{"id":423,"date":"2021-03-25T08:00:28","date_gmt":"2021-03-25T08:00:28","guid":{"rendered":"https:\/\/imperix.com\/doc\/?p=423"},"modified":"2025-12-17T14:42:45","modified_gmt":"2025-12-17T14:42:45","slug":"motor-speed-control","status":"publish","type":"post","link":"https:\/\/imperix.com\/doc\/implementation\/motor-speed-control","title":{"rendered":"Motor speed control"},"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\/motor-speed-control\/#General-principles-of-motor-speed-control\" >General principles of motor speed 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\/motor-speed-control\/#Tuning-of-the-digital-speed-control\" >Tuning of the digital speed control<\/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\/motor-speed-control\/#Cascaded-motor-torque-and-speed-control\" >Cascaded motor torque and speed control<\/a><\/li><\/ul><\/li><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-4\" href=\"https:\/\/imperix.com\/doc\/implementation\/motor-speed-control\/#Speed-control-implementation-with-ACG-SDK-on-Simulink\" >Speed control implementation with ACG SDK on Simulink<\/a><ul class='ez-toc-list-level-3' ><li class='ez-toc-heading-level-3'><a class=\"ez-toc-link ez-toc-heading-5\" href=\"https:\/\/imperix.com\/doc\/implementation\/motor-speed-control\/#Experimental-results\" >Experimental results<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-3'><a class=\"ez-toc-link ez-toc-heading-6\" href=\"https:\/\/imperix.com\/doc\/implementation\/motor-speed-control\/#Motor-parameters\" >Motor parameters<\/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\/motor-speed-control\/#Test-conditions\" >Test conditions<\/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\/motor-speed-control\/#Results\" >Results<\/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\/motor-speed-control\/#Academic-references\" >Academic references<\/a><\/li><\/ul><\/nav><\/div>\n\n<p>This technical note explains how to implement speed control for an electric motor. First, the note introduces the general operating principles of motor speed control, regardless of which type of motor is used. Then, the speed controller is tuned using the symmetrical optimum method. Finally, a practical control implementation on a laboratory-scale electric drive (motor and inverter) is introduced, targeting the&nbsp;<a href=\"https:\/\/imperix.com\/products\/control\/bbox\">B-Box RCP<\/a>&nbsp;or&nbsp;<a href=\"https:\/\/imperix.com\/products\/control\/bboard\">B-Board PRO<\/a>&nbsp;with&nbsp;the&nbsp;<a href=\"https:\/\/imperix.com\/software\/acg-sdk\/simulink\/\">ACG SDK on Simulink<\/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<\/a>.<\/p>\n\n\n\n<figure class=\"wp-block-embed is-type-video is-provider-youtube wp-block-embed-youtube wp-embed-aspect-16-9 wp-has-aspect-ratio\"><div class=\"wp-block-embed__wrapper\">\n<iframe loading=\"lazy\" title=\"Motor control examples - Testbench overview\" width=\"720\" height=\"405\" src=\"https:\/\/www.youtube.com\/embed\/NgeNpTzvIcU?feature=oembed\" frameborder=\"0\" allow=\"accelerometer; autoplay; clipboard-write; encrypted-media; gyroscope; picture-in-picture; web-share\" referrerpolicy=\"strict-origin-when-cross-origin\" allowfullscreen><\/iframe>\n<\/div><\/figure>\n\n\n\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"General-principles-of-motor-speed-control\"><\/span>General principles of motor speed control<span class=\"ez-toc-section-end\"><\/span><\/h2>\n\n\n\n<p>An electric motor can be modeled mechanically as a rotating mass. Its inertia&nbsp;\\(J_m\\)&nbsp;can be rotated by applying a torque on it, which is the difference between electromagnetic torque&nbsp;\\(T_{em}\\)&nbsp;and a load torque&nbsp;\\(T_L\\). The load is external to the motor and cannot be controlled. However, the speed&nbsp;\u03c9m&nbsp;of the motor can be changed by controlling the electromagnetic torque.<\/p>\n\n\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-large\"><img loading=\"lazy\" decoding=\"async\" width=\"326\" height=\"116\" src=\"https:\/\/imperix.com\/doc\/wp-content\/uploads\/2021\/03\/image-48.png\" alt=\"Rotating machine physics\" class=\"wp-image-430\" title=\"Rotating mass momentum balance\" srcset=\"https:\/\/imperix.com\/doc\/wp-content\/uploads\/2021\/03\/image-48.png 326w, https:\/\/imperix.com\/doc\/wp-content\/uploads\/2021\/03\/image-48-300x107.png 300w\" sizes=\"auto, (max-width: 326px) 100vw, 326px\" \/><figcaption class=\"wp-element-caption\">Rotating motor physics<\/figcaption><\/figure>\n<\/div>\n\n\n<p>The relation between the speed, the inertia, and the torque is formalized by the second law of Newton for&nbsp;rotational movement&nbsp;[1]:<\/p>\n\n\n\n<p>$$(1) \\qquad k_F \\omega _m + J_{m} \\frac{d \\omega _m}{dt} = T_{em} &#8211; T_L $$<\/p>\n\n\n\n<p>\\(T_L\\)&nbsp;is the external load torque applied to the shaft and&nbsp;\\(k_F \\omega_m\\)&nbsp;is the torque due to the friction. The transfer function