技术领域Technical Field
本发明属于PID控制优化技术领域，具体涉及一种膝关节牵引器的自适应牵引力控制方法。The invention belongs to the technical field of PID control optimization, and in particular relates to an adaptive traction force control method for a knee joint traction device.
背景技术Background technique
膝关节牵引器是一种用于改善膝关节状况的设备，其工作原理是通过施加牵引力来改善膝关节的血液循环和营养供应，从而促进关节的修复和康复。这种设备可以拉伸关节周围的肌肉、韧带和骨骼结构，纠正关节的错位和不稳定，减少关节炎的发生。使用膝关节牵引器时，需要根据患者的具体情况，调整合适的屈膝角度和牵引力度，一般来说，屈膝角度应为30度至60度之间，牵引力度应根据患者的疼痛程度和体质来决定。A knee traction device is a device used to improve the condition of the knee joint. Its working principle is to improve the blood circulation and nutrient supply of the knee joint by applying traction, thereby promoting the repair and recovery of the joint. This device can stretch the muscles, ligaments and bone structures around the joint, correct the dislocation and instability of the joint, and reduce the occurrence of arthritis. When using a knee traction device, it is necessary to adjust the appropriate knee flexion angle and traction strength according to the patient's specific situation. Generally speaking, the knee flexion angle should be between 30 degrees and 60 degrees, and the traction strength should be determined according to the patient's pain level and physical condition.
过度的牵引力会导致患者感到不适，甚至造成损伤；自适应牵引力控制能够实时监测患者的反应，一旦检测到异常情况，如疼痛加剧或肌肉痉挛，它会自动调整牵引力，避免对患者造成进一步的伤害。进一步地，通过精确控制牵引力，自适应牵引器可以减少患者在治疗过程中的不适感。它能够确保牵引力的施加平稳、均匀，避免突然的拉力变化，从而提高患者的治疗体验和满意度。更进一步地，自适应牵引力控制减少了医护人员手动调整牵引力的需求，降低了操作的复杂性和误差率。这不仅提高了治疗效率，还降低了医护人员的工作负担。Excessive traction can cause discomfort or even injury to patients; adaptive traction control can monitor the patient's response in real time. Once an abnormality is detected, such as increased pain or muscle spasm, it will automatically adjust the traction to avoid further harm to the patient. Furthermore, by precisely controlling the traction, the adaptive traction device can reduce the discomfort of patients during treatment. It can ensure that the traction is applied smoothly and evenly, avoiding sudden changes in tension, thereby improving the patient's treatment experience and satisfaction. Furthermore, adaptive traction control reduces the need for medical staff to manually adjust the traction, reducing the complexity and error rate of the operation. This not only improves treatment efficiency, but also reduces the workload of medical staff.
目前，膝关节牵引器的牵引力控制器常采用PID控制算法，虽然这种算法在很多情况下表现出色，但也存在一些固有的缺陷，特别是在膝关节牵引器这样的特定应用中；膝关节是一个典型的非线性系统，其力学特性和响应方式随着牵引力、角度和速度等因素的变化而变化。PID算法作为一种线性控制器，很难完全适应这种非线性特性，导致控制效果不佳；其次，微分项在PID控制中用于预测误差变化趋势，但对于噪声和突变信号非常敏感。在膝关节牵引器的应用中，由于人体运动的不确定性和测量设备的精度限制，微分信号可能受到噪声干扰，导致控制不稳定。At present, the traction controller of the knee traction device often adopts the PID control algorithm. Although this algorithm performs well in many cases, it also has some inherent defects, especially in specific applications such as knee traction devices. The knee joint is a typical nonlinear system, and its mechanical characteristics and response mode change with the changes of factors such as traction, angle and speed. As a linear controller, it is difficult for the PID algorithm to fully adapt to this nonlinear characteristic, resulting in poor control effect. Secondly, the differential term is used in PID control to predict the error change trend, but it is very sensitive to noise and mutation signals. In the application of knee traction devices, due to the uncertainty of human motion and the accuracy limitation of the measurement equipment, the differential signal may be interfered by noise, resulting in unstable control.
特征兵优化算法包括三个阶段，初始化阶段完成候选解的初始化，使候选解尽可能地分散在问题解空间中；全局搜索阶段采用特定的策略来探索解决方案空间，在探索阶段完成对解决方案空间的全面探索；在开发阶段先前探索的全局最优解进行了更准确的探索，以提高求解的精度；但是特征兵优化算法的全局搜索和局部开发平衡性较差，且易陷入局部最优解。The feature soldier optimization algorithm consists of three stages. The initialization stage completes the initialization of candidate solutions so that the candidate solutions are dispersed as much as possible in the problem solution space; the global search stage adopts a specific strategy to explore the solution space, and the exploration stage completes the comprehensive exploration of the solution space; in the development stage, the previously explored global optimal solution is explored more accurately to improve the accuracy of the solution; however, the global search and local development of the feature soldier optimization algorithm are poorly balanced, and it is easy to fall into the local optimal solution.
发明内容Summary of the invention
本发明的目的在于提供一种膝关节牵引器的自适应牵引力控制方法，通过元启发式算法优化膝关节牵引器的牵引力控制器，以解决上述背景技术中提出的膝关节牵引器在牵引力控制不稳定的问题。The purpose of the present invention is to provide an adaptive traction force control method for a knee traction device, which optimizes the traction force controller of the knee traction device through a meta-heuristic algorithm to solve the problem of unstable traction force control of the knee traction device proposed in the above background technology.
为实现上述目的，本发明提供如下技术方案：一种膝关节牵引器的自适应牵引力控制方法，利用特征兵优化算法对牵引器的牵引力源的PID控制优化，实现牵引器牵引力的精确控制，具体步骤为。To achieve the above objectives, the present invention provides the following technical solutions: an adaptive traction force control method for a knee traction device, which optimizes the PID control of the traction force source of the traction device by using a characteristic optimization algorithm to achieve precise control of the traction force of the traction device, and the specific steps are as follows.
S1、将膝关节牵引器的实时牵引力数值与牵引器牵引力源控制数值建立转换数学模型。S1. Establish a conversion mathematical model between the real-time traction value of the knee joint traction device and the traction source control value of the traction device.
