Permanent magnet synchronous motor single current sensor control method based on single vector model prediction

Abstract

The invention discloses a permanent magnet synchronous motor single current sensor control method based on single vector model prediction. Firstly, a current prediction model of the permanent magnet synchronous motor is analyzed and calculated, a rolling optimization principle is combined, a cost function is designed, delay time caused by actual use of a digital controller is considered, a deadbeat prediction model containing one-beat delay compensation is designed, and after problems possibly generated in three-phase current reconstruction are analyzed, a deadbeat prediction model containing one-beat delay compensation is designed; and the most / suboptimal vector is selected by setting a sinking threshold, so that the whole permanent magnet synchronous motor single-current sensor control based on single-vector model prediction is completed. According to the method, the structural complexity of a control system is effectively reduced, the dynamic response speed of a driving system is increased, the waveform quality of reconstructed three-phase current is improved, and current ripples are reduced.

Description

Technical Field

[0001] The present invention relates to the technical field of motor drive control, and in particular to a single current sensor control method for a permanent magnet synchronous motor based on single vector model prediction. Background Art

[0002] For the system structure of permanent magnet synchronous motor, the traditional control system generally uses at least two current sensors for current acquisition, which has high system cost and complexity and is not conducive to improving the overall reliability performance. Using a single current sensor for current acquisition can effectively reduce costs and size, while avoiding errors caused by the lack of synchronization of multiple sensors. However, accurate current sampling is the basis for ensuring high-performance control. While using a single current sensor to reduce system complexity, it also poses challenges to the accuracy of current acquisition, mainly in two aspects: First, due to the use of a single current sensor, the current can only be collected within the active vector action time. If the active vector action time does not meet the sampling window time, it will cause current sampling failure and cause reconstruction dead zone problems; second, two-phase currents need to be sampled separately within a control cycle, and the sampling time is set in different active vector action times, while the ideal three-phase current must meet the simultaneous condition. Time-sharing sampling is bound to cause reconstruction errors in the three-phase current reconstruction.

[0003] Traditional single current sensor control is generally installed on the DC bus side of the inverter, and different phase currents are collected as the active action vector switches. However, due to hardware limitations, current collection requires a certain sampling time, so the active action vector action time is required to meet the minimum sampling time. If it cannot be met, the corresponding phase current information cannot be collected, that is, a reconstruction dead zone occurs. At the same time, since the phase current information is sampled at different times, the reconstruction calculation of the three-phase current cannot meet the basic conditions of Kirchhoff's current law, that is, a reconstruction error occurs.

[0004] Studying the single current sensor control scheme is not only conducive to simplifying the system structure and reducing hardware costs, but also conducive to the fault-tolerant control of the current sensor. When a fault occurs, the system can ensure that the equipment does not stop and improve reliability by reconfiguring the current sensor's collection method. Summary of the invention

[0005] The present invention aims at the deficiencies in the prior art and provides a single current sensor control method for a permanent magnet synchronous motor based on single vector model prediction, which reduces the structural complexity of the control system, improves the dynamic response speed of the drive system, improves the waveform quality of the reconstructed three-phase current, and reduces the current ripple.

[0006] To achieve the above object, the present invention adopts the following technical solutions:

[0007] In a first aspect, the present invention provides a single current sensor control method for a permanent magnet synchronous motor based on single vector model prediction, the method comprising the following steps:

[0008] S1: The problem of establishing a current prediction model for permanent magnet synchronous motors using model predictive control is analyzed.

[0009] S2: By designing the cost function and rolling optimization principle, an optimal vector selection scheme is proposed.

[0010] S3: The deadbeat model predictive control principle is analyzed and the optimal vector selection scheme with one-beat delay compensation is added.

[0011] S4: The reconstruction effect of three-phase current is analyzed and the optimal / suboptimal vector selection scheme based on the sinking threshold is proposed.

[0012] Furthermore, in step S1, the permanent magnet synchronous motor current prediction model under model predictive control is:

[0013] First, the stator voltage equation of the permanent magnet synchronous motor in the dq coordinate system is:

[0014]

[0015] where u d and u q is the stator voltage of the motor in the dq coordinate system, i d and i q is the stator current of the motor in the dq coordinate system, R s is the stator resistance, L d and L q is the inductance of the motor in the dq coordinate system, ω e is the rotor electrical angular velocity, ψ f is the permanent magnet flux.

