AC excitation motor current distribution method based on torque distribution factor

Abstract

The invention relates to the technical field of motor current control, in particular to an alternating-current excitation motor current distribution method based on a torque distribution factor, which comprises the following steps: constructing a d-q coordinate system mathematical model of an alternating-current excitation motor, and enabling double-winding current distribution to be equivalent to single-winding current distribution by adopting an equivalent winding method; defining a torque distribution factor, and deducing a mapping relation between an equivalent current and a double-winding d-q current according to the equivalent single-winding model; according to the reference torque instruction, a double-winding d-q axis current given value is solved by adopting the maximum torque current ratio; the value of a torque distribution factor is designed according to the load working condition, when the two sets of windings operate at the same time, the difference value of the current utilization rates of the two sets of windings serves as an error, the torque distribution factor is adjusted online through a control algorithm, and current instructions of all the windings are generated in combination with amplitude limiting. The method provides a self-adaptive motor current distribution strategy and is suitable for a low-speed large-load working condition.

Description

Technical Field

[0001] This invention relates to the field of AC excitation motor technology, and in particular to an AC excitation motor current distribution method based on torque distribution factor. Background Technology

[0002] AC excitation motors overcome the problem of difficult adjustment of the air gap magnetic field in traditional permanent magnet synchronous motors. They are a new type of motor with high power density, high operating efficiency, and wide operating range, and have broad application prospects in aerospace and other fields.

[0003] An AC-excited motor is a dual-winding motor. During the motor's starting phase, to obtain the required electromagnetic torque, the current in the two windings needs to be coordinated and distributed. Existing current distribution methods mostly use a fixed ratio to determine the given current. This fixed ratio distribution may lead to uneven utilization of the two windings, resulting in winding overload. Therefore, to avoid winding overload, an effective current distribution method urgently needs to be proposed. Summary of the Invention

[0004] The purpose of this invention is to provide a current distribution method for AC excitation motors based on torque distribution factors, which solves the problem of uneven utilization of the two sets of windings in AC excitation motors and the occurrence of winding overload.

[0005] To address the aforementioned technical problems, this invention provides a current distribution method for an AC excitation motor based on a torque distribution factor, used to determine the d-axis current command and q-axis current command of the excitation winding and armature winding in a dual-winding motor. The method includes the following steps: A dq coordinate mathematical model of a two-winding motor is established, and the voltage equations of the armature winding and the excitation winding under the dq coordinate mathematical model are established. Based on the dq coordinate mathematical model of a dual-winding motor, an equivalent single-winding model is constructed, which includes its corresponding voltage equation, flux linkage equation, and electromagnetic torque equation. The ratio of the electromagnetic torques corresponding to the excitation winding and the armature winding is defined as the torque distribution factor, and the current relationship between the dual-winding motor and the equivalent single-winding model is constructed. Construct the objective function, use the maximum torque-current ratio to solve for the current setpoint of the equivalent single winding model, and derive the dq current of the excitation winding and armature winding by combining the voltage equation; The torque distribution factor is designed according to the load conditions. When the two sets of windings are running at the same time, the difference in the current utilization rate of the two sets of windings is used as the error. The torque distribution factor is adjusted online through the control algorithm, and the current command of each winding is generated by combining the amplitude limit. The motor current distribution is completed based on the current command.

[0006] Preferably, the process of deriving the voltage equation for the equivalent single-winding model includes: The equivalent winding method is used to perform parameter conversion on the dq coordinate mathematical model, and the armature winding with N1 turns and the excitation winding with N2 turns are equivalent to two sets of three-phase windings with symmetrical structure N1+N2. The analysis yielded the inductance, flux linkage, and stator resistance relationships before and after the equivalent transformation. Substituting the inductance, flux linkage, and stator resistance relationships into the original voltage equations for the armature winding and the excitation winding, we obtain the equivalent voltage equations for the armature winding and the excitation winding. By adding the d-axis voltage equations and q-axis voltage equations of the two equivalent windings, the voltage equations of the equivalent single winding model are obtained.

[0007] Preferably, the process of deriving the flux linkage equations for the conductive pivot winding and the excitation winding includes: Based on the equivalent single winding model, the relationship between the electromagnetic torque of the double winding and the electromagnetic torque of the equivalent winding is analyzed, and the flux linkage equations of the armature winding and the excitation winding are derived.