S2、通过牵引器力学传感器实时采集牵引器牵引力数值，将实时牵引力数值输入到S1所述转换数学模型，输出实时牵引器牵引力源控制数值。S2. Collect the traction force value of the tractor in real time through the traction force mechanical sensor, input the real-time traction force value into the conversion mathematical model described in S1, and output the real-time traction force source control value of the tractor.
S3、计算实时牵引器牵引力源控制数值与预设的牵引力源控制目标数值的误差值；利用所述误差与上一时刻时的误差的误差值。S3, calculating the error value between the real-time traction force source control value of the traction device and the preset traction force source control target value ; Using the error With the previous moment Error The error value .
S4、利用改进特征兵优化算法整定牵引器的牵引力源PID控制器的比例项参数Kp、积分参数Ki和微分参数Kd，得到控制性能最佳的Kp、Ki和Kd参数值。S4. Use the improved characteristic optimization algorithm to adjust the proportional term parameter Kp, integral parameter Ki and differential parameter Kd of the traction force source PID controller of the traction device to obtain the Kp, Ki and Kd parameter values with the best control performance.
S5、将S4所述最佳的Kp数值与S3所述的误差值相乘，得到牵引力源PID的比例项输出；最佳的Ki数值与进行积分得到积分项输出；最佳的Kd数值与进行差分运算得到微分项输出。S5, compare the optimal Kp value described in S4 with the error value described in S3 Multiply them to get the proportional term output of the traction source PID; the optimal Ki value is Integrate to get the integral output; the best Kd value and Perform a differential operation to obtain the differential term output.
S6、将S5所述的比例项、积分项和微分项的输出进行加权求和，得到牵引力源PID控制器的牵引力源控制数值增量Δu(t)；将所述Δu(t)应用于膝关节牵引器的牵引力源系统，反复执行S2至S6，调整牵引力源的控制数值，实现对膝关节牵引器的牵引力的精确控制。S6. Perform weighted summation on the outputs of the proportional term, integral term and differential term described in S5 to obtain the traction source control value increment Δu(t) of the traction source PID controller; apply the Δu(t) to the traction source system of the knee joint traction device, repeatedly execute S2 to S6, adjust the control value of the traction source, and achieve precise control of the traction force of the knee joint traction device.
进一步地，膝关节牵引器的牵引力源系统包括牵引力源和牵引力源PID控制器；其中，牵引器牵引力源为永磁同步电机，永磁同步电机转速越快，牵引器牵引力越大，牵引力数值与牵引器牵引力源控制数值的转换数学模型为：Furthermore, the traction source system of the knee joint traction device includes a traction source and a traction source PID controller; wherein the traction source of the traction device is a permanent magnet synchronous motor, the faster the permanent magnet synchronous motor rotates, the greater the traction force of the traction device, and the conversion mathematical model of the traction force value and the traction source control value of the traction device is:
（1）； (1);
式（1）中， 为当前时刻t时牵引力数值，为比例系数，取值为0.5，表示当前时刻t时，牵引力源控制数值增量与牵引力之间的直接比例关系；β为偏置项，取值为2，表示牵引力源控制数值增量为零时系统存在的基础牵引力；为拟合参数，取值为0.8。In formula (1), is the traction value at the current time t, is the proportional coefficient, with a value of 0.5, indicating the direct proportional relationship between the traction source control value increment and the traction at the current time t; β is the bias term, with a value of 2, indicating the basic traction of the system when the traction source control value increment is zero; is the fitting parameter and its value is 0.8.
进一步地，膝关节牵引器的自适应牵引力控制的目的是通过特征兵优化算法对牵引器的牵引力源的PID控制优化，实现牵引器牵引力的精确控制，其中精确控制为：在实际牵引器应用过程中，使得当前时刻牵引器牵引力源控制数值与预设的牵引力源控制目标数值的误差值最快速度和更快稳定的趋于零。Furthermore, the purpose of the adaptive traction control of the knee traction device is to optimize the PID control of the traction source of the traction device through the characteristic optimization algorithm to achieve precise control of the traction of the traction device, wherein the precise control means that in the actual traction device application process, the error value between the current traction source control value of the traction device and the preset traction source control target value is The fastest speed and the faster stable approach to zero.
进一步地，误差与上一时刻时的误差的误差值反映了误差的动态变化情况；通过两次误差的差值调整膝关节牵引器的牵引力的大小。Furthermore, the error With the previous moment Error The error value It reflects the dynamic change of the error; the traction force of the knee joint traction device is adjusted by the difference between the two errors.
进一步地，牵引力源PID采用增量式PID，数学模型为：Furthermore, the traction source PID adopts an incremental PID, and the mathematical model is:
（2）； (2);
式（2）中，Δu(t)为牵引力源控制数值增量，Δe(t)为当前时刻误差e(t)与上一时刻的误差e(t-1)的误差值，e(t-2)为t-2时刻牵引器牵引力源控制数值与预设的牵引力源控制目标数值的误差值。In formula (2), Δu(t) is the increment of the traction source control value, Δe(t) is the error between the error e(t) at the current moment and the error e(t-1) at the previous moment, and e(t-2) is the error between the traction source control value of the traction device at moment t-2 and the preset traction source control target value.
进一步地，牵引力源PID的比例项输出作用在于根据牵引力数值误差变化的速率快速调整牵引力源PID控制器的输出。针对膝关节牵引器控制是一个典型的非线性系统，积分项作用在于消除稳态误差，使牵引力源控制系统输出能够逐渐趋近于预设的牵引力数值；微分项的作用在于预测误差的变化趋势，提前进行调整，有助于减小膝关节牵引器系统的超调和震荡。Furthermore, the proportional term output of the traction source PID is used to quickly adjust the output of the traction source PID controller according to the rate of change of the traction value error. The knee traction device control is a typical nonlinear system. The integral term is used to eliminate the steady-state error so that the output of the traction source control system can gradually approach the preset traction value; the differential term is used to predict the change trend of the error and make adjustments in advance, which helps to reduce the overshoot and oscillation of the knee traction device system.
