Open-Closed-Loop Iterative Learning Control Method for DC Motor with Randomly Changing Trajectory Length
Through the iterative learning control method of the open and closed loop of DC motor with randomly changing trajectory length, the problem of delay response and uncertainty in high-precision control of DC motors is solved, and faster convergence speed and more stable error indicators are achieved, reducing the number of energy consumption.
Patent Information
- Application Number
- CN202210988763.6
- Authority / Receiving Office
- CN · China
- Patent Type
- Patents(China)
- Current Assignee / Owner
- Filing Date
- 2022-08-17
- Publication Date
- 2024-12-24
- Estimated Expiration
- 2042-08-17
AI Technical Summary
There are delay response and uncertain factors in high-precision control occasions, resulting in external load disturbances and parameter changes affecting its high-speed dynamic response and high-precision tracking performance. Traditional control algorithms are difficult to effectively handle, and iterative learning control time is long. Unstable.
The iterative learning control method of the DC motor with randomly changing trajectory length is adopted. By setting the sampling period of the controlled system, the expected output trajectory is obtained, the iterative learning control gain is calculated, the iterative learning control law is set, and iterated repeatedly until the error function is less than the allowable range. .
When the initial state of the system remains unchanged and randomly changes, the tracking error is reduced, the convergence speed is accelerated, the system operation time and energy consumption are reduced, and the stability of the convergence effect is improved.
Smart Images
Figure CN115421382B_ABST
Abstract
Description
Technical Field
[0001] The invention relates to the field of direct current motors, and in particular to an open-closed loop iterative learning control method for a direct current motor with randomly changing track length. Background Art
[0002] The DC motor works according to the principle of the force exerted on the conductor by the current in the magnetic field. The armature is connected to the power supply voltage to generate the armature current. The magnetic field generated by the excitation winding drives the rotor to rotate, and drives the moving parts to rotate or move linearly. In some high-precision control engineering occasions, we require the controlled system to repeatedly complete the same work within a certain range, and also require that the output of each work of the controlled system can better fit the expected output trajectory. Due to the delayed response of the DC motor system, there will be a response lag after the control input acts on the actual system. At the same time, there are generally uncertain factors and interference in the various components of the DC motor, which have an adverse effect on its performance. How to reduce the influence of external load disturbances and parameter changes is of great significance to the high-speed dynamic response and high-precision tracking performance of the actual DC motor. If the accurate model of the system cannot be obtained, most mainstream control algorithms based on time domain information cannot complete high-speed and accurate tracking control. In addition, in actual applications, there are external interferences that traditional control algorithms cannot effectively handle.
[0003] Taking the DC motor-driven robot on a machine tool as an example, when the robot needs to complete a certain action, each iterative learning process consumes a certain amount of time and energy. Therefore, the fewer iterative learning times are needed to achieve the engineering goals required by the industry. The traditional iterative learning control algorithm takes a long time to reach the convergence index, and the convergence effect is unstable. For this reason, we propose an open-loop and closed-loop iterative learning control method for a DC motor with a randomly changing trajectory length. Summary of the invention
[0004] 1. Technical issues to be solved
[0005] In view of the deficiencies in the prior art, the present invention provides an open-closed loop iterative learning control method for a DC motor with randomly varying trajectory length to solve the above-mentioned problems.
[0006] (II) Technical solution
[0007] In order to achieve the above-mentioned purpose, the present invention provides the following technical solutions:
[0008] An open-closed loop iterative learning control method for a DC motor with a randomly varying trajectory length comprises the following steps:
[0009] Step 1: Set the sampling period T of the controlled continuous system s ;
[0010] Step 2: Get the expected output trajectory y d (i);
[0011] Step 3: Set the initial continuous input signal of the controlled system to u0(i);
[0012] Step 4: Input the signal u0(i) into the actual controlled system to obtain the actual controlled system output y j (i), according to the sampling period T s For j (i) Sampling is performed to obtain the output sequence
[0013] Step 5: Output the sample sequence The expected output trajectory sequence Combined, define the error sequence;
[0014] Step 6: Calculate the iterative learning control gain L, which is required to meet the convergence condition;
[0015] Step 7: setting an iterative learning control law according to the sampling error sequence and the iterative learning control gain;
[0016] Step 8: Repeat steps 4 to 7, and stop iterating when the error function is smaller than the allowable range.