[0008] Preferably, the process of deriving the electromagnetic torque equations for the conductive pivot winding and the excitation winding includes: The electromagnetic torque equation of the equivalent single-winding model is obtained from the voltage equation of the equivalent single-winding model.

[0009] Preferably, the process of constructing the current relationship between a dual-winding motor and its equivalent single-winding model includes: Establish an expression for the torque distribution factor, where torque is represented by flux linkage and current; Based on the flux linkage relationship between the two windings, the flux linkage is replaced by the number of turns of the windings to obtain the expression for the relationship between the torque distribution factor, current and number of turns, which is the current relationship between the dual-winding motor and the equivalent single-winding model.

[0010] Preferably, the objective function is constructed using a Lagrangian function to maximize the torque-to-current ratio and obtain the optimal current value.

[0011] Preferably, when the partial derivative of the objective function is equal to zero, the objective function obtains an extreme value, and the extreme point corresponds to the optimal current value, thereby deriving the optimal current expression.

[0012] Preferably, the process of distributing motor current based on current commands includes: Based on the load torque command, it is divided into a non-magnetizing region and a magnetizing region: In the non-magnetizing region, only the armature winding is in operation. At this time, the torque distribution factor is 0, and the current distribution is determined based on the number of turns of the two windings. In the magnetization zone, the two sets of windings operate simultaneously. Different torque distribution factors are selected to obtain different current distribution results. The error is constructed based on the difference in current utilization rates of the two sets of windings. The torque distribution factor is adjusted online based on the error. When the error is greater than 0, the distribution ratio of the excitation winding is reduced and the distribution ratio of the stator winding is increased; when the error is less than 0, the distribution ratio of the excitation winding is increased.

[0013] Preferably, in the dq coordinate mathematical model of a two-winding motor, the voltage equations for the armature winding and the excitation winding include: The d-axis voltage equations and q-axis voltage equations of the armature winding, And the d-axis voltage equation and q-axis voltage equation of the excitation winding.

[0014] Preferably, the control algorithm is a PI control algorithm, which uses a PI update law to generate the torque distribution factor.

[0015] The AC excitation motor current distribution method based on torque distribution factor provided by this invention has the following beneficial effects: This invention constructs a dq coordinate coefficient mathematical model of an AC excitation motor, and uses an equivalent winding method to convert the dual-winding current distribution into a single-winding current distribution. The method defines a torque distribution factor and derives the mapping relationship between the equivalent current and the dual-winding dq current based on the equivalent single-winding model. Based on the reference torque command, the maximum torque-to-current ratio is used to obtain the given value of the dual-winding dq axis current. The torque distribution factor is designed according to the load conditions. When both windings are running simultaneously, the difference in current utilization rates between the two windings is used as the error. The torque distribution factor is adjusted online through a control algorithm, and combined with amplitude limiting to generate current commands for each winding, the motor current distribution is achieved. This invention is suitable for low-speed, high-load conditions. Attached Figure Description

[0016] To more clearly illustrate the technical solutions of the embodiments of the present invention or the prior art, the drawings used in the description of the embodiments or the prior art will be briefly introduced below. Obviously, the drawings described below are only some embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0017] Figure 1 This is a flowchart illustrating the steps of the AC excitation motor current distribution method provided in an embodiment of the present invention; Figure 2 This is a block diagram of the AC excitation motor current distribution strategy based on the adaptive torque distribution factor. Detailed Implementation

[0018] The core of this invention is to provide a current distribution method for AC excitation motors based on a torque distribution factor. Existing current distribution methods mostly use a fixed ratio to determine the given current. Fixed ratio distribution may lead to uneven utilization of the two sets of windings, resulting in winding overload.

[0019] The present invention provides an AC excitation motor current distribution method based on torque distribution factor, which designs a torque distribution factor and proposes a motor current distribution strategy with adaptive torque distribution factor, realizing coordinated distribution of current in dual windings and solving the problems of existing current distribution methods.