进一步地，标准特征兵优化算法通过一个特殊命令因子控制特征兵优化算法寻优策略，特征兵优化算法根据特殊命令因子每次迭代的取值，执行算法三个位置更新策略的其中一个策略，包括：大规模搜索策略、过渡策略和救援策略；特殊命令因子是一个随机呈曲线趋势下降的因子，在一定程度上可以减小算法陷入局部最优的风险，但是其随机性导致算法不能根据在每次迭代中算法的性能自适应变化，导致标准特征兵优化算法只有将两个阶段平稳过渡才能使算法性能得以更好表现。Furthermore, the standard feature soldier optimization algorithm is implemented by a special command factor Control the optimization strategy of the characteristic soldier optimization algorithm. The characteristic soldier optimization algorithm is based on special command factors. The value of each iteration executes one of the three position update strategies of the algorithm, including: large-scale search strategy, transition strategy and rescue strategy; special command factor It is a factor that decreases randomly in a curve trend. It can reduce the risk of the algorithm falling into the local optimum to a certain extent. However, its randomness causes the algorithm to be unable to adaptively change according to the performance of the algorithm in each iteration. As a result, the standard feature optimization algorithm can only achieve better performance by smoothly transitioning the two stages.
进一步地，采用复合式的改进方法，引入特征兵优化算法寻优适应度函数值和正弦策略对特殊命令因子改进，使得改进后的特殊命令因子可以根据特征兵优化算法在寻优过程中的优劣，自适应调整当前迭代时的值，从而使标准特征兵优化算法可以更精确执行最适合当前迭代的策略；适应度函数值是反应算法寻优过程中性能优劣的指标；改进后的特殊命令因子的数学模型公式为：Furthermore, a composite improvement method is adopted to introduce the characteristic soldier optimization algorithm to optimize the fitness function value and the sine strategy for special command factors. Improved, so that the improved special command factor The value of the current iteration can be adaptively adjusted according to the performance of the feature soldier optimization algorithm in the optimization process, so that the standard feature soldier optimization algorithm can more accurately execute the strategy that best suits the current iteration; the fitness function value is an indicator of the performance of the algorithm in the optimization process; the improved special command factor The mathematical model formula is:
（3）； (3);
式（3）中，为第y次迭代时特征兵位置的适应度最小值，为第y-1次迭代时特征兵位置的适应度最小值，为特征兵位置的全局适应度最小值，为当前迭代次数，为最大迭代次数。In formula (3), is the minimum fitness value of the feature soldier position at the yth iteration, is the minimum fitness value of the feature soldier position at the y-1th iteration, is the minimum global fitness of the feature soldier position, is the current iteration number, is the maximum number of iterations.
进一步地，利用改进特征兵优化算法整定牵引器的牵引力源PID控制器的比例项参数Kp、积分参数Ki和微分参数Kd，具体步骤为：Furthermore, the improved characteristic optimization algorithm is used to adjust the proportional parameter Kp, integral parameter Ki and differential parameter Kd of the traction source PID controller of the traction device. The specific steps are as follows:
S41、利用Piecewise混沌映射初始化改进特征兵优化算法，算法种群初始位置和算法搜索空间上下界，所述算法种群初始位置为牵引力源PID控制器的Kp、Ki和Kd初始值；所述算法搜索空间上下界为牵引力源PID控制器的Kp、Ki和Kd值的范围；S41, using Piecewise chaotic mapping to initialize the improved characteristic soldier optimization algorithm, the algorithm population initial position and the algorithm search space upper and lower bounds, the algorithm population initial position is the initial values of Kp, Ki and Kd of the traction source PID controller; the algorithm search space upper and lower bounds are the range of Kp, Ki and Kd values of the traction source PID controller;
S42、将牵引力源PID控制器的Kp、Ki和Kd值作为一个三维的向量与改进特征兵优化算法的特征兵个体的位置采用实数映射；构建N个特征兵个体的位置模型；S42, using real number mapping to map the Kp, Ki and Kd values of the traction source PID controller as a three-dimensional vector to the position of the characteristic soldier individual of the improved characteristic soldier optimization algorithm; constructing a position model of N characteristic soldier individuals;
S43、采用时间乘绝对误差积分和时间乘方误差积分设计适应度函数；所述适应度函数的输入为当前时刻牵引器牵引力源控制数值与预设的牵引力源控制目标数值的误差值；S43, using time multiplied by absolute error integral and time multiplied by square error integral to design fitness function; the input of the fitness function is the error value between the current traction force source control value of the traction device and the preset traction force source control target value ;
S44、模拟改进特征兵优化算法的大规模搜索策略、改进的过渡策略以及救援策略，建立位置更新数学模型，通过更新特征兵种群位置，更新牵引力源PID控制器的Kp、Ki和Kd值参数解集；S44, simulating the large-scale search strategy, improved transition strategy and rescue strategy of the improved characteristic soldier optimization algorithm, establishing a position update mathematical model, and updating the Kp, Ki and Kd value parameter solution set of the traction source PID controller by updating the position of the characteristic soldier population;
S45、计算改进特征兵优化算法的当前迭代的个体的适应度值，与之前迭代的最优适应度值比较，并保留目前所有迭代的最优适应度值对应的最优特征兵个体位置；S45. Calculate the fitness value of the individual in the current iteration of the improved feature soldier optimization algorithm , compared with the optimal fitness value of the previous iteration, and retain the optimal fitness value of all current iterations The corresponding optimal characteristic soldier individual position;
S46、判断当前迭代次数是否满足，若满足，则将最优特征兵个体位置解码，输出牵引力源PID控制器的最佳Kp、Ki和Kd值。S46, determine the current number of iterations Is it satisfied? , if satisfied, the optimal characteristic soldier individual position is decoded and the optimal Kp, Ki and Kd values of the traction source PID controller are output.