[0016] Convert it into current i d and i q The state equation form of the state variable is obtained:

[0017]

[0018] To facilitate the application of discrete controllers, it is assumed that the system control period T sp If it is short enough, the forward Euler method can be used to discretize the above formula to obtain:

[0019]

[0020] in

[0021]

[0022] Among them, idq (k) and u dq (k),ω e (k) represent the sampling values ​​of dq axis current, applied voltage and feedback speed at the initial moment of the kth cycle respectively. dq (k+1) represents the predicted value of the dq-axis current at the initial moment of the k+1th cycle.

[0023] Furthermore, in step S2, the cost function and rolling optimization principle are designed and the optimal vector selection scheme is proposed:

[0024] The design of the cost function includes the following steps:

[0025] First, the common form of the cost function is:

[0026]

[0027] Among them, ||·|| represents the absolute value of the error term, w i Represents the weight coefficient of the i-th error. To achieve the MPC current tracking reference value, set the dq axis current reference value and the predicted value i dq The difference between (k+1) is used as the error term, and the weight coefficients are set equal, then the cost function can be constructed as:

[0028]

[0029] In order to ensure that the stator current does not exceed the limit value i max , set the current limit item f lim (i dq (k+1)) is:

[0030]

[0031] Secondly, selecting the optimal vector according to the rolling optimization principle includes the following steps:

[0032] After constructing the cost function, it needs to be optimized in a rolling manner to select the optimal voltage vector. The principle of rolling optimization is:

[0033] In the k cycle, by i Substitute (k+1) into the cost function and select the optimal voltage vector V3 for the k-cycle corresponding to the best current tracking effect; in the k+1 cycle, replace x i Substitute (k+2) into the cost function and screen out the k+1 cycle optimal voltage vector corresponding to the best current tracking effect as V2.

[0034] Furthermore, in step S3, the deadbeat model predictive control principle is analyzed and a compensation scheme using one-beat delay is given:

[0035] The steps of deadbeat model predictive control are as follows:

[0036] First, the dq axis voltage value can be calculated as:

[0037]

[0038] The purpose of the deadbeat model prediction is to make the current at time k+1 track the given value, so the reference current Instead of the current at time k+1, that is:

[0039]

[0040] The reference voltage vector is calculated as:

[0041]

[0042] in, is the reference voltage vector at time k Components in the dq axis.

[0043] Secondly, the steps of the one-beat delay compensation method are as follows:

[0044] The one-beat delay compensation method is used to delay the calculated reference voltage vector by one control cycle. Therefore, it is necessary to calculate the reference voltage vector of the k+1th cycle. The calculated predicted current i d (k+1) and i q (k+1) is substituted and the reference current is used Substituting for the current at k+2, the reference voltage is calculated as

[0045]

[0046] The cost function is constructed using the error between the reference voltage vector and the candidate vector, and then:

[0047]

[0048] in, are the components of the reference voltage vector at time k+1 under dq and αβ, are the components of the candidate vector at time k+1 on the dq and αβ axes. The above formula represents the distance between the candidate vector and the reference voltage. By traversing the eight candidate vectors, the optimal candidate vector closest to the reference voltage vector can be selected, which is defined as

[0049] Furthermore, in step S4, the reconstruction effect of the three-phase current is analyzed and the optimal / suboptimal vector selection scheme according to the sinking threshold is proposed:

[0050] The steps for three-phase current reconstruction are as follows:

[0051] The reconstruction of three-phase current requires obtaining at least two different phase current information. Under DC bus current sampling, phase current information can only be collected during the action time of the active vector. In the model predictive control proposed above, only one voltage vector acts in one control cycle, and only one phase current information can be collected in one cycle. Therefore, the sampling moments of two different phase currents are set in different sampling cycles. At the same time, since the vector acting in each cycle is uncertain, the sampling intervals of different phase currents are also uncertain.

[0052] Define the first phase current collected first as i x1 (x=a,b,c), the second phase current is i x2 , the third phase current can be calculated as:

[0053] i x3 =-i x1 -i x2

[0054] in i x1 After collection to successful collection x2 Before, the three-phase current cannot be reconstructed, so i x1 and i x2 The larger the sampling interval is, the longer the three-phase current cannot be reconstructed, and the larger the reconstructed current error is.