[0017] Preferably, the discrete sequence of sampling in the first step is
[0018] The corresponding discrete time series is
[0019] Preferably, in the second step, according to the sampling period T s Sampling is performed to obtain the sampled expected output sequence y d (i·T s ), Define the permutation sequence as
[0020] Preferably, in the third step, u0(i) needs to satisfy
[0021] Preferably, in the fourth step
[0022] Preferably, the error sequence in the fifth step is:
[0023] Preferably, the convergence condition in the sixth step is ||E{x j (0)}-xd (0)||≤ε.
[0024] Preferably, the iterative learning control law in the seventh step is:
[0025]
[0026]
[0027]
[0028] in, Represents the input control signal of the system at the jth iteration.
[0029] Preferably, according to the iterative learning control law, the control input signal u of the next iteration is updated j+1 (i), u j+1 (i) Satisfy:
[0030]
[0031] (III) Beneficial effects
[0032] Compared with the prior art, the present invention provides an open-closed loop iterative learning control method for a DC motor with randomly changing trajectory length, which has the following beneficial effects:
[0033] 1. The open-closed loop iterative learning control method for a DC motor with randomly changing trajectory length, when the iterative trajectory length changes randomly, in two cases where the system initial state remains unchanged and the system initial state changes randomly, it is confirmed that this patent can accelerate the convergence speed on the basis of ensuring the reduction of tracking error, and when the system initial state changes randomly, the error index fluctuation range is smaller, the convergence effect is more stable, which can effectively reduce the system operation time and avoid unnecessary energy consumption. BRIEF DESCRIPTION OF THE DRAWINGS
[0034] Figure 1 A schematic diagram of the implementation steps of an open- and closed-loop iterative learning control algorithm for a DC motor according to an embodiment of the present invention;
[0035] Figure 2 This is a schematic diagram of a DC motor model according to an embodiment of the present invention;
[0036] Figure 3 It is a schematic diagram of the effect of randomly changing the iterative trajectory length under the DC motor model according to an embodiment of the present invention;
[0037] Figure 4 The figure is a schematic diagram comparing the error convergence effects of a traditional iterative learning algorithm and an open-loop and closed-loop iterative learning algorithm under a DC motor model according to an embodiment of the present invention when the initial state of the system remains unchanged.
[0038] Figure 5 It is a schematic diagram of the system output and expected output trajectory of the 8th, 12th and 20th iterations of the open-closed loop iterative learning algorithm under the DC motor model of an embodiment of the present invention, when the initial state of the system remains unchanged;
[0039] Figure 6 A schematic diagram of a system state in which the initial state of the system is randomly changed under a DC motor model according to an embodiment of the present invention;
[0040] Figure 7 It is a schematic diagram comparing the error convergence effects of the traditional iterative learning algorithm and the open-closed loop iterative learning algorithm when the initial state of the system is randomly changed under the DC motor model of the embodiment of the present invention;
[0041] Figure 8 Schematic diagram of system output and expected output trajectory of the 8th, 12th and 20th iterations of the open-closed loop iterative learning algorithm under the DC motor model of an embodiment of the present invention when the initial state of the system is randomly changed. DETAILED DESCRIPTION
[0042] The following will be combined with the drawings in the embodiments of the present invention to clearly and completely describe the technical solutions in the embodiments of the present invention. Obviously, the described embodiments are only part of the embodiments of the present invention, not all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without creative work are within the scope of protection of the present invention.
[0043] Example
[0044] See attached Figure 1-8 The open-closed loop iterative learning control method of a DC motor with randomly changing trajectory length provided in this embodiment comprises the following steps:
[0045] Step 1: Set the sampling period T of the controlled continuous system s ;
[0046] Step 2: Get the expected output trajectory y d (i);
[0047] Step 3: Set the initial continuous input signal of the controlled system to u0(i);
[0048] Step 4: Input the signal u0(i) into the actual controlled system to obtain the actual controlled system output y j (i), according to the sampling period T s For j (i) Sampling is performed to obtain the output sequence
[0049] Step 5: Output the sample sequence The expected output trajectory sequence Combined, define the error sequence;
[0050] Step 6: Calculate the iterative learning control gain L, which is required to meet the convergence condition;
[0051] Step 7: setting an iterative learning control law according to the sampling error sequence and the iterative learning control gain;
[0052] Step 8: Repeat steps 4 to 7, and stop iterating when the error function is smaller than the allowable range.