进一步地，所述步骤S44模拟改进特征兵优化算法的大规模搜索策略、改进的过渡策略以及救援策略，建立位置更新数学模型的具体步骤为：Furthermore, the step S44 simulates the large-scale search strategy, improved transition strategy and rescue strategy of the improved feature soldier optimization algorithm, and the specific steps of establishing the position update mathematical model are:
S441、计算改进后的特殊命令因子的值，当大于0.5时，执行步骤S442；当大于0.3且小于0.5时，执行步骤S443和S444；否则执行步骤S445；S441, Calculate the improved special command factor When When it is greater than 0.5, execute step S442; when When it is greater than 0.3 and less than 0.5, execute steps S443 and S444; otherwise, execute step S445;
S442、在全局搜索阶段，模拟特种兵执行大规模的搜索任务，在大规模搜索中，在可行的范围内随机搜索任何潜在的目标；按照公式（5）建立位置更新数学模型；S442, in the global search phase, simulate the special forces to perform a large-scale search task, in which any potential target is randomly searched within a feasible range; establish a position update mathematical model according to formula (5);
（5）； (5);
式（5）中，为第y+1次迭代时第i个特征兵个体位置，为第y次迭代时第i个特征兵个体位置，为全局最佳特征兵位置，为取值在0到1之前的随机数，为第y次迭代的权重系数，为特征兵搜索的位置上界，为特征兵搜索的位置下界；为第y次迭代时第i个特征兵个体的搜索控制因子，数学模型为：In formula (5), is the position of the i-th feature soldier at the y+1th iteration, is the position of the i-th feature soldier at the y-th iteration, is the global best feature soldier position, is a random number between 0 and 1. is the weight coefficient of the yth iteration, is the upper bound of the position of the feature soldier search, The lower bound of the position to search for the characteristic soldier; is the search control factor of the i-th characteristic soldier individual at the y-th iteration, and the mathematical model is:
（6）； (6);
式（6）中，为第y次迭代时第i个特征兵位置的适应度值，为第y次迭代时特征兵位置的适应度最小值；In formula (6), is the fitness value of the i-th feature soldier position at the y-th iteration, is the minimum fitness value of the feature soldier position at the yth iteration;
S443、利用改进的过渡策略，全局搜索和局部开发阶段过渡时，模拟特征兵核实被救人员位置是否发生变动，若发生变动，则改变搜索方向，按照公式（6）判断被救人员位置是否发生变动；S443, using the improved transition strategy, when the global search and local development phases transition, the simulated feature soldier verifies whether the position of the rescued person has changed. If so, the search direction is changed, and the rescued person's position is determined according to formula (6);
S444、若公式（6）的值G小于0.5，说明被救人员位置发生变动，利用公式（7）改变搜索方向，即跳出局部最优；否则按照公式（5）模拟原地等待指令；S444. If the value G of formula (6) is less than 0.5, it means that the position of the rescued person has changed, and formula (7) is used to change the search direction, that is, jump out of the local optimum; otherwise, according to formula (5), simulate waiting for instructions in place;
（7）； (7);
式（7）中，为第y次迭代的权重系数，数学模型为：In formula (7), is the weight coefficient of the yth iteration, and the mathematical model is:
； ;
式中，为惯性权重的最小值，为惯性权重的最大值；In the formula, is the minimum value of the inertia weight, is the maximum value of the inertia weight;
S445、在局部开发阶段，模拟特征兵救援策略，确定好人质位置后，展开救援，按照公式（8）建立位置更新数学模型；S445. In the local development stage, simulate the rescue strategy of the characteristic soldiers, determine the hostage position, and then start the rescue. Establish the mathematical model of position update according to formula (8);
（8）； (8);
式（8）中，为第y次迭代时特征兵的最佳位置；为第y次迭代时特征兵种群的平均位置，为取值在0到1之前的随机数。In formula (8), is the optimal position of the feature soldier at the yth iteration; is the average position of the characteristic soldier population at the yth iteration, A random number between 0 and 1.
进一步地，利用Piecewise混沌映射初始化特征兵种群，将Piecewise生成的序列映射到特征兵搜索空间的数学模型为：Furthermore, the Piecewise chaotic mapping is used to initialize the feature soldier population, and the mathematical model of mapping the sequence generated by Piecewise to the feature soldier search space is:
（9）； (9);
式（9）中，为特征兵种群的第i个个体的初始位置，为最大种群规模，为问题维度，设置为3，为特征兵搜索的位置上界，为特征兵搜索的位置下界。In formula (9), is the initial position of the i-th individual in the characteristic soldier population, is the maximum population size, is the problem dimension, set to 3, is the upper bound of the position of the feature soldier search, The lower bound of the position to search for the feature soldier.
本发明有益效果是：The beneficial effects of the present invention are:
D1、通过特征兵优化算法优化膝关节牵引器PID控制器，实现对膝关节牵引器牵引力的精确控制，有效解决牵引力控制的不稳定问题，提高治疗的精度和安全性；D1. Optimize the PID controller of the knee traction device through the characteristic soldier optimization algorithm to achieve accurate control of the traction force of the knee traction device, effectively solve the instability problem of traction force control, and improve the accuracy and safety of treatment;
D2、本发明还引入了复合式的改进方法，结合特征兵优化算法的寻优适应度函数值和正弦策略对特殊命令因子进行改进，使算法可以更精确执行最适合当前迭代的策略，增强了特征兵优化算法的全局搜索能力和局部开发能力；D2. The present invention also introduces a composite improvement method, combining the optimization fitness function value of the characteristic soldier optimization algorithm and the sine strategy to improve the special command factor, so that the algorithm can more accurately execute the strategy most suitable for the current iteration, and enhance the global search ability and local development ability of the characteristic soldier optimization algorithm;
D3、改进特征兵优化算法的过渡策略，在救援过程中，增加考虑人质被歹徒转移位置的特殊情况，防止特征兵优化算法陷入错误的最优解，即陷入局部最优，建立数学模型对过渡策略的特征兵位置更新，提高特征兵优化算法避免陷入局部最优的能力；D3. Improve the transition strategy of the feature soldier optimization algorithm. In the rescue process, consider the special situation that the hostages are transferred by the criminals to prevent the feature soldier optimization algorithm from falling into the wrong optimal solution, that is, falling into the local optimum. Establish a mathematical model to update the feature soldier position of the transition strategy, and improve the ability of the feature soldier optimization algorithm to avoid falling into the local optimum.
D4、考虑到膝关节的非线性特性，本发明通过改进的特征兵优化算法整定PID控制器的参数，使其更好地适应膝关节的力学特性和响应方式，进一步提高控制的精确性和稳定性。D4. Taking into account the nonlinear characteristics of the knee joint, the present invention adjusts the parameters of the PID controller through an improved characteristic optimization algorithm to make it better adapt to the mechanical characteristics and response mode of the knee joint, and further improve the accuracy and stability of control.
附图说明BRIEF DESCRIPTION OF THE DRAWINGS
图1为膝关节牵引器的自适应牵引力控制方法的步骤图。FIG. 1 is a step diagram of an adaptive traction force control method of a knee traction device.
