Method and apparatus for torque control of a machine

[0002] The invention relates generally to torque control of a machine, and in particular to torque control of permanent magnet (PM) synchronous machines used in electric power steering systems.

[0003] PM synchronous motors are attractive as servo drives because of their high power densities. The stator phases of such motors may be electrically excited to produce a controlled torque on the rotor, the torque being proportional to the field intensity of the rotor magnets and the amplitude of the stator phase excitation, thus permitting control of the rotor motion. When such motors are employed for high performance servo drive applications, which require precise control of rotor motion, feedback signals representing rotor position and rotor velocity are used. These feedback sensors are often generated using current sensors connected to phase windings of a PM synchronous motor to achieve effective torque control. An exemplary system using current sensors for rotor position control is described in U.S. Pat. No. 5,569,994. The use of current sensors, however, adds expense to the overall system and tends to cause low frequency torque ripple. Accordingly, there is a need in the art for a method and system for providing torque control without the use of current sensors coupled to the phase windings.

[0004] An exemplary embodiment of the invention is a method for torque control of a PM synchronous machine. The method includes obtaining a torque command signal and a machine speed and determining an operating mode in response to the torque command signal and the machine speed. The operating mode includes a first operating mode and a second operating mode. In the first operating mode, a stator phase voltage magnitude is computed and an angle between the stator phase voltage and a stator phase back emf is determined in response to the stator phase voltage magnitude. In the second operating mode, the stator phase voltage is set to a predetermined magnitude and the angle between the stator phase voltage and the stator phase back emf is determined in response to the predetermined magnitude.

[0005] The invention will be further described, by way of example, with reference to the accompanying drawings in which:

[0006] FIG. 1 illustrates torque control below the base speed in the voltage mode;

[0007] FIG. 2 illustrates torque control above the base speed in the voltage mode;

[0008] FIG. 3 is a flow diagram of an exemplary embodiment of the torque control system;

[0009] FIG. 4 illustrates torque vs. speed of a PM motor in voltage mode control; and

[0010] FIG. 5 illustrates phase current vs. speed of a PM motor in voltage mode control.

[0011] An exemplary embodiment of the invention is a method for controlling the torque of a PM machine in a first mode below the base speed and in a second mode above the base speed without the use of current sensors. In an exemplary embodiment, the machine is a motor. In this method, the machine phase voltages and their angles with respect to their back emfs are determined based on measured speed and known machine parameters. These voltages are fed to the machine by means of a PWM inverter at an optimum computed angle with respect to their back emfs to obtain required torque. This controller mimics the performance of a conventional current controller without low frequency torque ripple otherwise caused by current sensors due to the dc off-set.

[0012] The exemplary embodiment of the invention is applicable in two running modes of a PM synchronous machine. The first mode (referred to as a constant torque mode) is below a base speed where the back emf is less than the battery voltage. Based on known machine parameters and the speed, computed voltages are impressed across the machine terminals at an optimum angle such that the stator phase currents are co-phasal with their respective back emfs to produce maximum torque per ampere. This mode is shown in FIG. 1 and described in further detail herein. The second mode is above the base speed (referred to as extended mode) where the back emfs exceed the battery voltage. For a given torque command, the required computed voltages are impressed at the machine terminals at an optimum computed angle with respect to their back emfs. In the second mode, the phase current leads the back emf thereby reducing the air gap flux and producing the required torque. This mode is shown in FIG. 2 and described in further detail herein. The speed ranges defining the first mode and the second mode depends upon the inductance of the machine.

[0013] Control in the first mode will now be described with reference to FIG. 1. The variables shown in FIGS. 1 and 2 are as follows:

[0014] E=the stator phase back emf

[0015] V=the stator phase terminal voltage

[0016] I=the stator phase current

[0017] R=the stator resistance

[0018] X=ω_eL_a, the stator phase reactance

[0019] ω_e=the electrical angular frequency, in rad/s

[0020] L_a=the stator phase inductance

[0021] δ=the load angle between the phase back emf and the terminal voltage

[0022] α=the angle between phase back emf and current.

[0023] In order to optimize the drive performance in the constant torque mode below the base speed, the phase voltages are impressed across the machine terminals at an angle δ₀such that the phase currents I are in phase with the respective back emf E for maximum torque per ampere, as shown in FIG. 1.

[0024] The electromagnetic torque produced by the machine is given as

[0025] T_e=3K_eI  (1)

[0026] where,

[0027] K_e=E/ω_m=back emf constant.

