{"id":201,"date":"2021-03-23T14:56:47","date_gmt":"2021-03-23T14:56:47","guid":{"rendered":"https:\/\/imperix.com\/doc\/?p=201"},"modified":"2026-04-08T07:04:01","modified_gmt":"2026-04-08T07:04:01","slug":"field-oriented-control-of-pmsm","status":"publish","type":"post","link":"https:\/\/imperix.com\/doc\/implementation\/field-oriented-control-of-pmsm","title":{"rendered":"Field oriented control (FOC) of permanent magnet synchronous machine (PMSM)"},"content":{"rendered":"<div id=\"ez-toc-container\" class=\"ez-toc-v2_0_82_2 ez-toc-wrap-right-text counter-hierarchy ez-toc-counter ez-toc-grey ez-toc-container-direction\">\n<div class=\"ez-toc-title-container\">\n<p class=\"ez-toc-title\" style=\"cursor:inherit\">Table of Contents<\/p>\n<span class=\"ez-toc-title-toggle\"><\/span><\/div>\n<nav><ul class='ez-toc-list ez-toc-list-level-1 ' ><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-1\" href=\"https:\/\/imperix.com\/doc\/implementation\/field-oriented-control-of-pmsm\/#General-principles-of-field-oriented-control\" >General principles of field oriented control<\/a><ul class='ez-toc-list-level-3' ><li class='ez-toc-heading-level-3'><a class=\"ez-toc-link ez-toc-heading-2\" href=\"https:\/\/imperix.com\/doc\/implementation\/field-oriented-control-of-pmsm\/#System-level-modeling-of-the-field-oriented-control-algorithm\" >System-level modeling of the field oriented control algorithm<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-3'><a class=\"ez-toc-link ez-toc-heading-3\" href=\"https:\/\/imperix.com\/doc\/implementation\/field-oriented-control-of-pmsm\/#A-more-intuitive-approach\" >A more intuitive approach<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-3'><a class=\"ez-toc-link ez-toc-heading-4\" href=\"https:\/\/imperix.com\/doc\/implementation\/field-oriented-control-of-pmsm\/#Flux-and-torque-control\" >Flux and torque control<\/a><\/li><\/ul><\/li><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-5\" href=\"https:\/\/imperix.com\/doc\/implementation\/field-oriented-control-of-pmsm\/#B-Box-B-Board-implementation\" >B-Box \/ B-Board implementation<\/a><ul class='ez-toc-list-level-3' ><li class='ez-toc-heading-level-3'><a class=\"ez-toc-link ez-toc-heading-6\" href=\"https:\/\/imperix.com\/doc\/implementation\/field-oriented-control-of-pmsm\/#Software-resources\" >Software resources<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-3'><a class=\"ez-toc-link ez-toc-heading-7\" href=\"https:\/\/imperix.com\/doc\/implementation\/field-oriented-control-of-pmsm\/#ACG-SDK-for-Simulink\" >ACG SDK for Simulink<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-3'><a class=\"ez-toc-link ez-toc-heading-8\" href=\"https:\/\/imperix.com\/doc\/implementation\/field-oriented-control-of-pmsm\/#Experimental-results-of-the-field-oriented-control\" >Experimental results of the field oriented control<\/a><\/li><\/ul><\/li><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-9\" href=\"https:\/\/imperix.com\/doc\/implementation\/field-oriented-control-of-pmsm\/#Academic-references\" >Academic references<\/a><\/li><\/ul><\/nav><\/div>\n\n<p>This technical note presents a common control technique for Permanent Magnets Synchronous Machines (PMSM). The Field-Oriented Control (FOC) method is a motor control strategy that orients the stator current vector in a rotating reference frame of the machine. First, the note introduces the general operating principles of the Field-Oriented Control and then, details a possible design methodology. Finally, a practical control implementation is introduced to drive the machine with a power inverter, controlled either by the&nbsp;<a href=\"https:\/\/imperix.com\/products\/control\/bbox\">B-Box RCP<\/a>&nbsp;or&nbsp;the <a href=\"https:\/\/imperix.com\/products\/control\/bboard\">B-Board PRO<\/a>. Please note that imperix offers a <a href=\"https:\/\/imperix.com\/products\/electric-motor-drive-bundle\/\">ready-to-use motor drive system<\/a> to develop and test motor control techniques. More details can be found in the <a href=\"https:\/\/imperix.com\/doc\/help\/motor-testbench-quick-start-guide\">Motor Testbench quick start guide (PN181)<\/a>.