图2为模拟改进特征兵优化算法的大规模搜索策略、改进的过渡策略以及救援策略更新PID参数映射解集的方法流程图。FIG2 is a flow chart of a method for simulating a large-scale search strategy of an improved characteristic soldier optimization algorithm, an improved transition strategy, and a rescue strategy for updating a PID parameter mapping solution set.
图3为改进前后特征兵优化算法整定牵引器的自适应牵引力PID的Kp、Ki、Kd参数的变化图。Figure 3 is a graph showing the changes in Kp, Ki, and Kd parameters of the adaptive traction force PID of the traction device adjusted by the characteristic optimization algorithm before and after improvement.
图4为改进前后特征兵优化算法性能的适应度值对比图。Figure 4 is a comparison of the fitness values of the feature soldier optimization algorithm performance before and after improvement.
图5为膝关节牵引器的自适应牵引力在标准PID以及SFA-PID和SSFA-PID控制下的控制性能对比图。FIG5 is a control performance comparison diagram of the adaptive traction force of the knee traction device under standard PID, SFA-PID and SSFA-PID control.
具体实施方式Detailed ways
下面将结合本发明实施例中的附图，对本发明实施例中的技术方案进行清楚、完整地描述，显然，所描述的实施例仅仅是本发明一部分实施例，而不是全部的实施例；基于本发明中的实施例，本领域普通技术人员在没有作出创造性劳动前提下所获得的所有其它实施例，都属于本发明保护的范围。The technical solutions in the embodiments of the present invention will be clearly and completely described below in conjunction with the drawings in the embodiments of the present invention. Obviously, the described embodiments are only part of the embodiments of the present invention, rather than all the embodiments; based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without making creative work are within the scope of protection of the present invention.
请参阅图1-图5，本发明提供一种技术方案：一种膝关节牵引器的自适应牵引力控制方法，利用特征兵优化算法对牵引器的牵引力源的PID控制优化，实现牵引器牵引力的精确控制，如图1所示，具体步骤为。Please refer to Figures 1 to 5. The present invention provides a technical solution: an adaptive traction force control method for a knee traction device, which optimizes the PID control of the traction force source of the traction device by using a characteristic optimization algorithm to achieve precise control of the traction force of the traction device, as shown in Figure 1. The specific steps are as follows.
S1、将膝关节牵引器的实时牵引力数值与牵引器牵引力源控制数值建立转换数学模型。S1. Establish a conversion mathematical model between the real-time traction value of the knee joint traction device and the traction source control value of the traction device.
S2、通过牵引器力学传感器实时采集牵引器牵引力数值，将实时牵引力数值输入到S1所述转换数学模型，输出实时牵引器牵引力源控制数值。S2. The traction force value of the tractor is collected in real time through the traction force sensor, the real-time traction force value is input into the conversion mathematical model described in S1, and the real-time traction force source control value of the tractor is output.
S3、计算实时牵引器牵引力源控制数值与预设的牵引力源控制目标数值的误差值；利用所述误差与上一时刻时的误差的误差值。S3, calculating the error value between the real-time traction force source control value of the traction device and the preset traction force source control target value ; Using the error With the previous moment Error The error value .
S4、利用改进特征兵优化算法整定牵引器的牵引力源PID控制器的比例项参数Kp、积分参数Ki和微分参数Kd，得到控制性能最佳的Kp、Ki和Kd参数值。S4. Use the improved characteristic optimization algorithm to adjust the proportional parameter Kp, integral parameter Ki and differential parameter Kd of the traction force source PID controller of the traction device to obtain the Kp, Ki and Kd parameter values with the best control performance.
S5、将S4所述最佳的Kp数值与S3所述的误差值相乘，得到牵引力源PID的比例项输出；最佳的Ki数值与进行积分得到积分项输出；最佳的Kd数值与进行差分运算得到微分项输出。S5, compare the optimal Kp value described in S4 with the error value described in S3 Multiply them to get the proportional term output of the traction source PID; the optimal Ki value is Integrate to get the integral output; the best Kd value and Perform a differential operation to obtain the differential term output.
S6、将S5所述的比例项、积分项和微分项的输出进行加权求和，得到牵引力源PID控制器的牵引力源控制数值增量Δu(t)；将所述Δu(t)应用于膝关节牵引器的牵引力源系统，反复执行S2至S6，调整牵引力源的控制数值，实现对膝关节牵引器的牵引力的精确控制。S6. Perform weighted summation on the outputs of the proportional term, integral term and differential term described in S5 to obtain the traction source control value increment Δu(t) of the traction source PID controller; apply the Δu(t) to the traction source system of the knee joint traction device, repeatedly execute S2 to S6, adjust the control value of the traction source, and achieve precise control of the traction force of the knee joint traction device.
更为具体地，膝关节牵引器的牵引力源系统包括牵引力源和牵引力源PID控制器；其中，牵引器牵引力源为永磁同步电机，永磁同步电机转速越快，牵引器牵引力越大，牵引力数值与牵引器牵引力源控制数值的转换数学模型为：More specifically, the traction source system of the knee traction device includes a traction source and a traction source PID controller; wherein the traction source of the traction device is a permanent magnet synchronous motor, the faster the permanent magnet synchronous motor rotates, the greater the traction force of the traction device, and the conversion mathematical model of the traction value and the traction source control value of the traction device is:
（1）； (1);
式（1）中， 为当前时刻t时牵引力数值，为比例系数，取值为0.5，表示当前时刻t时，牵引力源控制数值增量与牵引力之间的直接比例关系；β为偏置项，取值为2，表示牵引力源控制数值增量为零时系统存在的基础牵引力；为拟合参数，取值为0.8。In formula (1), is the traction value at the current time t, is the proportional coefficient, with a value of 0.5, indicating the direct proportional relationship between the traction source control value increment and the traction at the current time t; β is the bias term, with a value of 2, indicating the basic traction of the system when the traction source control value increment is zero; is the fitting parameter and its value is 0.8.