[0055] The steps to set the sinking threshold are as follows:

[0056] Since the phase current information is only contained in the active vector, in order to improve the accuracy of the reconstructed current and ensure that the current can be collected in each cycle, it is considered to cancel the zero vector and only use six active vectors as candidate vectors for traversal.

[0057] The phase current information number contained in the applied voltage V(k) in the k cycle is defined as:

[0058]

[0059] In order to evaluate the reconstruction effect of the three-phase current, the sinking number N is defined as sunk It indicates the number of cycles in which the control cycle continuously updates the current information of the same phase, expressed as:

[0060]

[0061] For analysis of N sunk The impact on the current reconstruction effect is shown in Figure 1. Take the A-phase current as an example. Assuming that the A-phase current is an ideal sine wave, it can be expressed as:

[0062]

[0063] Among them, I m and are the amplitude and phase angle of phase A current respectively. sunk Caused by a Sampling delay error i a_delay It can be expressed as:

[0064]

[0065] It can be seen that N sunk The smaller the sampling delay error i a_delay The smaller it is, the smaller the phase current reconstruction error is, that is, the shorter the time interval for collecting two-phase current information is, the better the system control performance is. Similarly, N sunk The larger the value is, the larger the phase current reconstruction error will be. If the accurate reconstructed current cannot be obtained for a long time, the system performance will be seriously degraded.

[0066] The steps of the optimal / suboptimal vector selection scheme for the sinking threshold are as follows:

[0067] The phase current information contained in two adjacent vectors in the same sector is different. Therefore, in order to ensure the reconstruction effect of the current, the suboptimal replacement principle is considered to introduce the adjacent voltage vector of the optimal vector in the same sector as the suboptimal vector. Define the sinking threshold N max , when N sunk Not exceeding N max When N sunk More than N max When , the suboptimal vector is selected to act on the next switching cycle. The optimal vector is defined as The suboptimal vector is Then we have:

[0068]

[0069] Then a single current sensor control system based on single vector model prediction can be constructed.

[0070] The beneficial effects of the present invention are:

[0071] 1. The present invention proposes a model predictive control method, which simplifies the system structure and improves the dynamic response performance.

[0072] 2. The selection of the sinking threshold proposed in the present invention limits the sampling time interval of different phase currents, thereby improving the current reconstruction accuracy.

[0073] 3. The suboptimal replacement principle proposed in the present invention improves the stability of phase current reconstruction. BRIEF DESCRIPTION OF THE DRAWINGS

[0074] Figure 1It is a flow chart of a single current sensor control method for a permanent magnet synchronous motor based on single vector model prediction according to an embodiment of the present invention.

[0075] Figure 2 It is a structural diagram of a single current sensor control method for a permanent magnet synchronous motor based on single vector model prediction in an embodiment of the present invention.

[0076] Figure 3 It is a schematic diagram of rolling optimization according to an embodiment of the present invention.

[0077] Figure 4 It is an optimal vector screening diagram based on the deadbeat model prediction in an embodiment of the present invention.

[0078] Figure 5 This is a single vector model prediction synthetic vector diagram according to an embodiment of the present invention.

[0079] Figure 6 Schematic diagram of sampling delay error according to an embodiment of the present invention.

[0080] Figure 7 It is a schematic diagram of the sinking threshold and the optimal vector selection rate according to an embodiment of the present invention.

[0081] Figure 8 It is a schematic diagram of the actual effect of single current sensor control of a permanent magnet synchronous motor predicted by a single vector model according to an embodiment of the present invention. Specific implementation plan

[0082] The present invention is further described in detail below with reference to the accompanying drawings and specific embodiments.

[0083] Embodiment 1

[0084] Figure 1 It is a single current sensor control flow chart of permanent magnet synchronous motor based on single vector model prediction. Figure 2 This is a structural diagram of a method for controlling a permanent magnet synchronous motor with a single current sensor based on single vector model prediction according to an embodiment of the present invention. This embodiment proposes a method for controlling a permanent magnet synchronous motor with a single current sensor based on single vector model prediction, and the method comprises the following steps:

[0085] S1: The problem of establishing a current prediction model for permanent magnet synchronous motors using model predictive control is analyzed.

[0086] S2: By designing the cost function and rolling optimization principle, an optimal vector selection scheme is proposed.