[0053] The dynamic equation of the DC motor provided in this embodiment is as follows:
[0054]
[0055] x(t)=[i f (t) ω(t) θ(t)] T ,<y(t)=θ(t),
[0056] in, C=[0 0 1],
[0057] The parameters and signals of the model are as follows: R f , L f are the resistance and inductance of the field winding, k m is the motor torque ratio, J and f are the inertia momentum and friction ratio of the mechanical load respectively, v f (t) and i f (t) are the source voltage and current of the excitation winding, ω(t) and θ(t) are the motor shaft speed and angle, respectively.
[0058] The motor needs to be controlled so that its output is in the time interval [0, t f ] periodically follows the given expected signal. In order to determine the input voltage of the motor according to the EPID type ILC, the motor model needs to be discretized first. For this purpose, we set the sampling period to T = 0.01s, and the motor parameters are:
[0059] R f =15Ω,L f =1.25H,
[0060] t f =12sec.
[0061] The DC motor model can be modeled as the following discrete system:
[0062]
[0063] Where j represents the number of iterations, and
[0064] C D =[0 0 1].
[0065] The tracking error of this system can be expressed as:
[0066]
[0067] in is the discretized expected trajectory.
[0068] Field winding source voltage V fj (i) As the system input u j (i).
[0069] See also Figure 1-8 , an open-closed loop iterative learning control method for a DC motor with a randomly varying trajectory length, comprising the following steps:
[0070] A: Set the sampling period T of the controlled continuous system s , the sampled discrete sequence is
[0071]
[0072] The corresponding discrete time series is
[0073] B: Get the expected output trajectory y d (i), according to the sampling period T s Sampling is performed to obtain the sampled expected output sequence y d (i·T s ), Define the permutation sequence as
[0074] C: Set the initial continuous input signal of the controlled system to u0(i), which satisfies
[0075]
[0076] Input the signal u0(i) to the actual controlled system;
[0077] D: Control input u j (i) Applied to the control system, the actual controlled system output y is obtained j (i), according to the sampling period T s For j (i) Sampling is performed to obtain the output sequence y j (i·T s ), Define the sequence as follows Specific format:
[0078]
[0079] E: Output sequence according to the sampling Combined, the expected output trajectory sequence We can define the error sequence as:
[0080]
[0081] F: Calculate the iterative learning control gain L, which is required to meet the following convergence conditions:
[0082] ||E{x j (0)}-x d (0)||≤ε;
[0083] G: According to the sampling error function sequence and the iterative learning control gain, the iterative learning control law is set as follows:
[0084]
[0085]
[0086]
[0087] in, Represents the input control signal of the system at the jth iteration.
[0088] According to the iterative learning control law, update the control input signal u of the next iteration j+1 (i), u j+1 (i) Satisfy:
[0089]
[0090] H: Repeat steps D to G, and stop iterating when the error function is smaller than the allowable range;
[0091] The DC motor model used in this patent is as follows:
[0092]
[0093] in,
[0094] C D =[0 0 1]
[0095] The expected trajectory is
[0096]
[0097] and are the sampling values of current, motor shaft speed and angle respectively. The motor current is set to 0A, the motor shaft speed is set to 0rad / s, and the angle is set to 0° at the initial moment of each iteration. f is the excitation winding resistance, which is 15Ω, L f is the inductance, the value is 1.25H, k m is the motor torque ratio, which is J is the inertial moment, which is f is the friction ratio of the mechanical load, which is According to the convergence condition ||E{x j (0)}-x d (0)||≤ε, the open-loop learning gains L and R are calculated to be 15 and 10 respectively, and the closed-loop learning gain M is 20.
[0098] See also Figure 1 , the error indicator function is: SE k =sum|y d (i)-y j (i)|,
[0099] x1k(0)x2k(0)x3k(0) respectively correspond to the DC motor model Three system initial states.
[0100] In this application, for Figure 2 The DC motor model shown in Figure 3 Under the condition that the iterative trajectory length changes randomly as shown in the figure, the error convergence effects of the traditional iterative learning algorithm and the open- and closed-loop iterative learning algorithm, as well as the expected trajectory tracking effect of the open- and closed-loop iterative learning algorithm are discussed when the initial state of the system remains unchanged and the initial state changes randomly.