[0020] To enable those skilled in the art to better understand the present invention, the invention will be further described in detail below with reference to the accompanying drawings and specific embodiments. Obviously, the described embodiments are merely some embodiments of the present invention, and not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0021] This embodiment provides a current distribution method for AC excitation motors based on torque distribution factors. In this embodiment, the current distribution method for AC excitation motors is applied to execute current distribution strategies in AC excitation motors. However, this method is also applicable to other dual-winding motors, such as dual three-phase permanent magnet synchronous motors, dual-winding induction motors, etc. The winding form can be centralized or distributed, and the winding connection method can be star, delta, or open winding.

[0022] The AC excitation motor comprises two sets of windings: an excitation winding and an armature winding. The armature winding and the excitation winding are supplied with alternating current of the same frequency. The excitation current can both regulate the air gap magnetic field and generate independent electromagnetic torque.

[0023] Please refer to Figure 1 and Figure 2 , Figure 1 This is a flowchart illustrating the steps of the AC excitation motor current distribution method provided in an embodiment of the present invention. Figure 2 This is a block diagram of the AC excitation motor current distribution strategy based on the adaptive torque distribution factor.

[0024] See Figure 1 In this embodiment of the invention, the AC excitation motor current distribution method is used to determine the d-axis current command and q-axis current command of the excitation winding and armature winding in the AC excitation motor. The method includes the following steps (S1 to S5): S1. Establish the dq coordinate mathematical model of the dual-winding motor, and establish the voltage equations of the armature winding and the excitation winding under the dq coordinate mathematical model.

[0025] Specifically, the voltage equations for the armature winding and the excitation winding include: The d-axis voltage equations and q-axis voltage equations of the armature winding, And the d-axis voltage equation and q-axis voltage equation of the excitation winding.

[0026] In this embodiment, the voltage equations for the armature winding and the excitation winding are expressed as follows: ; Wherein, Uds and Uqs represent the d-axis voltage and q-axis voltage of the armature winding, respectively; Udf and Uqf represent the d-axis voltage and q-axis voltage of the field winding, respectively; ids and iqs represent the d-axis current and q-axis current of the armature winding, respectively; idf and iqf represent the d-axis current and q-axis current of the field winding, respectively; Lds and Lqs represent the d-axis inductance and q-axis inductance of the armature winding, respectively; Ldf and Lqf represent the d-axis inductance and q-axis inductance of the field winding, respectively; ωe represents the electric angular velocity of the motor; Rf and Rs represent the resistance values ​​of the armature winding and the field winding, respectively; Lmd and Lmq represent the d-axis mutual inductance and q-axis mutual inductance of the armature winding and the field winding, respectively; and ψpms and ψpmf represent the permanent magnet flux linkage amplitudes of the armature winding and the field winding, respectively.

[0027] S2. Based on the dq coordinate mathematical model of the dual-winding motor, construct an equivalent single-winding model, which includes its corresponding voltage equation, flux linkage equation and electromagnetic torque equation.

[0028] In this embodiment, the process of deriving the voltage equation for the equivalent single-winding model includes: The equivalent winding method is used to perform parameter conversion on the dq coordinate mathematical model, and the armature winding with N1 turns and the excitation winding with N2 turns are equivalent to two sets of three-phase windings with symmetrical structure N1+N2. The analysis yielded the inductance, flux linkage, and stator resistance relationships before and after the equivalent transformation. Substituting the inductance, flux linkage, and stator resistance relationships into the original voltage equations for the armature and field windings, we obtain the equivalent voltage equations for the armature and field windings, i.e., the mathematical model expressions for the three-phase windings are as follows: ; Where Ldd, Lqq, Rss, and ψf are the d-axis inductance, q-axis inductance, stator resistance, and permanent magnet flux linkage of the two sets of windings after the number of turns is equivalent, respectively. By adding the d-axis and q-axis voltage equations of the two windings respectively, we obtain the equivalent single-winding model (voltage equation), as shown below: .

[0029] Furthermore, the derivation process of the inductance, flux linkage, and stator resistance relationships before and after the equivalent transformation is as follows: According to the definition of inductance, in a synchronously rotating coordinate system, inductance can be expressed as: ; Where x = d, q; Lxs is the self-inductance of the armature winding; Lmx is the mutual inductance of the two windings in the d and q axis directions; Lxf is the self-inductance of the excitation winding; Λxs and Λxf represent the magnetic permeability of the magnetic circuits of the two windings respectively; Λmx represents the mutual magnetic permeability of the two windings.