<\/p>\n\n\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"780\" height=\"383\" src=\"https:\/\/imperix.com\/doc\/wp-content\/uploads\/2024\/03\/PN181-motor-testbench-no-labels.png\" alt=\"Experimental setup to test a field oriented control of a PMSM with imperix products.\" class=\"wp-image-27034\" srcset=\"https:\/\/imperix.com\/doc\/wp-content\/uploads\/2024\/03\/PN181-motor-testbench-no-labels.png 780w, https:\/\/imperix.com\/doc\/wp-content\/uploads\/2024\/03\/PN181-motor-testbench-no-labels-300x147.png 300w, https:\/\/imperix.com\/doc\/wp-content\/uploads\/2024\/03\/PN181-motor-testbench-no-labels-768x377.png 768w\" sizes=\"auto, (max-width: 780px) 100vw, 780px\" \/><\/figure>\n\n\n\n<h2 class=\"wp-block-heading\" id=\"TN111:Fieldorientedcontrol(FOC)ofaPMSM-Generalprinciples\"><span class=\"ez-toc-section\" id=\"General-principles-of-field-oriented-control\"><\/span>General principles of field oriented control<span class=\"ez-toc-section-end\"><\/span><\/h2>\n\n\n\n<p>The&nbsp;Field Oriented Control (FOC)&nbsp;is a form of&nbsp;<a href=\"https:\/\/imperix.com\/doc\/implementation\/vector-current-control\">vector control<\/a>&nbsp;[1]. The machine currents, voltages, and magnetic fluxes are expressed as space vectors inside a Rotating Reference Frame (RRF). In the case of a synchronous machine, the stator and rotor fluxes are synchronous [2]. Therefore, a natural choice is to orient the RRF such that its d-axis is aligned with the rotor flux. The rotor position must be known to orient the RRF. The position is either measured with an encoder or estimated with a sensorless technique. Both options are presented in&nbsp;<a href=\"https:\/\/imperix.com\/doc\/help\/using-the-angle-decoder-modules\">PN104&nbsp;<\/a>and&nbsp;<a href=\"https:\/\/imperix.com\/doc\/implementation\/sliding-mode-observer-for-sensorless-pmsm-control\">TN136<\/a>, respectively. The working principle of FOC relies on the machine&#8217;s equations in that RRF. Let us first consider the stator equations of an isotropic PMSM in the RRF [2]:<\/p>\n\n\n\n<p>$$(1) \\qquad \\begin{array} \\displaystyle U_{ds} &amp;= R_s I_{ds} + \\cfrac{d \\Psi _{ds}}{dt} &#8211; \\omega _s \\Psi _{qs}\\\\[5pt] \\displaystyle U_{qs} &amp;= R_s I_{qs} + \\cfrac{d \\Psi _{qs}}{dt} + \\omega _s \\Psi _{ds}\\\\[5pt] \\displaystyle \\Psi _{ds} &amp;= L_d I_{ds} + \\Psi _{PM} \\\\[5pt] \\displaystyle \\Psi _{qs} &amp;= L_q I_{qs} \\end{array}$$<\/p>\n\n\n\n<p>Let us also consider the expression of the torque [2]:<\/p>\n\n\n\n<p>$$(2) \\qquad T_{em} = \\frac{3}{2} p (\\Psi _{ds} I_{qs} &#8211; \\Psi _{qs} I_{ds})$$<\/p>\n\n\n\n<p>Since the machine is assumed to be isotropic, \\(L_d = L_q = L_s\\), the equations from (1) and (2) can be re-arranged as such:<\/p>\n\n\n\n<p>$$(3) \\qquad  \\begin{array} \\displaystyle I_{ds}^* &amp;= \\cfrac{\\Psi _{ds}^* &#8211; \\Psi _{PM}}{L_s} \\\\[5pt] \\displaystyle I_{qs}^* &amp;= \\cfrac{T_{em}^*}{\\frac{3}{2} p \\Psi _{PM}} \\end{array}$$<\/p>\n\n\n\n<p>Equation (3) shows that the stator flux (d-axis component) and the torque can be controlled independently by the current\u00a0\\(I_{ds}\\)\u00a0and\u00a0\\(I_{qs}\\), respectively. The torque control sets the stator flux q-axis component since it is proportional to \\(I_{qs}\\).