[0087] S3: The deadbeat model predictive control principle is analyzed and the optimal vector selection scheme with one-beat delay compensation is added.

[0088] S4: The reconstruction effect of three-phase current is analyzed and the optimal / suboptimal vector selection scheme based on the sinking threshold is proposed.

[0089] S5: A single current sensor control method for permanent magnet synchronous motor based on single vector model prediction is proposed.

[0090] 1. Establishment of a deadbeat prediction model with one-beat delay

[0091] First, the stator voltage equation of the permanent magnet synchronous motor in the dq coordinate system is:

[0092]

[0093] where u d and u q is the stator voltage of the motor in the dq coordinate system, i d and i q is the stator current of the motor in the dq coordinate system, R s is the stator resistance, L d and L q is the inductance of the motor in the dq coordinate system, ω e is the rotor electrical angular velocity, ψ f is the permanent magnet flux.

[0094] Convert it into current i d and i q The state equation form of the state variable is obtained:

[0095]

[0096] To facilitate the application of discrete controllers, it is assumed that the system control period T sp If it is short enough, the forward Euler method can be used to discretize the above formula to obtain:

[0097]

[0098] in

[0099]

[0100] Among them, i dq (k) and u dq (k),ω e (k) represent the sampling values ​​of dq axis current, applied voltage and feedback speed at the initial moment of the kth cycle respectively. dq (k+1) represents the predicted value of the dq-axis current at the initial moment of the k+1th cycle.

[0101] After constructing the cost function, it is necessary to perform rolling optimization to screen out the optimal voltage vector. The rolling optimization diagram is shown in the figure below. Figure 3As shown in the figure, in the k cycle, by i Substitute (k+1) into the cost function and select the optimal voltage vector V3 for the k-cycle corresponding to the best current tracking effect; in the k+1 cycle, replace x i Substitute (k+2) into the cost function and screen out the k+1 cycle optimal voltage vector corresponding to the best current tracking effect as V2.

[0102] The cost function is constructed using the error between the reference voltage vector and the candidate vector, and then:

[0103]

[0104] in, are the components of the reference voltage vector at time k+1 under dq and αβ, are the components of the candidate vector at time k+1 on the dq and αβ axes. The above formula represents the distance between the candidate vector and the reference voltage. By traversing the eight candidate vectors, the optimal candidate vector closest to the reference voltage vector can be selected, which is defined as like Figure 4 As shown, when When it falls in the blue area in the figure, it is closest to candidate vector V2, that is, the cost function is the smallest, so V2 is selected as

[0105] 2. Principle of Three-phase Current Reconstruction

[0106] The reconstruction of three-phase current requires obtaining at least two different phase current information. Under DC bus current sampling, phase current information can only be collected during the action time of the active vector. Only one voltage vector acts in a control cycle, and only one phase current information can be collected in a cycle. Therefore, the sampling moments of two different phase currents are set in different sampling cycles. At the same time, since the vector acting in each cycle is uncertain, the sampling intervals of different phase currents are also uncertain.

[0107] Define the first phase current collected first as i x1 (x=a,b,c), the second phase current is i x2 , then the third phase current can be calculated as

[0108] i x3 =-i x1 -i x2

[0109] like Figure 5 As shown, the current is collected at the end of each cycle, and the first phase current i is obtained under the action of the V1 vector in the k cycle. a1 After a period of time, the second phase current i is collected under the action of the k+3 cycle V2 vector c2, then the third phase current can be calculated as i b3 =-i a1 -i c2 It is worth noting that in i x1 After collection to successful collection x2 Before, the three-phase current cannot be reconstructed, so i x1 and i x2 The larger the sampling interval is, the longer the three-phase current cannot be reconstructed, and the larger the reconstructed current error is.

[0110] 3. The optimal / suboptimal vector selection scheme based on the sinking threshold

[0111] Since the phase current information is only contained in the active vector, in order to improve the accuracy of the reconstructed current and ensure that the current can be collected in each cycle, it is considered to cancel the zero vector and only use six active vectors as candidate vectors for traversal.