[0030] Assuming the two windings are identical except for the number of turns, using constant power transformation, the armature windings and excitation windings with turns N1 and N2 are equivalent to two symmetrical three-phase windings N1+N2. After equivalence, the inductance, resistance, and flux linkage amplitude of the two windings are equal, and the inductance satisfies the following equation: ; After the equivalent transformation, the magnetic flux linkage satisfies the following relationship: ; The flux linkage relationship can be expressed as: ; Since both the armature winding and the field winding are equivalent to the same number of turns, the stator resistance relationship before and after the equivalence is satisfied: ; Where Ldd, Lqq, Rss, and ψf are the d-axis inductance, q-axis inductance, stator resistance, and permanent magnet flux linkage of the two sets of windings after the number of turns are equivalent, respectively; ψds, ψqs, ψdf, and ψqf are the dq-axis flux linkages of the armature winding and the excitation winding, respectively.

[0031] It should be noted that, in this embodiment, the current and inductance after the equivalent winding are defined as follows: ; ; The voltage equation after the equivalent winding is: ; Where Ldeq and Lqeq are the equivalent d-axis inductance and q-axis inductance of the winding, respectively; Udd and Uqq are the equivalent voltage values ​​of the winding.

[0032] Furthermore, the process of deriving the flux linkage equations for the conductive pivot winding and the excitation winding is as follows: Based on the equivalent single-winding model, the relationship between the electromagnetic torque of the dual-winding winding and the equivalent winding electromagnetic torque is analyzed, and the flux linkage equations of the armature winding and the excitation winding are obtained, as follows: ; Wherein, ψds and ψqs are the d-axis flux linkage and q-axis flux linkage of the armature winding, respectively, and ψdf and ψqf are the d-axis flux linkage and q-axis flux linkage of the excitation winding, respectively.

[0033] It should be noted that the excitation winding current can regulate the air gap magnetic field; therefore, ψds and ψqs contain flux linkage components introduced by the excitation winding current through mutual inductance coupling. Furthermore, in this embodiment, the excitation flux linkage term represents the superposition of the permanent magnet flux linkage and the flux linkage generated by the excitation winding, and the excitation current can participate in current distribution as a distribution variable.

[0034] Furthermore, after the equivalent winding, the expression for the electromagnetic torque equation of the AC excitation motor is as follows: ; Where Ts is the electromagnetic torque of the armature winding, Tf is the electromagnetic torque of the excitation winding, and T is the torque of the equivalent winding; id and iq represent the d-axis current and q-axis current of the equivalent single winding model, respectively; ψds and ψqs represent the d-axis flux linkage and q-axis flux linkage of the equivalent single winding model, respectively; and p0 is the number of pole pairs of the motor.

[0035] S3. Define the ratio of the electromagnetic torques of the excitation winding to the armature winding as the torque distribution factor, and construct the current relationship between the dual-winding motor and the equivalent single-winding model.

[0036] In this embodiment, when both sets of windings are running simultaneously, the calculation expression for the torque distribution factor is as follows: ; Where η represents the torque distribution factor.

[0037] The derivation process of the torque distribution factor is as follows: Because the flux linkage relationship between the two sets of windings satisfies When the armature winding and the field winding operate simultaneously, the torque distribution factor can be derived, and thus the current relationship between the field winding and the armature winding can be obtained. The expression is as follows: When the currents in the excitation winding and the armature winding satisfy the above current relationship, the torque can be guaranteed to meet the torque distribution factor.

[0038] Furthermore, based on the definition of current after equivalent winding, the current relationship before and after equivalence can be derived, as shown in the following expression: ; Where isdq represents the dq-axis current relationship of the armature winding, and ifdq represents the dq-axis current relationship of the excitation winding.

[0039] Furthermore, the electromagnetic torque equation after the equivalent winding transformation is as follows: ,in, To achieve the maximum torque-to-current ratio, the following equation must be satisfied: .

[0040] S4. Construct the objective function, use the maximum torque-current ratio to solve for the current setpoint of the equivalent single winding model, and derive the dq current of the excitation winding and armature winding by combining the voltage equation.

[0041] In this embodiment, the objective function is constructed using the Lagrange function, and the expression of the objective function is as follows: ; Where H represents the objective function and λ is the Lagrange multiplier.