[0028] The terminal phase voltage is given as

[0029] V²=(E+IR)²+(IX)²  (2)

[0030] For a given torque command T_cmd, (neglecting friction losses) substituting (1) in to (2), the terminal voltage is expressed in terms of machine parameters and the measured speed as

[0031] V²={(K_eω_m+K₁T_cmd)²+K₂(T_cmdω_m)²}  (3)

[0032] Where,

[0033] K₁=R/(3K_e)  (4)

[0034] K₂={(PL_a)/(3K_e)}²  (5)

[0035] P=number of poles

[0036] ω_m=Pω_e=mechanical angular frequency, rad/s

[0037] T_cmdis the torque required of the motor by the system, i.e., power steering system. V can be obtained from a V²vs V lookup table to minimize the computational time. The angle δ₀is computed in terms of known parameters as

[0038] sin δ₀=(T_cmdω_mK₃/V)  (6)

[0039] Where,

[0040] K₃=(PL_a/6K_e)  (7)

[0041] The required phase voltages for a given torque command are given as

[0042] V_a=Vsin(δ₀+θ)  (8)

[0043] V_b=Vsin(δ₀+θ+240)  (9)

[0044] V_c=Vsin(δ₀+θ+120)  (10)

[0045] These voltages are impressed across the machine by a driver such as a PWM inverter as described below with reference to FIG. 3.

[0046] Operation in the second mode, above the base speed as shown in FIG. 2, will now be described. To operate above the base speed, for a given torque command the maximum available phase voltages are impressed across the machine terminals at an angle δ₁computed from the known parameters. Under this condition the phase current leads the back emf and its demagnetizing component reduces the air gap flux such that the machine produces the required torque.

[0047] From FIG. 2, the angle between stator phase current I and the back emf E is calculated as

[0048] cos α={R(Vcos δ₁−E)+V×sin δ₁)}/{1(R²+X²)}  (11)

[0049] The electromagnetic torque under this condition is given as

[0050] T_e=3K_eIcos α  (12)

[0051] T_cmdcan be obtained as a function of load angle, δ₁using (11) and (12) as

[0052] T_cmd={3K_e/(R²+X²)}{(V_mcos δ₁−K_eω_m)R+(XV_msin δ₁)}  (13)

[0053] Where, V_mis the maximum available phase voltage of the PWM inverter. Since the torque command T_cmdis the function of sin δ₁and cos δ₁, the angle δ₁is computed by an iteration method until the condition defined in equation (13) is satisfied. The maximum available voltages are impressed across the machine terminals by mean of PWM inverter at an angle δ₁with respect to the back emfs to obtain the required torque. Frictional losses may be taken into account by defining T_cmd=T_e+T_friction.

[0054] FIG. 3 is an exemplary block diagram of a control system for a permanent magnet synchronous machine in both the first and second modes. A three phase pulse width modulation (PWM) inverter 104 converts battery voltage from battery 102 to phase voltages and provides the phase voltages to the PM motor 105. An encoder 106 is coupled to the shaft of the PM motor 105 to measure the rotation angle θ of the PM motor 105. A controller shown as 101 receives the rotation angle θ and other inputs and generates phase voltages V_a, V_band V_cas described herein. The controller 101 may be implemented using a microprocessor along with conventional associated components (e.g., memory, communications device, etc.). Components such as look up tables may be used in controller 101 as described herein. The steps performed by the controller 101 are shown in flowchart form within controller 101.

[0055] The rotation angle θ is used to provide a calculation of the mechanical angular frequency ω in radians/second at speed computation step 110. The stator phase voltage magnitude V is determined using the torque command signal T_cmdrequesting a torque from the PM motor and ω as inputs to calculate V². As shown at step 118, V²is equal to

[0056] V²={(K_eω_m+K₁T_cmd)²+K₂(T_cmdω_m)²}  (3)

[0057] Where,

[0058] K₁=R/(3K_e)  (4)

[0059] K₂=[(PL_a)/(3K_e)]²  (5)

[0060] V may be determined from V²by a look up table accessed at 118.

[0061] To determine whether the motor is to operate in the first mode or second mode, the voltage V determined at 118 is compared to a maximum inverter voltage V_mthat can be generated by inverter 104. The maximum inverter voltage V_mis determined as

[0062] V_m=K₄V_bat,

[0063] where K₄is a constant and V_batis the battery voltage provided by battery 102.

