CN110488600B - lQR optimized brushless DC motor speed regulation neural network PID controller - Google Patents
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Abstract
The invention designs an LQR optimized brushless direct current motor speed regulation neural network PID controller, which is used for improving the control performance of the traditional neural network PID controller and the traditional LQR optimized PID controller. Designed LQR optimization type neural network PID controller (LNPID) utilizes BP neural network to control K of controllerP，KI，KDThe gain is adjusted, so that the dynamic characteristic and robustness of the controller are improved; the three-layer BP neural network adopted by the invention has stronger nonlinear mapping capability, and can effectively inhibit the nonlinear condition of the controlled object; however, the traditional BP neural network is an optimization method of local search, so that the optimal output of the BP neural network is optimized by introducing an LQR control algorithm, so that the output data is closer to the target PID gain; and finally, inputting the control output value of the controller into the brushless direct current motor to achieve the rotation speed control of the motor. Meanwhile, the LNPID is adopted to continuously monitor the change of the parameters and the real-time feedback of the parameters, so that the control effect is ideal.
Description
Technical Field
The invention belongs to the technical field of brushless direct current motor speed regulation, and particularly relates to an LQR (Linear quadratic regression) optimized brushless direct current motor speed regulation neural network PID (proportion integration differentiation) controller.
Background
The brushless direct current motor has the advantages of simple structure, high efficiency, low maintenance cost, high dynamic response and the like, and is widely applied to the fields of aerospace, robots, electric automobiles and the like. It is well known that speed control is an important aspect of the field of brushless dc motor drives. With the continuous and rapid development of modern power electronic technology, sensor technology, automatic control technology and manufacturing technology, the research on the brushless direct current motor speed regulation controller with high response speed, strong regulation capability and high control precision has important practical significance and application prospect. However, the complex strongly coupled non-linear characteristic makes it difficult for the conventional control method to achieve good speed control performance. Therefore, in recent decades, many new rotational speed controllers have been proposed to improve the performance of brushless dc motors.
To improve the transient and steady state characteristics of a brushless dc motor, a PID controller is usually the best choice for brushless dc motor speed regulation. The PI-based DC-free motor speed control controller improves the sensitivity of the speed controller and reduces the speed overshoot by increasing the proportional gain. However, the conventional PID has strong dependence on gain selection, which causes the performance of the brushless dc motor to be degraded, and has various uncertainties and nonlinearities. Therefore, many methods are proposed to simplify or improve the PID gain tuning process, and neural network based algorithms can achieve better results.
The PID gain update algorithm based on the neural network has been successfully applied to the control of servo motors, numerical control machines, and the like. Single neuron PID controllers have controlled brushless dc motors. Vikas et al propose a neural network-based PID controller consisting of a mixed local recurrent neural network, containing at most three hidden nodes, which is easy to implement, but the main drawback of this strategy is the need to determine the number of parameters before training, which requires a priori process knowledge. Furthermore, training algorithms based on gradient descent are a time-consuming process. For this purpose, some optimization methods are proposed. And initializing the weight of the adaptive PID neural network controller by adopting a particle swarm optimization algorithm, and adjusting the parameters of the PID neural network by adopting an improved gradient descent algorithm. The method has the defect that the time for initializing the PID neural network by the particle swarm optimization algorithm is long. Classical optimal control theory has developed over decades to create a well-known linear secondary regulator that minimizes deviations in the trajectory of the system states and requires minimal controller effort. This typical behavior of LQR prompts control designers to use it to tune PID controllers. Although the LQR-optimized PID controller has good tracking performance and stable performance, the robustness thereof still needs to be improved. In order to further improve various performance indexes of the brushless direct current motor, the LQR optimized brushless direct current motor speed regulation neural network PID controller is provided.