[0042] Preferably, the objective function H reaches an extreme value when the partial derivative of the objective function H is zero. The extreme value corresponds to the optimal current value, thus leading to the following derivation: ; Based on the above equation, the optimal current expression is derived as follows: ; Where id is the current setpoint of the equivalent single-winding motor, and Ldeq and Lqeq are the d-axis inductance and q-axis inductance of the last two sets of windings in the equivalent winding, respectively.

[0043] S5. The torque distribution factor is designed according to the load conditions. When the two sets of windings are running at the same time, the difference in the current utilization rate of the two sets of windings is used as the error. The torque distribution factor is adjusted online through the PI control algorithm, and the current command of each winding is generated in combination with the amplitude limit. The motor current distribution is completed based on the current command.

[0044] In this embodiment, the process of distributing motor current based on current commands includes: Based on the load torque command, it is divided into a non-magnetizing region and a magnetizing region: In the non-magnetizing region, only the armature winding is in operation. At this time, η=0, and the current distribution is as follows: ; In the magnetization region, both windings operate simultaneously. Different η values ​​result in different current distributions. To avoid overcurrent in one winding due to unreasonable distribution, the other winding has redundancy. The construction error is: ; in, Ismax and Ifmax are the maximum current amplitudes of the stator winding and the excitation winding, respectively. Based on the error e, the torque distribution factor η is adjusted online. When e>0, it indicates that the current utilization rate of the excitation winding is higher than that of the stator winding. In order to prevent overcurrent in the excitation winding and make full use of the current margin of the stator winding, the distribution ratio of the excitation winding should be reduced and the distribution ratio of the stator winding should be increased. Conversely, it indicates that the current utilization rate of the stator winding is higher, and the distribution ratio of the excitation winding should be increased to make the current utilization rates of the two windings tend to be consistent, thereby improving the system's output torque capability under current constraints and avoiding single winding overcurrent.

[0045] This embodiment uses a PI control algorithm to achieve the above adaptive adjustment, and uses a PI update law to generate the torque distribution factor, the expression of which is as follows: ; Where η is the torque distribution factor, η0 is the initial torque, and kp and ki are the proportional coefficient and integral coefficient, respectively.

[0046] It should be noted that the control algorithm used in this embodiment is the PI control algorithm. The method in this embodiment can also use other control algorithms to achieve adaptive adjustment, such as the fuzzy control algorithm or neural network control algorithm in intelligent control algorithms, and the sliding mode control algorithm in classical control algorithms.

[0047] The various embodiments in this specification are described in a progressive manner, with each embodiment focusing on its differences from other embodiments. Similar or identical parts between embodiments can be referred to interchangeably. For the apparatuses, devices, and computer-readable storage media disclosed in the embodiments, since they correspond to the methods disclosed in the embodiments, the descriptions are relatively simple; relevant details can be found in the method section.

[0048] Those skilled in the art will further recognize that the units and algorithm steps of the various examples described in conjunction with the embodiments disclosed herein can be implemented in electronic hardware, computer software, or a combination of both. To clearly illustrate the interchangeability of hardware and software, the components and steps of the various examples have been generally described in terms of functionality in the foregoing description. Whether these functions are implemented in hardware or software depends on the specific application and design constraints of the technical solution. Those skilled in the art can use different methods to implement the described functions for each specific application, but such implementation should not be considered beyond the scope of this application.

[0049] The electromagnetic malfunction prevention control method provided in this application has been described in detail above. Specific examples have been used to illustrate the principles and implementation methods of this application. The descriptions of the embodiments above are only for the purpose of helping to understand the method and its core ideas. It should be noted that those skilled in the art can make several improvements and modifications to this application without departing from the principles of this application, and these improvements and modifications also fall within the protection scope of the claims of this application.