<\/p>\n\n\n\n<h3 class=\"wp-block-heading\" id=\"TN111:Fieldorientedcontrol(FOC)ofaPMSM-System-levelmodeling\"><span class=\"ez-toc-section\" id=\"System-level-modeling-of-the-field-oriented-control-algorithm\"><\/span>System-level modeling of the field oriented control algorithm<span class=\"ez-toc-section-end\"><\/span><\/h3>\n\n\n\n<p>The independent control of&nbsp;\\(I_{ds}\\)and&nbsp;\\(I_{qs}\\) can consist of two <a href=\"https:\/\/imperix.com\/doc\/implementation\/basic-pi-control\">PI regulators<\/a> with a decoupling network, as any vector control strategy [1]. The FOC algorithm usually generates voltage references that a PWM modulator transforms into gating signals for a voltage source inverter. In the present implementation, the rotor position measurement is derived from an incremental encoder. The figure below shows the complete block diagram of the implementation, with a <a href=\"https:\/\/imperix.com\/doc\/software\/carrier-based-pwm\">carrier-based PWM modulator<\/a> and an encoder\/decoder module. Please note that <a href=\"https:\/\/imperix.com\/doc\/implementation\/space-vector-modulation\">space vector modulation<\/a> could alternatively be used to improve the<a href=\"https:\/\/imperix.com\/doc\/implementation\/svpwm-vs-spwm-modulation-techniques\"> DC bus utilization<\/a>.<\/p>\n\n\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-large\"><img loading=\"lazy\" decoding=\"async\" width=\"556\" height=\"258\" src=\"https:\/\/imperix.com\/doc\/wp-content\/uploads\/2021\/03\/image-2.png\" alt=\"Block diagram of field oriented control\" class=\"wp-image-203\" srcset=\"https:\/\/imperix.com\/doc\/wp-content\/uploads\/2021\/03\/image-2.png 556w, https:\/\/imperix.com\/doc\/wp-content\/uploads\/2021\/03\/image-2-300x139.png 300w\" sizes=\"auto, (max-width: 556px) 100vw, 556px\" \/><figcaption class=\"wp-element-caption\">Block diagram of field oriented control (FOC)<\/figcaption><\/figure>\n<\/div>\n\n\n<h3 class=\"wp-block-heading\" id=\"TN111:Fieldorientedcontrol(FOC)ofaPMSM-Amoreintuitiveapproach\"><span class=\"ez-toc-section\" id=\"A-more-intuitive-approach\"><\/span>A more intuitive approach<span class=\"ez-toc-section-end\"><\/span><\/h3>\n\n\n\n<p>The d and q axes of a rotating reference frame have a physical meaning in the case of an electrical machine: the d-axis is&nbsp;<em>directly<\/em>&nbsp;aligned on a rotor magnetic pole and the q-axis is shifted from 90\u00b0E (electrical degrees), thus the name&nbsp;<em>quadrature axis<\/em>. As always, two magnetic poles of opposite polarity are shifted by 180\u00b0E.<\/p>\n\n\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-large\"><img loading=\"lazy\" decoding=\"async\" width=\"258\" height=\"216\" src=\"https:\/\/imperix.com\/doc\/wp-content\/uploads\/2021\/03\/image-3.png\" alt=\"Direct and quadrature axes\" class=\"wp-image-204\"\/><figcaption class=\"wp-element-caption\">Direct and quadrature axes<\/figcaption><\/figure>\n<\/div>\n\n\n<p>Referring to equation (1), the total stator flux \\(\\Psi _s\\) is divided into two parts: the flux \\(L_s \\, I_s\\) due to the stator current and the contribution \\(\\Psi _{PM}\\) from the rotor. If the magnetic poles of the stator are aligned with their opposite poles on the rotor, the system is at equilibrium and the stator flux vector \\(L_s \\, I_s\\) is aligned on the d-axis. Conversely, if the magnetic poles of the stator are not aligned with their opposite counterparts, their attractive and repulsive forces generate a torque on the rotor. In this case, the stator flux \\(L_s \\, I_s\\) is not aligned with the d-axis, and the angle difference between the two &#8211; commonly called the&nbsp;<em>load angle<\/em>&nbsp;(or&nbsp;<em>power angle<\/em>)&nbsp;[3] &#8211; is non-zero. In summary, the q-axis component of the stator flux contributes to the torque generation and the d-axis component only magnetizes the machine.