Disclosure of Invention
The inventionThe designed LQR optimization type neural network PID controller (LNPID) performs speed regulation control on the steady state and the transient state of the brushless direct current motor, optimizes the control output of the BP neural network by utilizing an LQR algorithm, and optimally controls K of the output regulation controllerP，KI，KDGain, improve the dynamics and robustness of the controller, ensure that under different operating conditions (reference, load disturbance and noise signal variation) the LNPID is faster and more efficient than the traditional neural network PID (nnpid) and LQR optimized PID controller (LQRPID).
The invention provides an LQR (Linear quadratic Quadrature) optimized brushless direct current motor speed regulation neural network PID (proportion integration differentiation) controller, which specifically comprises the following control steps:
s1, establishing a three-layer BP neural network, wherein the input layer is 3 neurons, the hidden layer is 6 neurons, the output layer is 3 neurons, and randomly generating initial values W of weighting coefficients among layersij(0)、Wjk(0) The learning rate η is selected, and k = 1.
S2 calculating the output O of the BP neural network output layerkoutCalculating BPNN control error E (k) based on LQR optimization, and calculating the BP neural network output O of the LQR optimization at the momentkI.e. 3 adjustable parameters K of the controllerP，KI，KD；
S3 correcting weighting coefficients W of BP neural network output layer and hidden layer based on LQR optimizationij(k)、Wjk(k) (ii) a And recalculating k = k +1 until the output error of the BP neural network output layer meets the requirement.
And S4, inputting the final control output into the brushless direct current motor system to realize speed control.
The step S1 is to establish a three-layer BP neural network, and further comprises sampling to obtain an input rotation speed r (k) and an output rotation speed y (k), calculating a speed error e (k) = r (k) -y (k), and normalizing e (k), e (k) — e (k-1), e (k) — 2e (k-1) + e (k-2) according to the speed error e (k), wherein the normalization processing is used as an input x of BPNN1,x2,x3。
In the step S3, weighting coefficients W of the BP neural network output layer and the hidden layer based on LQR optimization are correctedij(k)、Wjk(k) The method specifically comprises the following steps: statorPerformance index of BP neural network based on LQR optimizationJ k ，Connection weight Wij(k) And Wjk(k) And (3) adjusting by adopting a steepest descent method:
Wjk(k+1)=Wjk(k)－η(ƏJ k /ƏW jk )
Wij(k+1)=Wij(k)－η(ƏJ k /ƏW ij )
where η is the learning rate. And recalculating the steps by k = k +1 until the output error of the BP neural network output layer meets the requirement.
The invention has the beneficial effect that the invention adopts the K of the three-layer BP neural network to the controllerP，KI，KDGain is adjusted, the three-layer BP neural network has stronger nonlinear mapping capability, the nonlinear condition of a controlled object can be effectively inhibited, and the dynamic characteristic and robustness of the controller are improved; however, the traditional BP neural network is an optimization method of local search, so that the optimal output of the BP neural network is optimized by adopting LQR, and the output data is closer to the target PID gain. In the control process, the LQR optimization type brushless direct current motor speed regulation neural network PID controller can continuously monitor the change of parameters and the real-time feedback of the parameters, so that the control effect is ideal.
Drawings
Fig. 1 is a schematic diagram of an LQR optimized brushless dc motor speed regulation neural network PID controller according to the present invention.
Fig. 2 is a specific flow chart of the LQR optimized brushless dc motor speed regulation neural network PID controller of the present invention.
Fig. 3 is a schematic diagram of the structure of a BP neural network of the speed regulation neural network PID controller of the LQR optimized brushless DC motor.
Detailed Description
In the following, embodiments of the present invention will be described in further detail with reference to the accompanying drawings, it should be noted that the technical features and combinations of the technical features described in the embodiments below should not be considered as isolated, and they may be combined with each other to achieve better technical effects.
As shown in fig. 1, a specific architecture of a speed regulation neural network PID controller for an LQR optimized brushless dc motor provided by the present invention includes an LQR optimized BP neural network module, a PID controller, a logic switch, a position and speed sensor, a pulse width modulation inverter, and a brushless dc motor, and the specific control method is as follows.