[0112] The phase current information number contained in the applied voltage V(k) in the k cycle is defined as:

[0113]

[0114] In order to evaluate the reconstruction effect of the three-phase current, the sinking number N is defined as sunk It indicates the number of cycles in which the control cycle continuously updates the current information of the same phase, expressed as:

[0115]

[0116] For analysis of N sunk The impact on the current reconstruction effect is shown in Figure 1. Take the A-phase current as an example. Assuming that the A-phase current is an ideal sine wave, it can be expressed as:

[0117]

[0118] Among them, I m and are the amplitude and phase angle of phase A current respectively. sunk Caused by a Sampling delay error i a_delay like Figure 6 As shown. Since the switching cycle is very small, i a_delay It can be expressed as:

[0119]

[0120] It can be seen that N sunk The smaller the sampling delay error i a_delay The smaller it is, the smaller the phase current reconstruction error is, that is, the shorter the time interval for collecting two-phase current information is, the better the system control performance is. Similarly, N sunkThe larger the value is, the larger the phase current reconstruction error will be. If the accurate reconstructed current cannot be obtained for a long time, the system performance will be seriously degraded.

[0121] In order to avoid excessive impact on the current tracking performance, different sinking number thresholds were used at 150rpm, 450rpm and 1000rpm to observe The selection ratio.

[0122] like Figure 7 As shown, with N max The increase of The selection ratio increases accordingly. max When it is greater than 4, the The selection rate is over 90%, and the voltage tracking performance is less affected. Therefore, based on the comprehensive reconstruction effect and voltage tracking performance, the optimal threshold N is selected on the basis of multiple simulation experiments. max =4.

[0123] In an embodiment of the present invention, a single current sensor control method for a permanent magnet synchronous motor using single vector model prediction improves the stability of current reconstruction and simplifies the control structure by using the proposed method. Figure 7 The steady-state performance simulation comparison of the two algorithms at 750rpm and 5N·m load shows that, compared with FCS-MPC, DL-MPC has a significant reduction in reconstruction error and a smaller q-axis current ripple. (FCS-MPC is a traditional model predictive control method, and DL-MPC is a single-vector model predictive control method.

Claims

1. A single current sensor control method for a permanent magnet synchronous motor based on single vector model prediction, comprising the following steps: S1: The problem of establishing a current prediction model for permanent magnet synchronous motors using model predictive control is analyzed. S2: By designing the cost function and rolling optimization principle, the optimal vector selection scheme is proposed. S3: The deadbeat model predictive control principle is analyzed and the optimal vector selection scheme with one-beat delay compensation is added. S4: The reconstruction effect of three-phase current is analyzed and the optimal / suboptimal vector selection scheme based on the sinking threshold is proposed.

2. The control method according to claim 1, characterized in that: In step S1, the permanent magnet synchronous motor current prediction model under model predictive control is: First, the stator voltage equation of the permanent magnet synchronous motor in the dq coordinate system is: where u d and u q is the stator voltage of the motor in the dq coordinate system, i d and i q is the stator current of the motor in the dq coordinate system, R s is the stator resistance, L d and L q is the inductance of the motor in the dq coordinate system, ω e is the rotor electrical angular velocity, ψ f is the permanent magnet flux. Convert it into current i d and i q The state equation form of the state variable is obtained: To facilitate the application of discrete controllers, it is assumed that the system control period T sp If it is short enough, the forward Euler method can be used to discretize the above formula to obtain: in Among them, i dq (k) and u dq (k),ω e (k) represent the sampling values ​​of dq axis current, applied voltage and feedback speed at the initial moment of the kth cycle respectively. dq (k+1) represents the predicted value of the dq-axis current at the initial moment of the k+1th cycle.

3. The control method according to claim 1, characterized in that: In step S2, the cost function and rolling optimization principle are designed and the optimal vector selection scheme is proposed: Design of cost function The following steps are involved: First, the common form of the cost function is: Among them, ||·|| represents the absolute value of the error term, w i Represents the weight coefficient of the i-th error. To achieve the MPC current tracking reference value, set the dq axis current reference value and the predicted value i dq The difference between (k+1) is used as the error term, and the weight coefficients are set equal, then the cost function can be constructed as: In order to ensure that the stator current does not exceed the limit value i max , set the current limit item f lim (i dq (k+1)) is: Secondly, selecting the optimal vector according to the rolling optimization principle includes the following steps: After constructing the cost function, it needs to be optimized in a rolling manner to select the optimal voltage vector. The principle of rolling optimization is: In the k cycle, by i Substitute (k+1) into the cost function and select the optimal voltage vector V3 for the k-cycle corresponding to the best current tracking effect; in the k+1 cycle, replace x i Substitute (k+2) into the cost function and screen out the k+1 cycle optimal voltage vector corresponding to the best current tracking effect as V2.