<\/p>\n\n\n\n<div class=\"wp-block-columns is-layout-flex wp-container-core-columns-is-layout-9d6595d7 wp-block-columns-is-layout-flex\">\n<div class=\"wp-block-column is-layout-flow wp-block-column-is-layout-flow\"><div class=\"wp-block-image\">\n<figure class=\"aligncenter size-large\"><img loading=\"lazy\" decoding=\"async\" width=\"300\" height=\"197\" src=\"https:\/\/imperix.com\/doc\/wp-content\/uploads\/2022\/12\/magnetic_flux_vector_1.png\" alt=\"Alignment of the magnetic flux vector with zero torque\" class=\"wp-image-13728\"\/><figcaption class=\"wp-element-caption\">Alignment of the magnetic flux vector with zero torque<\/figcaption><\/figure>\n<\/div><\/div>\n\n\n\n<div class=\"wp-block-column is-layout-flow wp-block-column-is-layout-flow\"><div class=\"wp-block-image\">\n<figure class=\"aligncenter size-large\"><img loading=\"lazy\" decoding=\"async\" width=\"300\" height=\"197\" src=\"https:\/\/imperix.com\/doc\/wp-content\/uploads\/2022\/12\/magnetic_flux_vector_2.png\" alt=\"Alignment of the magnetic flux vector with maximum torque\" class=\"wp-image-13729\"\/><figcaption class=\"wp-element-caption\">Alignment of the magnetic flux vector with maximum torque<\/figcaption><\/figure>\n<\/div><\/div>\n<\/div>\n\n\n\n<h3 class=\"wp-block-heading\" id=\"TN111:Fieldorientedcontrol(FOC)ofaPMSM-Fluxandtorquecontrol\"><span class=\"ez-toc-section\" id=\"Flux-and-torque-control\"><\/span>Flux and torque control<span class=\"ez-toc-section-end\"><\/span><\/h3>\n\n\n\n<h4 class=\"wp-block-heading\" id=\"TN111:Fieldorientedcontrol(FOC)ofaPMSM-Plant\">Plant model<\/h4>\n\n\n\n<p>The phases of a PMSM at the stator being essentially RL circuits, the transfer functions linking the voltage to the current are:<\/p>\n\n\n\n<p>$$(4) \\qquad \\begin{array}{ll} H_d(s) &amp;= \\cfrac{I_{ds}(s)}{U_{ds}(s)} = \\cfrac{1\/R_s}{1 + s \\space L_d\/R_s} = \\cfrac{K_1}{1 + s \\space T_1}\\\\[5pt] H_q(s) &amp;= \\cfrac{I_{qs}(s)}{U_{qs}(s)} = \\cfrac{1\/R_s}{1 + s \\space L_q\/R_s} = \\cfrac{K_2}{1 + s \\space T_2}  \\end{array}$$<\/p>\n\n\n\n<h4 class=\"wp-block-heading\" id=\"TN111:Fieldorientedcontrol(FOC)ofaPMSM-Control\">Field oriented control implementation<\/h4>\n\n\n\n<p>The stator currents control consists of two digital PI controllers. Since the d and q axes are coupled, a decoupling network is necessary to achieve independent control of each current component, as developed&nbsp;in&nbsp;<a href=\"https:\/\/imperix.com\/doc\/implementation\/vector-current-control\">TN106<\/a>. The PI regulators can be tuned using the&nbsp;<em>magnitude optimum<\/em>&nbsp;criterion [4][5]:<\/p>\n\n\n\n<p>$$(5) \\qquad \\left\\{ \\begin{array} \\displaystyle T_n &amp;= T_1\\\\[5pt] \\displaystyle T_i &amp;= 2 \\space K_1 \\space T_{tot} \\\\[5pt] \\displaystyle K_p &amp;= T_n \\space \/ \\space T_i \\\\[5pt] \\displaystyle K_i &amp;= 1 \\space \/ \\space T_i \\end{array} \\right.$$<\/p>\n\n\n\n<p>The parameter&nbsp;\\(T_{tot}\\) represents the sum of all the small delays in the system. The product note&nbsp;<a href=\"https:\/\/imperix.com\/doc\/help\/discrete-control-delay\">PN142&nbsp;<\/a>explains how to determine the total delay of the system. A numerical example is given below.<\/p>\n\n\n\n<h4 class=\"wp-block-heading\" id=\"TN111:Fieldorientedcontrol(FOC)ofaPMSM-Fluxreference\">Flux reference<\/h4>\n\n\n\n<p>The field-oriented control (FOC) is mainly used as a torque controller. Therefore the d-axis current reference is usually set to zero, to maximize the torque production [1]. However, some flux optimization techniques set the d-axis current to a non-zero reference. For example, field weakening techniques reduce the stator flux on the d-axis to operate above the nominal speed.