,The value of the j-th dimension of the ith duck individual position is iterated for the t+1th time,For the value of the j-th dimension of the position updated for the ith individual duck of the t-th iteration,The j-th dimensional value of the post-position is updated for the t-th iteration worst-position individual,The minimum fitness value of the updated position of the duck group for the t-th iteration,The adaptation value with the largest position after the updating of the duck group for the t-th iteration,Is a minimum value, takes a value of 0.1,The variation rate of the ith duck individual is the t iteration.
Further, as shown in fig. 3, the specific steps of introducing an environmental pressure strategy and establishing a duck individual position updating mathematical model for improving the global searching and local development stage of the duck group optimization algorithm are as follows:
s61, updating the improved balance factor mu by using a formula (3) to obtain a balance factor value of an ith duck individual in the t-th iteration；
S62, if the balance factor value of the ith duck individual of the t-th iterationIf the value is greater than 0.5, executing step S63, otherwise, executing step S64;
S63, in the global searching stage, the ducks with strong simulated searching capability are close to the center of the food source, other individuals are attracted to be close to the center, a duck individual position updating mathematical model in the global searching stage is established according to a formula (8), and a duck individual position value is updated;
（8）；
in the formula (8), the amino acid sequence of the compound,The value of the j-th dimension of the ith duck individual position is iterated for the t+1th time,The value of the j-th dimension of the ith duck individual position for the t-th iteration,For the j-th dimension value of the individual position of the optimal position for the t-th iteration,Is a sign function, influences the process of seeking food for duck individuals,In order to search for the transition probabilities,A uniform random number within 0 to 1; The ith iteration is the ith around the ith duck individualThe j-th dimensional value of the individual position of the individual duck,Is a random number within the range of 0 to 1,AndThe cooperation and competition coefficients among the ducks in the searching stage are calculated;
s64, in a local development stage, simulating foraging of a duck group, wherein all duck individuals approach food, the next position is influenced by the adjacent individuals and the food position or the pilot duck, a duck individual position updating mathematical model in the local development stage is established according to a formula (8), and a duck individual position value is updated;
（9）；
In the formula (9), the amino acid sequence of the compound,、、Is explained in the same manner as in the formula (8),The fitness value of the ith duck individual position of the t-th iteration,Is the fitness value of the ith duck individual position of the t+1th iteration,AndTo develop the cooperation and competition coefficients between ducks individuals; AndThe ith iteration is the ith around the ith duck individualAndAnd (5) a j-th dimensional value of the individual position of the individual ducks.
S3, inputting the optimal control parameters of the position type PID obtained by setting in the step S22 and an error e (k) between the real-time pumping pressure and the target pumping pressure of the miniature liquid injection pump into a position type PID controller unit of the miniature liquid injection pump control system.
S4, outputting a control quantity u (k) by using a position type PID controller of the micro infusion pump control system in the step S3, controlling a direct current motor driving source of the micro infusion pump, repeating the steps S2 to S4, and realizing optimal robust control of the tooth grinding water spraying speed of the dental therapeutic machine.
Further, the miniature injection pump control system comprises a position type PID controller unit, an error calculation unit for the real-time pumping pressure and the target pumping pressure of the miniature injection pump, a target function unit, an improved duck group optimization algorithm unit, a control signal output unit and a driving source direct current motor rotating speed real-time acquisition unit; the method comprises the steps of calculating a PID control output value u (k) of a miniature injection pump of a dental therapeutic machine through a position PID mathematical model optimized by an improved duck group optimization algorithm according to an error value e (k) of a real-time pump pressure and a target pump pressure of the miniature injection pump, driving a direct current motor to move by using the output value u (k), calculating the real-time rotating speed of the direct current motor by using an encoder, converting the real-time pump pressure of the miniature injection pump by using a formula (1), namely, controlling the water spraying speed by the pump pressure until the k reaches a control maximum time T, and realizing closed-loop control of the miniature injection pump of the dental therapeutic machine, wherein the position PID mathematical model is as follows:
（10）。
Furthermore, the control parameters of the proportional coefficient Kp, the integral coefficient Ki and the differential coefficient Kd of the position PID of the miniature injection pump control system are set by an improved duck group optimization algorithm (IDSA) in Matlab; setting up a system simulation model in Simulink, wherein the system simulation model comprises a position PID, an objective function and a control system mathematical model, writing an improved duck group optimization algorithm (IDSA) in Matlab, setting the maximum population size N=40, the problem dimension D=3, the upper bound ub= [200,150,40] and the lower bound lb= [0, 0] of a solution value of the improved duck group optimization algorithm and the maximum iteration times of the improved duck group optimization algorithm=50, Set up the initial value of the ambient pressure of the modified duck group optimization algorithm (IDSA)=0.5, Initial mutation rate=0.5; The fitness function takes the minimum value of the objective function, and the fitness value guides an algorithm to optimize the control parameters of the proportional coefficient Kp, the integral coefficient Ki and the differential coefficient Kd of the position PID of the miniature injection pump control system; and (3) operating the Matlab file to obtain the optimal control parameters of the position PID of the miniature injection pump control system, and inputting the optimal control parameters into a miniature injection pump control system simulation model of the Simulink, wherein the optimal control parameters are shown in fig. 4, and the optimal control parameters are a proportionality coefficient Kp= 197.157, an integral coefficient Ki=1.375 and a differential coefficient Kd=0.714.
Furthermore, in order to verify the advancement of the method provided by the invention, a standard duck group optimization algorithm (DSA) is introduced for comparison, and firstly, the adaptation value of the duck group optimization algorithm before and after improvement when setting the position PID (proportion coefficient Kp), integral coefficient Ki and differential coefficient Kd parameters of the miniature injection pump control system is compared with the change of iteration times, and the smaller the adaptation value, the objective function is describedThe smaller the value, the smaller the error between the target pump pressure and the real-time pump pressure of the miniature injection pump, the higher the accuracy of the optimal control parameter of the position PID of the miniature injection pump control system, the better the optimizing performance of the algorithm, as shown in figure 5, the improved duck group optimizing algorithm (IDSA) can reach a lower fitness value when the iteration number is smaller, the faster the convergence speed of the improved duck group optimizing algorithm (IDSA) is shown, the optimizing performance is better, and meanwhile, the final fitness value of the IDSA is lower than that of the DSA, which shows that the found control parameter enables the error between the target pump pressure and the real-time pump pressure of the miniature injection pump to be smaller, and the control accuracy is higher.
Furthermore, the simulation model of the miniature injection pump control system in Simulink outputs the control effect of the pump pressure under the control of the optimal PID controller, and the pump pressure determines the water spraying speed of the teeth grinding of the dental therapeutic machine; as shown in fig. 6, in the initial response period (about 2 seconds), the temperature control value of DSA-PID rapidly increases and reaches about 3.5, and a larger overshoot is exhibited, whereas the temperature control value of IDSA-PID rapidly stabilizes at about 2.0, which is the target value, with a smaller overshoot during the increase of the temperature control value of IDSA-PID; in conclusion, the PID control system for improving the duck group optimization algorithm (IDSA-PID) setting has the advantages of higher response speed, smaller overshoot and longer time for achieving the steady state, and the PID control system for improving the standard duck group optimization algorithm (DSA-PID) setting has the advantages of larger overshoot in the initial response stage and longer time for achieving the steady state.