Claims

1. A current distribution method for an AC exciter motor based on a torque distribution factor, characterized in that, The method for determining the d-axis current command and q-axis current command of the excitation winding and armature winding in a two-winding motor includes the following steps: A dq coordinate mathematical model of a two-winding motor is established, and the voltage equations of the armature winding and the excitation winding under the dq coordinate mathematical model are established. Based on the dq coordinate mathematical model of a dual-winding motor, an equivalent single-winding model is constructed, which includes its corresponding voltage equation, flux linkage equation, and electromagnetic torque equation. The ratio of the electromagnetic torques corresponding to the excitation winding and the armature winding is defined as the torque distribution factor, and the current relationship between the dual-winding motor and the equivalent single-winding model is constructed. Construct the objective function, use the maximum torque-current ratio to solve for the current setpoint of the equivalent single winding model, and derive the dq current of the excitation winding and armature winding by combining the voltage equation; The torque distribution factor is designed according to the load conditions. When the two sets of windings are running at the same time, the difference in the current utilization rate of the two sets of windings is used as the error. The torque distribution factor is adjusted online through the control algorithm, and the current command of each winding is generated by combining the amplitude limit. The motor current distribution is completed based on the current command.

2. The AC excitation motor current distribution method according to claim 1, characterized in that, The process of deriving the voltage equation for the equivalent single-winding model includes: The equivalent winding method is used to perform parameter conversion on the dq coordinate mathematical model, and the armature winding with N1 turns and the excitation winding with N2 turns are equivalent to two sets of three-phase windings with symmetrical structure N1+N2. The analysis yielded the inductance, flux linkage, and stator resistance relationships before and after the equivalent transformation. Substituting the inductance, flux linkage, and stator resistance relationships into the original voltage equations for the armature winding and the excitation winding, we obtain the equivalent voltage equations for the armature winding and the excitation winding. By adding the d-axis voltage equations and q-axis voltage equations of the two equivalent windings, the voltage equations of the equivalent single winding model are obtained.

3. The AC excitation motor current distribution method according to claim 2, characterized in that, The process of deriving the flux linkage equations for the conductive pivot winding and the excitation winding includes: Based on the equivalent single winding model, the relationship between the electromagnetic torque of the double winding and the electromagnetic torque of the equivalent winding is analyzed, and the flux linkage equations of the armature winding and the excitation winding are derived.

4. The AC excitation motor current distribution method according to claim 3, characterized in that, The process of deriving the electromagnetic torque equations for the conductive pivot winding and the excitation winding includes: The electromagnetic torque equation of the equivalent single-winding model is obtained from the voltage equation of the equivalent single-winding model.

5. The AC excitation motor current distribution method according to claim 1, characterized in that, The process of constructing the current relationship between a two-winding motor and its equivalent single-winding model includes: Establish an expression for the torque distribution factor, where torque is represented by flux linkage and current; Based on the flux linkage relationship between the two windings, the flux linkage is replaced by the number of turns of the windings to obtain the expression for the relationship between the torque distribution factor, current and number of turns, which is the current relationship between the dual-winding motor and the equivalent single-winding model.

6. The AC excitation motor current distribution method according to claim 1, characterized in that, The objective function is constructed using a Lagrangian function to maximize the torque-to-current ratio and obtain the optimal current value.

7. The AC excitation motor current distribution method according to claim 6, characterized in that, When the partial derivative of the objective function is equal to zero, the objective function reaches an extreme value. The extreme point corresponds to the optimal current value, thus deriving the expression for the optimal current.

8. The AC excitation motor current distribution method according to claim 1, characterized in that, The process of distributing motor current based on current commands includes: Based on the load torque command, it is divided into a non-magnetizing region and a magnetizing region: In the non-magnetizing region, only the armature winding is in operation. At this time, the torque distribution factor is 0, and the current distribution is determined based on the number of turns of the two windings. In the magnetization zone, the two sets of windings operate simultaneously. Different torque distribution factors are selected to obtain different current distribution results. The error is constructed based on the difference in current utilization rates of the two sets of windings. The torque distribution factor is adjusted online based on the error. When the error is greater than 0, the distribution ratio of the excitation winding is reduced and the distribution ratio of the stator winding is increased; when the error is less than 0, the distribution ratio of the excitation winding is increased.

9. The AC excitation motor current distribution method according to claim 1, characterized in that, In the dq coordinate mathematical model of a two-winding motor, the voltage equations for the armature winding and the field winding include: The d-axis voltage equations and q-axis voltage equations of the armature winding, And the d-axis voltage equation and q-axis voltage equation of the excitation winding.

10. The AC excitation motor current distribution method according to claim 1, characterized in that, The control algorithm is a PI control algorithm, which uses a PI update law to generate the torque distribution factor.

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