<\/p>\n\n\n\n<h2 class=\"wp-block-heading\" id=\"TN111:Fieldorientedcontrol(FOC)ofaPMSM-B-Box\/B-Boardimplementation\"><span class=\"ez-toc-section\" id=\"B-Box-B-Board-implementation\"><\/span>B-Box \/ B-Board implementation<span class=\"ez-toc-section-end\"><\/span><\/h2>\n\n\n\n<h3 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"Software-resources\"><\/span>Software resources<span class=\"ez-toc-section-end\"><\/span><\/h3>\n\n\n\n<div class=\"wp-block-file\"><a href=\"https:\/\/imperix.com\/doc\/wp-content\/uploads\/2021\/03\/TN111_Field_Oriented_Ctrl_of_PMSM.zip\">TN111_Field_Oriented_Ctrl_of_PMSM.zip<\/a><a href=\"https:\/\/imperix.com\/doc\/wp-content\/uploads\/2021\/03\/TN111_Field_Oriented_Ctrl_of_PMSM.zip\" class=\"wp-block-file__button wp-element-button\" download>Download<\/a><\/div>\n\n\n\n<div class=\"wp-block-simple-alerts-for-gutenberg-alert-boxes sab-alert sab-alert-info\" role=\"alert\">An implementation of field oriented control compatible with the Motor Testbench can be found in the <a href=\"https:\/\/imperix.com\/doc\/help\/motor-testbench-quick-start-guide\">Motor Testbench quick start guide (PN181)<\/a>. Also, a PLECS model is available for download in\u00a0<a href=\"https:\/\/imperix.com\/doc\/implementation\/motor-speed-control\">TN114<\/a>.<\/div>\n\n\n\n<h3 class=\"wp-block-heading\" id=\"TN111:Fieldorientedcontrol(FOC)ofaPMSM-ACGSDKforSimulink\"><span class=\"ez-toc-section\" id=\"ACG-SDK-for-Simulink\"><\/span>ACG SDK for Simulink<span class=\"ez-toc-section-end\"><\/span><\/h3>\n\n\n\n<h4 class=\"wp-block-heading\" id=\"TN111:Fieldorientedcontrol(FOC)ofaPMSM-Currentcontroller\">Current controller for field oriented control<\/h4>\n\n\n\n<p>The figure below shows a possible implementation of a current controller for FOC with Simulink. One can identify the two <a href=\"https:\/\/imperix.com\/doc\/implementation\/basic-pi-control\">PIs<\/a> for the d and q axes and the decoupling network in between. The saturation limits of the PIs are set dynamically, depending on the DC bus voltage.<\/p>\n\n\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-large is-resized\"><img loading=\"lazy\" decoding=\"async\" width=\"932\" height=\"1024\" src=\"https:\/\/imperix.com\/doc\/wp-content\/uploads\/2021\/03\/image-4-932x1024.png\" alt=\"Implementation of a current controller for field oriented control\" class=\"wp-image-207\" style=\"width:699px;height:768px\" title=\"dq current PI controller\" srcset=\"https:\/\/imperix.com\/doc\/wp-content\/uploads\/2021\/03\/image-4-932x1024.png 932w, https:\/\/imperix.com\/doc\/wp-content\/uploads\/2021\/03\/image-4-273x300.png 273w, https:\/\/imperix.com\/doc\/wp-content\/uploads\/2021\/03\/image-4-768x844.png 768w, https:\/\/imperix.com\/doc\/wp-content\/uploads\/2021\/03\/image-4.png 944w\" sizes=\"auto, (max-width: 932px) 100vw, 932px\" \/><figcaption class=\"wp-element-caption\">Implementation of a current controller for field oriented control (FOC)<\/figcaption><\/figure>\n<\/div>\n\n\n<h4 class=\"wp-block-heading\" id=\"TN111:Fieldorientedcontrol(FOC)ofaPMSM-TuningofthePIcontrollers\">Tuning of the PI controllers<\/h4>\n\n\n\n<p>Here is a complete numerical example of how to tune the <a href=\"https:\/\/imperix.com\/doc\/implementation\/basic-pi-control\">PI controllers<\/a> of the FOC. The machine parameters are presented in the&nbsp;<em>Experimental results<\/em>&nbsp;section. Since the available PMSM is isotropic, the inductance is the same on the d and q axes. Therefore, both PIs have the same following transfer function and the same tuning.