更为具体地，膝关节牵引器的自适应牵引力控制的目的是通过特征兵优化算法对牵引器的牵引力源的PID控制优化，实现牵引器牵引力的精确控制，其中精确控制为：在实际牵引器应用过程中，使得当前时刻牵引器牵引力源控制数值与预设的牵引力源控制目标数值的误差值最快速度和更快稳定的趋于零。More specifically, the purpose of the adaptive traction control of the knee joint traction device is to optimize the PID control of the traction source of the traction device through the characteristic optimization algorithm to achieve precise control of the traction of the traction device, wherein the precise control means that in the actual traction device application process, the error value between the current traction source control value of the traction device and the preset traction source control target value is The fastest speed and the faster stable approach to zero.
更为具体地，误差与上一时刻时的误差的误差值反映了误差的动态变化情况；通过两次误差的差值调整膝关节牵引器的牵引力的大小。More specifically, the error With the previous moment Error The error value It reflects the dynamic change of the error; the traction force of the knee joint traction device is adjusted by the difference between the two errors.
更为具体地，牵引力源PID采用增量式PID，数学模型为：More specifically, the traction source PID adopts an incremental PID, and the mathematical model is:
（2）； (2);
式（2）中，Δu(t)为牵引力源控制数值增量，Δe(t)为当前时刻误差e(t)与上一时刻的误差e(t-1)的误差值，e(t-2)为t-2时刻牵引器牵引力源控制数值与预设的牵引力源控制目标数值的误差值。In formula (2), Δu(t) is the increment of the traction source control value, Δe(t) is the error between the error e(t) at the current moment and the error e(t-1) at the previous moment, and e(t-2) is the error between the traction source control value of the traction device at moment t-2 and the preset traction source control target value.
更为具体地，牵引力源PID的比例项输出作用在于根据牵引力数值误差变化的速率快速调整牵引力源PID控制器的输出。针对膝关节牵引器控制是一个典型的非线性系统，积分项作用在于消除稳态误差，使牵引力源控制系统输出能够逐渐趋近于预设的牵引力数值；微分项的作用在于预测误差的变化趋势，提前进行调整，有助于减小膝关节牵引器系统的超调和震荡。More specifically, the proportional term output of the traction source PID is used to quickly adjust the output of the traction source PID controller according to the rate of change of the traction value error. As the knee traction device control is a typical nonlinear system, the integral term is used to eliminate the steady-state error so that the output of the traction source control system can gradually approach the preset traction value; the differential term is used to predict the change trend of the error and make adjustments in advance, which helps to reduce the overshoot and oscillation of the knee traction device system.
更为具体地，标准特征兵优化算法通过一个特殊命令因子控制特征兵优化算法寻优策略，特征兵优化算法根据特殊命令因子每次迭代的取值，执行算法三个位置更新策略的其中一个策略，包括：大规模搜索策略、过渡策略和救援策略；特殊命令因子是一个随机呈曲线趋势下降的因子，在一定程度上可以减小算法陷入局部最优的风险，但是其随机性导致算法不能根据在每次迭代中算法的性能自适应变化，导致标准特征兵优化算法只有将两个阶段平稳过渡才能使算法性能得以更好表现。More specifically, the standard feature soldier optimization algorithm is implemented by a special command factor Control the optimization strategy of the characteristic soldier optimization algorithm. The characteristic soldier optimization algorithm is based on special command factors. The value of each iteration executes one of the three position update strategies of the algorithm, including: large-scale search strategy, transition strategy and rescue strategy; special command factor It is a factor that decreases randomly in a curve trend. It can reduce the risk of the algorithm falling into the local optimum to a certain extent. However, its randomness causes the algorithm to be unable to adaptively change according to the performance of the algorithm in each iteration. As a result, the standard feature optimization algorithm can only achieve better performance by smoothly transitioning the two stages.
更为具体地，采用复合式的改进方法，引入特征兵优化算法寻优适应度函数值和正弦策略对特殊命令因子改进，使得改进后的特殊命令因子可以根据特征兵优化算法在寻优过程中的优劣，自适应调整当前迭代时的值，从而使标准特征兵优化算法可以更精确执行最适合当前迭代的策略；适应度函数值是反应算法寻优过程中性能优劣的指标；改进后的特殊命令因子的数学模型公式为：More specifically, a composite improvement method is adopted to introduce the characteristic soldier optimization algorithm to optimize the fitness function value and the sine strategy for special command factors. Improved, so that the improved special command factor The value of the current iteration can be adaptively adjusted according to the performance of the feature soldier optimization algorithm in the optimization process, so that the standard feature soldier optimization algorithm can more accurately execute the strategy that best suits the current iteration; the fitness function value is an indicator of the performance of the algorithm in the optimization process; the improved special command factor The mathematical model formula is:
（3）； (3);
式（3）中，为第y次迭代时特征兵位置的适应度最小值，为第y-1次迭代时特征兵位置的适应度最小值，为特征兵位置的全局适应度最小值，为当前迭代次数，为最大迭代次数。In formula (3), is the minimum fitness value of the feature soldier position at the yth iteration, is the minimum fitness value of the feature soldier position at the y-1th iteration, is the minimum global fitness of the feature soldier position, is the current iteration number, is the maximum number of iterations.