Firstly, the actual output rotating speed y (k) of the motor is compared with the input rotating speed r (k) to obtain the final rotating speed error e (k) = r (k) — y (k), and normalization processing is carried out on e (k), e (k) = e (k-1), e (k) — 2e (k-1) + e (k-2) according to the speed error e (k) and is used as the input x of BPNN1,x2,x3. Outputting O through BP neural network output layerkoutCalculating BPNN control error E (k) based on LQR optimization, and modifying weighting coefficients W (W) of output layer and hidden layer of BP neural network based on LQR optimization on line according to E (k)ij(k)、Wjk(k) (ii) a Recalculating k = k +1 until the output error of the BP neural network output layer meets the requirement, and obtaining the output O of the BP neural network optimized by the LQR at the momentkI.e. 3 adjustable parameters K of the controllerP，KI，KDAnd inputting the three parameters into a PID controller, and finally, controlling the output result by the PID controller and inputting the output result into the brushless direct current motor to realize the rotation speed control.
As shown in fig. 2, the LQR optimized neural network PID controller for speed regulation of a brushless dc motor provided in the present invention specifically includes the following control steps:
s1, establishing a three-layer BP neural network, and determining initial values of all parameters;
wherein the input layer is 3 neurons, the hidden layer is 6 neurons, the output layer is 3 neurons, and the initial value W of the weighting coefficient between each layer is randomly generatedij(0)、Wjk(0) The learning rate η is selected, and k = 1. The structure is shown in fig. 3. Sampling to obtain an input rotating speed r (k) and an output rotating speed y (k), calculating a speed error e (k) = r (k) — y (k), and normalizing e (k), e (k) = e (k-1), e (k) — 2e (k-1) + e (k-2) according to the speed error e (k) to be used as an input x of the BPNN1,x2,x3。
S2 counterOutput O of BP neural network output layerkoutCalculating BPNN control error E (k) based on LQR optimization, and calculating the BP neural network output O of the LQR optimization at the momentkI.e. 3 adjustable parameters K of the controllerP，KI，KD(ii) a Output O of BP neural network output layerkoutCalculated as follows:
Okout=f 2(Σ6 i=1Wjk×f 1(Σ3 i=1Wij×xi-θj)-θk)
wherein x isiBeing the actual input to the network, Wij，Wjk，θj，θkRespectively control error, first layer weight, second layer weight, bias of jth hidden layer neuron and bias of kth output layer neuron,f 1(x)、f 2(x) Is an activation function of the hidden layer and the output layer.
Then the output O of the BP neural network optimized by the LQRkI.e. 3 adjustable parameters KP, KI, KD of the controller.
Ok(k)=－Mxi(k)+KE(k)+Okout(k)=－Mxi(k)+KE(k)+g(xi(k))
Where M and K are feedback gain and feedforward gain matrices of dimensions (M × n) and (M × l), respectively, g (x)i(k))=g(x1,x2,x3) Is a BPNN input to output nonlinear mapping function.
S3 correcting weighting coefficients W of BP neural network output layer and hidden layer based on LQR optimizationij(k)、Wjk(k) (ii) a And recalculating k = k +1 until the output error of the BP neural network output layer meets the requirement.
Defining performance index of BP neural network based on LQR optimizationJ k ，Connection weight Wij(k) And Wjk(k) And (3) adjusting by adopting a steepest descent method:
Wjk(k+1)=Wjk(k)－η(ƏJ k /ƏW jk )
Wij(k+1)=Wij(k)－η(ƏJ k /ƏW ij )
where η is the learning rate. And recalculating the steps by k = k +1 until the output error of the output layer of the BP neural network meets the requirement.
And S4, inputting the final control output into the brushless direct current motor system to realize speed control.