<\/p>\n\n\n\n<p>$$(6) \\qquad H_d(s) = H_q(s) = \\frac{1\/R_s}{1 + s \\space L_d\/R_s} = \\frac{K_1}{1 + s \\space T_1} = \\frac{0.294 \\space \\Omega ^{-1}}{1 + s \\space 3.57 \\,\\text{ms}}$$<\/p>\n\n\n\n<p>As explained in the&nbsp;<a href=\"https:\/\/imperix.com\/doc\/help\/discrete-control-delay\">PN142<\/a>, the execution of the digital control is affected by a delay along the control chain. It can be subdivided into the following delays:<\/p>\n\n\n\n<p>$$(7) \\qquad \\left\\{ \\begin{array} \\displaystyle T_{sens} \\approx 0 \\\\[5pt] \\displaystyle T_{ctrl} = T_s = \\cfrac{1}{20 \\, \\text{kHz}} = 50 \\,\\text{\u00b5s}\\\\[5pt] \\displaystyle T_{PWM} = \\cfrac{T_{sw}}{2} = \\cfrac{1}{2 \\times 20 \\, \\text{kHz}} = 25 \\,\\text{\u00b5s} \\end{array}\\right.$$<\/p>\n\n\n\n<p>According to the information provided by <a href=\"https:\/\/imperix.com\/doc\/help\/cockpit-user-guide#h-targets-timings\">imperix Cockpit<\/a> (formerly&nbsp;the <a href=\"https:\/\/imperix.com\/doc\/help\/timing-info-tab\">Timing info<\/a>&nbsp;tab in&nbsp;BB Control), the cycle delay is less than 20% of a sampling period. Since the sampling phase was set to&nbsp;\\(\\phi_s=0.5\\), the condition&nbsp;\\(T_{cy}&lt;(1\u2212\\phi_s)T_s\\)&nbsp;is true. That is why the control delay is only 1 switching period.<\/p>\n\n\n\n<p>The total delay is then the sum of the small time constants:<\/p>\n\n\n\n<p>$$(8) \\qquad T_{tot} = T_{sens} + T_{ctrl} + T_{PWM} = 75 \\,\\text{\u00b5s}$$<\/p>\n\n\n\n<p>According to the&nbsp;magnitude optimum&nbsp;criterion, the parameters of the PIs are computed as:<\/p>\n\n\n\n<p>$$(9) \\qquad \n\\begin{array}\n\\displaystyle T_n &amp;= T_1 = 3.57 \\,\\text{ms} \\\\[5pt]\n\\displaystyle T_i &amp;= 2 \\space K_1 \\space T_{tot}  = 4.41 \\times 10^{-5} \\,\\Omega ^{-1}\\,\\text{s}\\\\[5pt]\n\\displaystyle K_p &amp;= T_n \\space \/ \\space T_i = 80.95 \\,\\Omega\\\\[5pt]\n\\displaystyle K_i &amp;= 1 \\space \/ \\space T_i = 22675.7\\,\\Omega\\,\\text{s}^{-1}\n\\end{array}$$<\/p>\n\n\n\n<h3 class=\"wp-block-heading\" id=\"TN111:Fieldorientedcontrol(FOC)ofaPMSM-Experimentalresults\"><span class=\"ez-toc-section\" id=\"Experimental-results-of-the-field-oriented-control\"><\/span>Experimental results of the field oriented control<span class=\"ez-toc-section-end\"><\/span><\/h3>\n\n\n\n<p>The experimental setup consists of a PMSM supplied by a voltage source inverter controlled by a&nbsp;<a href=\"https:\/\/imperix.com\/products\/control\/bbox\/\">B-Box prototyping controller<\/a>. The FOC algorithm is implemented using the&nbsp;<a href=\"https:\/\/imperix.com\/software\/acg-sdk\/\">graphical programming of the ACG SDK<\/a>&nbsp;library for Simulink. The power converter is built from 4x&nbsp;<a href=\"https:\/\/imperix.com\/products\/power\/peb\/\">PEB 8032 phase-leg modules<\/a>&nbsp;(3 phases and 1 braking chopper leg). Another PMSM connected to 3 power resistors is used as a brake to generate a load torque.<\/p>\n\n\n\n<div class=\"wp-block-simple-alerts-for-gutenberg-alert-boxes sab-alert sab-alert-info\" role=\"alert\">The <a href=\"https:\/\/imperix.com\/products\/electric-motor-drive-bundle\/\">electric motor drive bundle<\/a> has superseded the equipment used in this section.<\/div>\n\n\n\n<div class=\"wp-block-simple-alerts-for-gutenberg-alert-boxes sab-alert sab-alert-success\" role=\"alert\">General\u00a0<strong>safety-related recommendations<\/strong>\u00a0for operating power converters in a laboratory environment are given in\u00a0<a href=\"https:\/\/imperix.com\/doc\/implementation\/safety-and-protection-in-the-lab\">TN181<\/a>.<\/div>\n\n\n\n<div class=\"wp-block-columns is-layout-flex wp-container-core-columns-is-layout-9d6595d7 wp-block-columns-is-layout-flex\">\n<div class=\"wp-block-column is-layout-flow wp-block-column-is-layout-flow\">\n<figure class=\"wp-block-image size-large\"><img loading=\"lazy\" decoding=\"async\" width=\"380\" height=\"369\" src=\"https:\/\/imperix.com\/doc\/wp-content\/uploads\/2021\/03\/image-5.png\" alt=\"Power converter and controller\" class=\"wp-image-208\" srcset=\"https:\/\/imperix.com\/doc\/wp-content\/uploads\/2021\/03\/image-5.png 