更为具体地，利用改进特征兵优化算法整定牵引器的牵引力源PID控制器的比例项参数Kp、积分参数Ki和微分参数Kd，具体步骤为：More specifically, the improved characteristic optimization algorithm is used to adjust the proportional parameter Kp, integral parameter Ki and differential parameter Kd of the traction force source PID controller of the traction device. The specific steps are:
S41、利用Piecewise混沌映射初始化改进特征兵优化算法，算法种群初始位置和算法搜索空间上下界，所述算法种群初始位置为牵引力源PID控制器的Kp、Ki和Kd初始值；所述算法搜索空间上下界为牵引力源PID控制器的Kp、Ki和Kd值的范围；S41, using Piecewise chaotic mapping to initialize the improved characteristic soldier optimization algorithm, the algorithm population initial position and the algorithm search space upper and lower bounds, the algorithm population initial position is the initial values of Kp, Ki and Kd of the traction source PID controller; the algorithm search space upper and lower bounds are the range of Kp, Ki and Kd values of the traction source PID controller;
S42、将牵引力源PID控制器的Kp、Ki和Kd值作为一个三维的向量与改进特征兵优化算法的特征兵个体的位置采用实数映射；构建N个特征兵个体的位置模型；S42, using real number mapping to map the Kp, Ki and Kd values of the traction source PID controller as a three-dimensional vector to the position of the characteristic soldier individual of the improved characteristic soldier optimization algorithm; constructing a position model of N characteristic soldier individuals;
S43、采用时间乘绝对误差积分和时间乘方误差积分设计适应度函数；所述适应度函数的输入为当前时刻牵引器牵引力源控制数值与预设的牵引力源控制目标数值的误差值；S43, using time multiplied by absolute error integral and time multiplied by square error integral to design fitness function; the input of the fitness function is the error value between the current traction force source control value of the traction device and the preset traction force source control target value ;
S44、模拟改进特征兵优化算法的大规模搜索策略、改进的过渡策略以及救援策略，建立位置更新数学模型，通过更新特征兵种群位置，更新牵引力源PID控制器的Kp、Ki和Kd值参数解集；S44, simulating the large-scale search strategy, improved transition strategy and rescue strategy of the improved characteristic soldier optimization algorithm, establishing a position update mathematical model, and updating the Kp, Ki and Kd value parameter solution set of the traction source PID controller by updating the position of the characteristic soldier population;
S45、计算改进特征兵优化算法的当前迭代的个体的适应度值，与之前迭代的最优适应度值比较，并保留目前所有迭代的最优适应度值对应的最优特征兵个体位置；S45. Calculate the fitness value of the individual in the current iteration of the improved feature soldier optimization algorithm , compared with the optimal fitness value of the previous iteration, and retain the optimal fitness value of all current iterations The corresponding optimal characteristic soldier individual position;
S46、判断当前迭代次数是否满足，若满足，则将最优特征兵个体位置解码，输出牵引力源PID控制器的最佳Kp、Ki和Kd值。S46, determine the current number of iterations Is it satisfied? , if satisfied, the optimal characteristic soldier individual position is decoded and the optimal Kp, Ki and Kd values of the traction source PID controller are output.
更为具体地，模拟改进特征兵优化算法的大规模搜索策略、改进的过渡策略以及救援策略，建立位置更新数学模型的具体步骤为：More specifically, the specific steps of simulating the large-scale search strategy, improved transition strategy and rescue strategy of the improved feature soldier optimization algorithm and establishing the position update mathematical model are as follows:
S441、计算改进后的特殊命令因子的值，当大于0.5时，执行步骤S442；当大于0.3且小于0.5时，执行步骤S443；否则执行步骤S444；S441, Calculate the improved special command factor When When it is greater than 0.5, execute step S442; when When it is greater than 0.3 and less than 0.5, execute step S443; otherwise, execute step S444;
S442、在全局搜索阶段，模拟特种兵执行大规模的搜索任务，在大规模搜索中，在可行的范围内随机搜索任何潜在的目标；按照公式（5）建立位置更新数学模型；S442, in the global search phase, simulate the special forces to perform a large-scale search task, in which any potential target is randomly searched within a feasible range; establish a position update mathematical model according to formula (5);
（5）； (5);
式（5）中，为第y+1次迭代时第i个特征兵个体位置，为第y次迭代时第i个特征兵个体位置，为全局最佳特征兵位置，为取值在0到1之前的随机数，为第y次迭代的权重系数，为特征兵搜索的位置上界，为特征兵搜索的位置下界；为第y次迭代时第i个特征兵个体的搜索控制因子，数学模型为：In formula (5), is the position of the i-th feature soldier at the y+1th iteration, is the position of the i-th feature soldier at the y-th iteration, is the global best feature soldier position, is a random number between 0 and 1. is the weight coefficient of the yth iteration, is the upper bound of the position of the feature soldier search, The lower bound of the position to search for the characteristic soldier; is the search control factor of the i-th characteristic soldier individual at the y-th iteration, and the mathematical model is:
（6）； (6);
式（6）中，为第y次迭代时第i个特征兵位置的适应度值，为第y次迭代时特征兵位置的适应度最小值；In formula (6), is the fitness value of the i-th feature soldier position at the y-th iteration, is the minimum fitness value of the feature soldier position at the yth iteration;
S443、利用改进的过渡策略，全局搜索和局部开发阶段过渡时，模拟特征兵核实被救人员位置是否发生变动，若发生变动，则改变搜索方向，按照公式（6）判断被救人员位置是否发生变动；S443, using the improved transition strategy, when the global search and local development phases transition, the simulated feature soldier verifies whether the position of the rescued person has changed. If so, the search direction is changed, and the rescued person's position is determined according to formula (6);
S444、若公式（6）的值G小于0.5，说明被救人员位置发生变动，利用公式（7）改变搜索方向，即跳出局部最优；否则按照公式（5）模拟原地等待指令；S444. If the value G of formula (6) is less than 0.5, it means that the position of the rescued person has changed, and formula (7) is used to change the search direction, that is, jump out of the local optimum; otherwise, according to formula (5), simulate waiting for instructions in place;
（7）； (7);
式（7）中，为第y次迭代的权重系数，数学模型为：In formula (7), is the weight coefficient of the yth iteration, and the mathematical model is:
； ;
式中，为惯性权重的最小值，为惯性权重的最大值；In the formula, is the minimum value of the inertia weight, is the maximum value of the inertia weight;
S445、在局部开发阶段，模拟特征兵救援策略，确定好人质位置后，展开救援，按照公式（8）建立位置更新数学模型；S445. In the local development stage, simulate the rescue strategy of the characteristic soldiers, determine the hostage position, and then start the rescue. Establish the mathematical model of position update according to formula (8);
（8）； (8);
式（8）中，为第y次迭代时特征兵的最佳位置；为第y次迭代时特征兵种群的平均位置，为取值在0到1之前的随机数。In formula (8), is the optimal position of the feature soldier at the yth iteration; is the average position of the characteristic soldier population at the yth iteration, A random number between 0 and 1.
更为具体地，利用Piecewise混沌映射初始化特征兵种群，将Piecewise生成的序列映射到特征兵搜索空间的数学模型为：More specifically, the mathematical model of using piecewise chaotic mapping to initialize the feature soldier population and map the sequence generated by piecewise to the feature soldier search space is:
（9）； (9);
式（9）中，为特征兵种群的第i个个体的初始位置，为最大种群规模，为问题维度，设置为3，为特征兵搜索的位置上界，为特征兵搜索的位置下界。In formula (9), is the initial position of the i-th individual in the characteristic soldier population, is the maximum population size, is the problem dimension, set to 3, is the upper bound of the position of the feature soldier search, The lower bound of the position to search for the feature soldier.