4. The control method according to claim 1, characterized in that: In step S3, the deadbeat model predictive control principle is analyzed and a compensation scheme using one-beat delay is given: The steps of deadbeat model predictive control are as follows: First, the dq axis voltage value can be calculated as: The purpose of the deadbeat model prediction is to make the current at time k+1 track the given value, so the reference current Instead of the current at time k+1, that is: The reference voltage vector is calculated as: in, is the reference voltage vector at time k Components in the dq axis. Secondly, the steps of the one-beat delay compensation method are as follows: The one-beat delay compensation method is used to delay the calculated reference voltage vector by one control cycle. Therefore, it is necessary to calculate the reference voltage vector of the k+1th cycle. The calculated predicted current i d (k+1) and i q (k+1) is substituted and the reference current is used Substituting for the current at k+2, the reference voltage is calculated as The cost function is constructed using the error between the reference voltage vector and the candidate vector, and then: in, are the components of the reference voltage vector at time k+1 under dq and αβ, are the components of the candidate vector at time k+1 on the dq and αβ axes. The above formula represents the distance between the candidate vector and the reference voltage. By traversing the eight candidate vectors, the optimal candidate vector closest to the reference voltage vector can be selected, which is defined as 5. The control method according to claim 1, characterized in that: In step S4, the reconstruction effect of the three-phase current is analyzed and the optimal / suboptimal vector selection scheme according to the sinking threshold is proposed: The steps for three-phase current reconstruction are as follows: The reconstruction of three-phase current requires obtaining at least two different phase current information. Under DC bus current sampling, phase current information can only be collected during the action time of the active vector. In the model predictive control proposed above, only one voltage vector acts in one control cycle, and only one phase current information can be collected in one cycle. Therefore, the sampling moments of two different phase currents are set in different sampling cycles. At the same time, since the vector acting in each cycle is uncertain, the sampling intervals of different phase currents are also uncertain. Define the first phase current collected first as i x1 (x=a,b,c), the second phase current is i x2 , the third phase current can be calculated as: i x3 =-i x1 -i x2 in i x1 After collection to successful collection x2 Before, the three-phase current cannot be reconstructed, so i x1 and i x2 The larger the sampling interval is, the longer the three-phase current cannot be reconstructed, and the larger the reconstructed current error is. The steps to set the sinking threshold are as follows: Since the phase current information is only contained in the active vector, in order to improve the accuracy of the reconstructed current and ensure that the current can be collected in each cycle, it is considered to cancel the zero vector and only use six active vectors as candidate vectors for traversal. The phase current information number contained in the applied voltage V(k) in the k cycle is defined as: In order to evaluate the reconstruction effect of the three-phase current, the sinking number N is defined as sunk It indicates the number of cycles in which the control cycle continuously updates the current information of the same phase, expressed as: For analysis of N sunk The impact on the current reconstruction effect is shown in Figure 1. Take the A-phase current as an example. Assuming that the A-phase current is an ideal sine wave, it can be expressed as: Among them, I m and are the amplitude and phase angle of phase A current respectively. sunk Caused by a Sampling delay error i a_delay It can be expressed as: It can be seen that N sunk The smaller the sampling delay error i a_delay The smaller it is, the smaller the phase current reconstruction error is, that is, the shorter the time interval for collecting two-phase current information is, the better the system control performance is. Similarly, N sunk The larger the value is, the larger the phase current reconstruction error will be. If the accurate reconstructed current cannot be obtained for a long time, the system performance will be seriously degraded. The steps of the optimal / suboptimal vector selection scheme for the sinking threshold are as follows: The phase current information contained in two adjacent vectors in the same sector is different. Therefore, in order to ensure the reconstruction effect of the current, the suboptimal replacement principle is considered to introduce the adjacent voltage vector of the optimal vector in the same sector as the suboptimal vector. Define the sinking threshold N max , when N sunk Not exceeding N max When N sunk More than N max When , the suboptimal vector is selected to act on the next switching cycle. The optimal vector is defined as The suboptimal vector is Then we have: Then a single current sensor control system based on single vector model prediction can be constructed.

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