380w, https:\/\/imperix.com\/doc\/wp-content\/uploads\/2021\/03\/image-5-300x291.png 300w\" sizes=\"auto, (max-width: 380px) 100vw, 380px\" \/><figcaption class=\"wp-element-caption\">PMSM drive test bench with a digital controller<\/figcaption><\/figure>\n<\/div>\n\n\n\n<div class=\"wp-block-column is-vertically-aligned-center is-layout-flow wp-block-column-is-layout-flow\"><div class=\"wp-block-image\">\n<figure class=\"aligncenter size-large\"><img loading=\"lazy\" decoding=\"async\" width=\"380\" height=\"164\" src=\"https:\/\/cdn.imperix.com\/doc\/wp-content\/uploads\/2021\/03\/testbench_photo_machines.png\" alt=\"Motor bench and brake\" class=\"wp-image-7654\" srcset=\"https:\/\/imperix.com\/doc\/wp-content\/uploads\/2021\/03\/testbench_photo_machines.png 380w, https:\/\/imperix.com\/doc\/wp-content\/uploads\/2021\/03\/testbench_photo_machines-300x129.png 300w\" sizes=\"auto, (max-width: 380px) 100vw, 380px\" \/><figcaption class=\"wp-element-caption\">Motor bench and brake<\/figcaption><\/figure>\n<\/div><\/div>\n<\/div>\n\n\n\n<h4 class=\"wp-block-heading\" id=\"TN111:Fieldorientedcontrol(FOC)ofaPMSM-Machineparameters\">Machine parameters<\/h4>\n\n\n\n<p>The implemented field-oriented control algorithm was validated experimentally on a <a href=\"https:\/\/acim.nidec.com\/en\/motors\/leroy-somer\/Products\/servomotors\">Unimotor fm servomotor<\/a> from Control Techniques.<\/p>\n\n\n\n<figure class=\"wp-block-table is-style-stripes\"><table><tbody><tr><td><strong>Parameter<\/strong><\/td><td><strong>Value<\/strong><\/td><td><strong>Unit<\/strong><\/td><\/tr><tr><td>Rated power<\/td><td>1.23<\/td><td>kW<\/td><\/tr><tr><td>Pole pairs<\/td><td>3<\/td><td>&#8211;<\/td><\/tr><tr><td>Rated phase voltage<\/td><td>460<\/td><td>V<\/td><\/tr><tr><td>Rated phase current<\/td><td>2.7<\/td><td>A<\/td><\/tr><tr><td>Rated mechanical speed<\/td><td>314<\/td><td>rad\/s<\/td><\/tr><tr><td>Rated torque<\/td><td>3.9<\/td><td>Nm<\/td><\/tr><tr><td>Stator resistance<\/td><td>3.4<\/td><td>Ohm<\/td><\/tr><tr><td>Stator inductance (d and q axis)<\/td><td>12.15<\/td><td>mH<\/td><\/tr><tr><td>Permanent magnet flux<\/td><td>0.25<\/td><td>Wb<\/td><\/tr><tr><td>Moment of inertia (PMSM only)<\/td><td>2.9<\/td><td>kg cm<sup>2<\/sup><\/td><\/tr><\/tbody><\/table><figcaption class=\"wp-element-caption\">Parameter table of Control Techniques 095U2B300BACAA100190<\/figcaption><\/figure>\n\n\n\n<h4 class=\"wp-block-heading\" id=\"TN111:Fieldorientedcontrol(FOC)ofaPMSM-Testconditions\">Test conditions<\/h4>\n\n\n\n<ul class=\"wp-block-list\">\n<li>Load torque: 3.9 Nm (PMSM with resistors as load)<\/li>\n\n\n\n<li>Inverter DC link voltage: 500 V<\/li>\n\n\n\n<li>Control and sampling frequency: 20 kHz<\/li>\n\n\n\n<li>Sampling phase: 0.5<\/li>\n\n\n\n<li>PWM outputs: carrier-based<\/li>\n\n\n\n<li>Current measurements filtered with a 1.6 kHz cut-off frequency (using the front panel of the B-Box RCP)<\/li>\n<\/ul>\n\n\n\n<h4 class=\"wp-block-heading\" id=\"TN111:Fieldorientedcontrol(FOC)ofaPMSM-Results\">Experimental results of field oriented control<\/h4>\n\n\n\n<p>The tracking performance of the torque control was validated experimentally on a modular three-phase inverter by performing a reference step from -1 Nm to 3.9 Nm (nominal torque). The current controllers on both axes can follow their respective references with fast dynamics and no overshoot.