更为具体地，在Simulink中搭建膝关节牵引器的牵引力源控制仿真模型，包括：牵引力PID控制器的最佳参数输入模块、目标函数模块、传递函数模块，其中目标函数设计和适应度函数相同，传递函数根据膝关节牵引器的牵引力的非线性控制模拟得到，传递函数模型采用二阶非线性设计，数学模型为：More specifically, a traction source control simulation model of the knee traction device was built in Simulink, including: an optimal parameter input module of the traction PID controller, an objective function module, and a transfer function module. The objective function design is the same as the fitness function. The transfer function is obtained by simulating the nonlinear control of the traction force of the knee traction device. The model adopts second-order nonlinear design, and the mathematical model is:
； ;
式中，为t的复频域变量。In the formula, is the complex frequency domain variable of t.
更为具体地，在Matlab在设计改进的特征兵优化算法（SSFA）和标准特征特征兵（SFA）优化算法代码，设置算法参数，包括：最大迭代次数Y=60，最大种群规模=100，改进后的特殊命令因子=1，惯性权重的最小值=0.1，惯性权重的最大值=2，问题维度dim=3以及特征兵搜索的位置上界=[80,40,100]，特征兵搜索的位置下界=[0,0,0]，将适应度函数作为目标函数，训练整定PID控制器的控制参数，迭代完成后，输出最佳膝关节牵引器的牵引力PID控制参数如图3所示，改进的特征兵优化算法（SSFA）的整定最佳参数Kp=78.98、Ki=37.18、Kd=65.36；标准特征兵优化算法（SFA）的整定最佳参数Kp=38.52、Ki=1.05、Kd=91.57。More specifically, in Matlab, the improved feature-soldier optimization algorithm (SSFA) and the standard feature-soldier optimization algorithm (SFA) codes were designed, and the algorithm parameters were set, including: the maximum number of iterations Y = 60, the maximum population size =100, improved special command factor =1, minimum value of inertia weight =0.1, the maximum value of inertia weight =2, problem dimension dim=3 and the upper bound of the position of the feature soldier search =[80,40,100], the lower bound of the position of the feature soldier search =[0,0, 0], the fitness function is used as the objective function, the control parameters of the PID controller are trained and adjusted, and after the iteration is completed, the traction force PID control parameters of the optimal knee traction device are output as shown in Figure 3. The optimal parameters of the improved characteristic soldier optimization algorithm (SSFA) are Kp=78.98, Ki=37.18, Kd=65.36; the optimal parameters of the standard characteristic soldier optimization algorithm (SFA) are Kp=38.52, Ki =1.05, Kd=91.57.
更为具体地，如图4所示，图中的两条线代表了SFA（特征兵优化算法）和SSFA（改进的特征兵优化算法）的适应度值，SSFA在迭代初始阶段相较于SFA具有较小的适应度值，随迭代的增加SFA和SSFA均陷入局部最优解，但是在迭代35次时，SSFA跳出局部最优，并迅速下降，说明改进的特征兵优化算法具备更好的跳出局部最优的能力，且改进的特征兵优化算法的寻优速度更快；这个对比说明了SSFA算法相较于SFA算法在稳定性和优化效率上更优，SSFA算法的表现表明更快地收敛到最优解，并且在寻找最优解的过程中具有更好的稳定性；相比之下，SFA算法在迭代过程中需要更多的时间来探索解空间，且在接近最优解前其适应度值变化不大。More specifically, as shown in Figure 4, the two lines in the figure represent the fitness values of SFA (Feature Soldier Optimization Algorithm) and SSFA (Improved Feature Soldier Optimization Algorithm). SSFA has a smaller fitness value than SFA in the initial stage of iteration. As the iterations increase, both SFA and SSFA fall into the local optimal solution. However, after 35 iterations, SSFA jumps out of the local optimal solution and drops rapidly, indicating that the improved Feature Soldier Optimization Algorithm has a better ability to jump out of the local optimal solution, and the improved Feature Soldier Optimization Algorithm has a faster optimization speed. This comparison shows that the SSFA algorithm is better than the SFA algorithm in stability and optimization efficiency. The performance of the SSFA algorithm shows that it converges to the optimal solution faster and has better stability in the process of finding the optimal solution. In contrast, the SFA algorithm needs more time to explore the solution space during the iteration process, and its fitness value does not change much before approaching the optimal solution.
更为具体地，将最佳PID控制参数Kp、Ki、Kd输入到Simulink中搭建的牵引器的牵引力源仿真模型中，输出膝关节牵引器的牵引力的控制效果，如图5所示；图中展示了三种不同PID控制策略的系统响应曲线，SSFA-PID控制策略的上升时间最快，超调量最小，能够更快地达到设定点；常规PID控制策略在开始时超调最大，SFA-PID控制策略的超调次之，其上升时间长于SSFA-PID，综上，实验说明SSFA-PID在系统的快速稳定和减少超调方面的性能优于SFA-PID和常规PID，证明本实验提出的利用改进的特征兵优化算法对膝关节牵引器的牵引力源的PID控制优化方法更好。More specifically, the optimal PID control parameters Kp, Ki, and Kd are input into the traction force source simulation model of the traction device built in Simulink, and the control effect of the traction force of the knee traction device is output, as shown in Figure 5; the figure shows the system response curves of three different PID control strategies. The SSFA-PID control strategy has the fastest rise time and the smallest overshoot, and can reach the set point faster; the conventional PID control strategy has the largest overshoot at the beginning, and the SFA-PID control strategy has the second largest overshoot, and its rise time is longer than that of SSFA-PID. In summary, the experiment shows that SSFA-PID is better than SFA-PID and conventional PID in terms of rapid stabilization of the system and reduction of overshoot, which proves that the PID control optimization method for the traction force source of the knee traction device using the improved characteristic soldier optimization algorithm proposed in this experiment is better.
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| CN202410516564.4ACN118092146B (en) | 2024-04-28 | 2024-04-28 | An adaptive traction force control method for a knee joint traction device |
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| CN118747411A (en)* | 2024-09-04 | 2024-10-08 | 山东大学齐鲁医院 | A method for optimizing traction force control of spinal traction device |
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