[0064] At step 126, it is determined whether V is less than V_m. If not, the PM motor 105 is to operate in the first mode and flow proceeds to step 112 where the controller determines the three phase voltages based on V and angle δ₀. A value designated 1/V derived at step 118 and ω are used at 130 to determine δ₀as follows:

[0065] Sin δ₀=(Pl_a/6K_e)=(T_cmdK₃ω_m/V), where K₃=(Pl_a/6K_e).

[0066] A look up table may be used to determine 1/V from V at step 118. A further look up table may be used to compute δ₀based on 1/V and ω at step 130. The values of θ, δ₀and V are used at step 112 to determine phase voltages V_a, V_b, and V_c. The phase voltages V_a, V_b, and V_care coupled to the PWM inverter 104 for application to the PM motor 105.

[0067] If the T_cmdsignal input to step 118 generates a value V greater than V_m, this indicates the second mode of operation and decision element 126 directs flow to step 134 where V is set equal to V_m. Step 136 uses V_m, T_cmdand ω_mto calculate sin δ₁.

[0068] sin δ₁=(T_cmdK₃ω_m/V_m)

[0069] A lookup table may be used to determine the value of δ₁from sin δ₁.

[0070] Flow proceeds to step 138 where the angle δ₁may be adjusted based on an iterative loop described herein. On the initial determination of δ₁, step 138 may be omitted. At step 140, cos δ₁and sin δ₁values are derived (e.g., by look up tables) and provides to step 148 where a computed torque value Z is determined based on the voltage V_mand the angle δ₁. Z represents a computed torque value at the angle δ₁. A demanded torque value Y is calculated at step 150. The computed torque value Z and the demanded torque value Y are compared at step 152. If the computed torque value Z equals or exceeds the demanded torque value Y, then the angle δ₁is suitable to achieve the desired torque and flow proceeds to step 114 where phase voltages V_a, V_b, and V_care determined based on δ₁and V_m. The phase voltages V_a, V_b, and V_care coupled to the PWM inverter 104 for application to the PM motor 105.

[0071] If the computed torque value Z does not equal or exceed the demanded torque value Y at step 152, flow proceeds to step 154 where it is determined if the measured current I_dis greater than or equal to a current limit I_dmax. The measured current I_dmay be provided from a current sensor located outside of the phase windings. If step 154 results in a yes, the system cannot increase the current and the existing angle δ₁is used at step 114 for computation of the phase voltages. If I_dis less than I_dmax, flow proceeds to step 138 where the angle δ₁may be incremented or decremented as necessary. If the current demanded torque value Y_nis greater than or equal to the prior demanded torque value Y_n−1, then the value of δ₁is incremented by +Δδ. Alternatively, if Y_nis less than Y_n−1, δ₁is decremented by −Δδ and flow proceeds to step 140 where the iterative process continues until either the demanded torque value Y is met or exceeded or the maximum current I_dmaxis reached.

[0072] A 12V, PM motor was simulated using this method over the entire speed range taking the current limit of the machine into account. FIG. 4 shows the torquespeed characteristics at rated conditions while the FIG. 5 shows the current drawn at different speeds with and without phase angle advance of δ₁described above. Using this method higher torques can be obtained in the extended speed range as compared with the conventional operation. It is possible to optimally design the machine to obtain the required torque-speed characteristics over the entire speed range.

[0073] The exemplary embodiment of the invention described herein provides a cost effective torque control method without current sensors over the extended speed range. The control method and controller may be implemented in conjunction with an electric power steering system to control torque generation in the power steering system. The exemplary embodiment of the invention described herein provides numerous advantages. Torque per ampere in the constant torque region below the base speed is maximized by placing the back emf and current signals in phase as shown in FIG. 1. Torque control capability in the extended speed range above the base speed is provided for optimum performance. Low frequency torque due to the use of current sensors is eliminated. This elimination is desirable when the controller is used in connection with a steering column mounted electric power steering system. The controller can be easily implemented in a low cost microcontroller since the mathematical operations involved include only additions and multiplications along with look up tables.

[0074] While preferred embodiments have been shown and described, various modifications and substitutions may be made thereto without departing from the spirit and scope of the invention. Accordingly, it is to be understood that the present invention has been described by way of illustration only, and such illustrations and embodiments as have been disclosed herein are not to be construed as limiting to the claims.