<\/p>\n\n\n\n<figure class=\"wp-block-image size-large\"><img loading=\"lazy\" decoding=\"async\" width=\"800\" height=\"300\" src=\"https:\/\/imperix.com\/doc\/wp-content\/uploads\/2021\/03\/image-7.png\" alt=\"Field oriented control experimental results - current tracking performance\" class=\"wp-image-210\" title=\"Current tracking performance\" srcset=\"https:\/\/imperix.com\/doc\/wp-content\/uploads\/2021\/03\/image-7.png 800w, https:\/\/imperix.com\/doc\/wp-content\/uploads\/2021\/03\/image-7-300x113.png 300w, https:\/\/imperix.com\/doc\/wp-content\/uploads\/2021\/03\/image-7-768x288.png 768w\" sizes=\"auto, (max-width: 800px) 100vw, 800px\" \/><figcaption class=\"wp-element-caption\">Experimental results for the field-oriented control (FOC) of a PMSM &#8211; current tracking performance<\/figcaption><\/figure>\n\n\n\n<p>The corresponding phase currents are also shown below. Since the current on the d-axis is zero, the q-axis current corresponds to the envelope of the phase currents.<\/p>\n\n\n\n<figure class=\"wp-block-image size-large\"><img loading=\"lazy\" decoding=\"async\" width=\"800\" height=\"300\" src=\"https:\/\/imperix.com\/doc\/wp-content\/uploads\/2021\/03\/image-8.png\" alt=\"Field oriented control experimental results - phase current\" class=\"wp-image-211\" title=\"Motor phase currents\" srcset=\"https:\/\/imperix.com\/doc\/wp-content\/uploads\/2021\/03\/image-8.png 800w, https:\/\/imperix.com\/doc\/wp-content\/uploads\/2021\/03\/image-8-300x113.png 300w, https:\/\/imperix.com\/doc\/wp-content\/uploads\/2021\/03\/image-8-768x288.png 768w\" sizes=\"auto, (max-width: 800px) 100vw, 800px\" \/><figcaption class=\"wp-element-caption\">Experimental results for the field-oriented control (FOC) of a PMSM &#8211; phase currents<\/figcaption><\/figure>\n\n\n\n<h2 class=\"wp-block-heading\" id=\"TN111:Fieldorientedcontrol(FOC)ofaPMSM-Academicreferences\"><span class=\"ez-toc-section\" id=\"Academic-references\"><\/span>Academic references<span class=\"ez-toc-section-end\"><\/span><\/h2>\n\n\n\n<p>[1] Nguyen Phung Quang, J\u00f6rg-Andreas Dittrich, &#8220;Vector Control of Three-Phase AC Machines&#8221;, Springer, 2015, ISBN 978-3-662-46914-9<br>[2] Slobodan N. Vukosavic, &#8220;Electrical Machines&#8221;, Springer, 2013, DOI 10.1007\/978-1-4614-0400-2<br>[3] Jan A. Melkebeek, &#8220;Electrical Machines and Drives: Fundamentals and Advanced Modelling&#8221;, Springer, 2018, ISBN 978-3-319-72729-5<br>[4] Hansruedi B\u00fchler, &#8220;R\u00e9glage de syst\u00e8mes d&#8217;\u00e9lectronique de puissance &#8211; Volume 1: th\u00e9orie&#8221;, Presses Polytechniques et Universitaires Romandes, 1997, ISBN-10: 2-88074-341-9<br>[5] Karl J. \u00c5str\u00f6m and Tore H\u00e4gglund; \u201cAdvanced PID Control\u201d; 1995<\/p>\n","protected":false},"excerpt":{"rendered":"<p>The Field-Oriented Control (FOC) method is a motor control strategy that orients the stator current vector in a rotating reference frame of the machine.<\/p>\n","protected":false},"author":8,"featured_media":3036,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"_acf_changed":false,"_kad_post_transparent":"","_kad_post_title":"","_kad_post_layout":"","_kad_post_sidebar_id":"","_kad_post_content_style":"","_kad_post_vertical_padding":"","_kad_post_feature":"","_kad_post_feature_position":"","_kad_post_header":false,"_kad_post_footer":false,"_kad_post_classname":"","footnotes":""},"categories":[4],"tags":[18],"software-environments":[103],"provided-results":[108],"related-products":[50,32,166,114,111],"guidedreadings":[60,119],"tutorials":[124],"user-manuals":[],"coauthors":[62],"class_list":["post-201","post","type-post","status-publish","format-standard","has-post-thumbnail","hentry","category-implementation","tag-motor-drives","software-environments-matlab","provided-results-experimental","related-products-acg-sdk","related-products-b-box-rcp","related-products-b-box-rcp-3-0","related-products-motor","related-products-pm","guidedreadings-electric-car-motor-control","guidedreadings-wind-turbine-generator-control-using-a-sensorless-algorithm","tutorials-field-oriented-control"],"acf":[],"yoast_head":"<!-- This site is optimized with the Yoast SEO plugin v27.4 - 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