Optimal parameter K is obtained through online learning of BP neural network optimized by LQRP，KI，KDAnd inputting the three parameters into a PID controller, and finally inputting the control output value of the PID controller into the brushless direct current motor to achieve the rotation speed control of the motor. The LQR optimized brushless direct current motor speed regulation neural network PID controller can continuously monitor the change of parameters and the real-time feedback of the parameters, so that the control effect is ideal.
The three-layer BP neural network adopted by the invention has stronger nonlinear mapping capability, and can effectively inhibit the nonlinear condition of the controlled object; however, the traditional BP neural network is an optimization method of local search, so the optimal output of the BP neural network is optimized by introducing an LQR control algorithm. Meanwhile, the change of parameters and the real-time feedback of the parameters can be continuously monitored by adopting the LQR optimized brushless direct current motor speed regulation neural network PID controller, so that the control effect is ideal.
Claims (1)
- The utility model provides a LQR optimization type brushless DC motor speed governing neural network PID controller which characterized in that: the designed LQR optimization type neural network PID controller (LNPID) utilizes the K of the BP neural network to the controllerP,KI,KDAdjusting the gain;optimizing the optimal output of the BP neural network by adopting LQR to enable the output data to be closer to the target PID gain; finally, the control output value of the controller is input into the brushless direct current motor to achieve the rotation speed control of the motor;the LQR optimization type brushless direct current motor speed regulation neural network PID controller is characterized in that: the method comprises the following steps:s1, establishing a three-layer BP neural network, wherein the input layer is 3 neurons, the hidden layer is 6 neurons, the output layer is 3 neurons, and randomly generating initial values W of weighting coefficients among layersij(0)、Wjk(0) Selecting a learning rate eta, and setting k to be 1;s2 calculating the output O of the BP neural network output layerkoutCalculating BPNN control error E (k) based on LQR optimization, and calculating the BP neural network output O of the LQR optimization at the momentkI.e. 3 adjustable parameters K of the controllerP，KI，KD；S3 correcting weighting coefficients W of BP neural network output layer and hidden layer based on LQR optimizationij(k)、Wjk(k) (ii) a Recalculating k to k +1 until the output error of the BP neural network output layer meets the requirement;s4, inputting the final control output into the brushless DC motor system to realize speed control;the step S1 is that a three-layer BP neural network is established, and the method further comprises the following steps:sampling to obtain an input rotating speed r (k) and an output rotating speed y (k), calculating a speed error e (k) ═ r (k) — y (k), and normalizing e (k), e (k) — e (k-1), e (k) — 2e (k-1) + e (k-2) according to the speed error e (k) to be used as an input x (k) of the BPNN1,x2,x3；The output O of the BP neural network output layer in the step S2koutCalculated as follows:Okout＝f2(Σ6 i＝1Wjk×f1(Σ3 i＝1Wij×xi-θj)-θk)wherein x isiBeing the actual input to the network, Wij，Wjk，θj，θkRespectively being the first layer weight, the second layer weight, the bias of the jth hidden layer neuron, the bias of the kth output layer neuron, f1(x)、f2(x) Is an activation function of the hidden layer and the output layer;then the output O of the BP neural network optimized by the LQRkI.e. 3 adjustable parameters K of the controllerP,KI,KD；Ok(k)＝－Mxi(k)+KE(k)+Okout(k)＝－Mxi(k)+KE(k)+g(xi(k))Where M and K are feedback gain and feedforward gain matrices of dimensions (M × n) and (M × l), respectively, g (x)i(k))＝g(x1,x2,x3) Nonlinear mapping function for input and output of BPNN;in the step S3, weighting coefficients W of the BP neural network output layer and the hidden layer based on LQR optimization are correctedij(k)、Wjk(k) The method specifically comprises the following steps:defining performance index J of BP neural network based on LQR optimizationkConnecting the weight Wij(k) And Wjk(k) Adjusting by adopting a steepest descent method:
wherein η is the learning rate; and recalculating k to k +1 until the output error of the output layer of the BP neural network meets the requirement.
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