[0101] Case 1: When the system initial state remains unchanged: Figure 4 It can be seen that the error index of the open-closed loop iterative learning algorithm converges to 0 within a finite number of times. As the number of iterations increases, the error index almost converges in the 5th iteration. Figure 5 The system output and expected output trajectory diagrams for the 8th, 12th, and 20th iterations show that the output trajectory of the motor system gradually tracks the expected output trajectory as the number of iterations increases. Compared with the traditional P-type iterative learning control method, even if the learning gains R and M are set to 0, it takes about 30 iterations for the error to converge. It can be seen that when the output error converges to 0, this patent reduces the number of iterations by nearly 25 compared to the traditional P-type algorithm.
[0102] Case 2: When the system initial state changes randomly: Figure 6In the case of random changes in the system state shown in Figure 7 It can be seen that the error index of the open-closed loop iterative learning algorithm converges to within the tolerance range around the 5th time, while the traditional P-type algorithm shows a certain convergence effect only at the 25th time. Figure 8 The system output and expected output trajectory diagrams for the 8th, 12th, and 20th iterations of the open-loop and closed-loop iterative learning algorithm show that, as the number of iterations increases, the system output curve gradually approaches the expected output curve.
[0103] Therefore, when the length of the iterative trajectory changes randomly, in both cases where the system initial state remains unchanged and where the system initial state changes randomly, it is confirmed that this patent can accelerate the convergence speed while ensuring that the tracking error is reduced, and when the system initial state changes randomly, the error indicator fluctuation range is smaller, the convergence effect is more stable, and the system operation time can be effectively reduced to avoid unnecessary energy consumption.
[0104] Although embodiments of the present invention have been shown and described, it will be appreciated by those skilled in the art that various changes, modifications, substitutions and variations may be made to the embodiments without departing from the principles and spirit of the present invention, and that the scope of the present invention is defined by the appended claims and their equivalents.
Claims
1. An open-closed loop iterative learning control method for a DC motor with a randomly varying trajectory length, characterized in that: The following steps are involved: Step 1: Set the sampling period of the controlled continuous system ; Step 2: Get the expected output trajectory ; Step 3: Set the initial continuous input signal of the controlled system to ; Step 4: Send the signal Input to the actual controlled system to get the actual controlled system output , according to the sampling period right Sampling is performed to obtain the output sequence ; Step 5: Output the sample sequence With the expected output trajectory sequence Combined, define the error sequence; Step 6: Calculate the iterative learning control gain L, which is required to meet the convergence condition; Step 7: Set the iterative learning control law according to the sampling error sequence and the iterative learning control gain; Step 8: Repeat steps 4 to 7, and stop iterating when the error function is smaller than the allowable range; The dynamic equation of a DC motor is as follows: ； ； in, ,B= ,C= , , are the resistance and inductance of the field winding, respectively. is the motor torque ratio, and are the friction ratio of inertial momentum and mechanical load, and are the source voltage and current of the excitation winding, respectively, and are the motor shaft speed and angle respectively; The dynamic equations of the DC motor are modeled as a discrete system: ； in, j represents the number of iterations, and the error sequence in the fifth step is: , , , , ; The convergence condition in the sixth step is ; The iterative learning control law in the seventh step is: ； ； ； in, Represents the input control signal of the system at the jth iteration.
2. The open-closed loop iterative learning control method for a DC motor with randomly varying trajectory length according to claim 1, characterized in that: The discrete sequence of samples in the first step is ; The corresponding discrete time series is .
3. The open-closed loop iterative learning control method for a DC motor with randomly varying trajectory length according to claim 1, characterized in that: In the second step, based on the sampling period Sampling is performed to obtain the sampled expected output sequence , , define the sequence as .
4. The open-closed loop iterative learning control method for a DC motor with randomly varying trajectory length according to claim 1, characterized in that: In the third step Needs to be satisfied 。 5. The open-closed loop iterative learning control method for a DC motor with randomly varying trajectory length according to claim 1, characterized in that: In the fourth step , .
6. The open-closed loop iterative learning control method for a DC motor with randomly varying trajectory length according to claim 2, characterized in that: According to the iterative learning control law, the control input signal of the next iteration is updated , satisfy: 。