linking the torque to the speed is then:<\/p>\n\n\n\n<p>$$(2) \\qquad H_1 (s) = \\frac{\\omega _m(s)}{T_{em}(s) &#8211; T_L} = \\frac{1\/k_F}{1 + s \\space J_m\/k_F} = \\frac{K_{1}}{1 + s \\space T_{1}} $$<\/p>\n\n\n\n<p>In most applications, the&nbsp;effect of friction is negligible in comparison to the load and motor torque. In this case, the transfer function simplifies to:<\/p>\n\n\n\n<p>$$ (3) \\qquad H_2 (s) = \\frac{\\omega _m(s)}{T_{em}(s) &#8211; T_L} = \\frac{1}{s \\space J_m} = \\frac{1}{s \\space T_{2}} $$<\/p>\n\n\n\n<h3 class=\"wp-block-heading\" id=\"TN114:Motorspeedcontrol-Tuningofthedigitalcontrol\"><span class=\"ez-toc-section\" id=\"Tuning-of-the-digital-speed-control\"><\/span>Tuning of the digital speed control<span class=\"ez-toc-section-end\"><\/span><\/h3>\n\n\n\n<p>According to the transfer function derived above, the plant is a 1<sup>st<\/sup>&nbsp;order system. Therefore, a PI controller is sufficient to follow a constant reference with no permanent error.&nbsp;Since the simplified plant from (3) contains a pure integrator, the proportional and integral terms are tuned using the&nbsp;<em>symmetrical optimum<\/em>&nbsp;criterion [1][2].<\/p>\n\n\n\n<p>$$(4) \\qquad \\left\\{\n\\begin{array}\n\\displaystyle T_n &amp;= 4 \\space T_{tot}\\\\[5pt]\n\\displaystyle T_i &amp;= 8 \\space T_{tot}^2 \/ T_2\\\\[5pt]\n\\displaystyle K_p &amp;= T_n \\space \/ \\space T_i \\\\[5pt]\n\\displaystyle K_i &amp;= 1 \\space \/ \\space T_i\n\\end{array} \\right. $$<\/p>\n\n\n\n<p>The parameter&nbsp;Ttot&nbsp;represents the total delay of the discrete control, which can be computed using the&nbsp;<a href=\"https:\/\/imperix.com\/doc\/help\/discrete-control-delay\">PN142<\/a>. An numerical example is presented below.<\/p>\n\n\n\n<p>The&nbsp;<em>symmetrical optimum<\/em>&nbsp;criterion is sensitive to abrupt changes on the reference value. In this case, a&nbsp;setpoint corrector&nbsp;can be used in order to reduce the overshoot [2]:<\/p>\n\n\n\n<p>$$(5) \\qquad H_{setpoint,corrector}(s) = \\frac{1}{1 + s \\space T_2}  $$<\/p>\n\n\n\n<p>An alternative is to use a&nbsp;rate limiter&nbsp;to limit the variation rate of the motor speed reference.<\/p>\n\n\n\n<h3 class=\"wp-block-heading\" id=\"TN114:Motorspeedcontrol-Cascadedcontrol\"><span class=\"ez-toc-section\" id=\"Cascaded-motor-torque-and-speed-control\"><\/span>Cascaded motor torque and speed control<span class=\"ez-toc-section-end\"><\/span><\/h3>\n\n\n\n<p>The motor speed controller generates only a torque reference and, therefore, must be cascaded with a torque controller in order to produce an effect on the motor. The torque controller can be implemented using, for instance, <a href=\"https:\/\/imperix.com\/doc\/implementation\/field-oriented-control-of-permanent-magnet-synchronous-machine\">Field-Oriented Control<\/a> or Direct Torque Control (<a href=\"https:\/\/imperix.com\/doc\/example\/direct-torque-control\">AN004<\/a>).<\/p>\n\n\n\n<p>As developed above, the tuning of the speed controller depends on the total control delay, which can be computed as in&nbsp;<a href=\"https:\/\/imperix.com\/doc\/help\/discrete-control-delay\">PN142<\/a>. In the case of the motor speed control, the speed controller is the outer control loop and the torque controller is the inner loop.<\/p>\n\n\n\n<p>The overall cascaded control diagram is shown below.<\/p>\n\n\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-large\"><img loading=\"lazy\" decoding=\"async\" width=\"493\" height=\"198\" src=\"https:\/\/imperix.com\/doc\/wp-content\/uploads\/2021\/03\/image-49.png\" alt=\"Motor speed control - cascaded control diagram\" class=\"wp-image-503\" title=\"Speed and torque cascaded controllers\" srcset=\"https:\/\/imperix.com\/doc\/wp-content\/uploads\/2021\/03\/image-49.png 493w, https:\/\/imperix.com\/doc\/wp-content\/uploads\/2021\/03\/image-49-300x120.png 300w\" sizes=\"auto, (max-width: 493px) 100vw, 493px\" \/><figcaption class=\"wp-element-caption\">Motor speed control &#8211; cascaded control diagram<\/figcaption><\/figure>\n<\/div>\n\n\n<h2 class=\"wp-block-heading\" id=\"TN114:Motorspeedcontrol-B-Box\/B-Boardimplementation\"><span class=\"ez-toc-section\" id=\"Speed-control-implementation-with-ACG-SDK-on-Simulink\"><\/span>Speed control implementation with ACG SDK on Simulink<span class=\"ez-toc-section-end\"><\/span><\/h2>\n\n\n\n<p>The <a href=\"https:\/\/imperix.com\/software\/acg-sdk\/\">ACG SDK<\/a> is a toolbox for Simulink and PLECS that enables quick and easy graphical programming of a B-Box or B-Board <a href=\"https:\/\/imperix.com\/products\/power-electronic-controllers\/\">power electronics controller<\/a>. This section describes the motor speed control implementation and its experimental validation with imperix prototyping tools. The Simulink and PLECS models can be downloaded below:<\/p>\n\n\n\n<div class=\"wp-block-file\"><a href=\"https:\/\/imperix.com\/doc\/wp-content\/uploads\/2021\/03\/TN114_Motor_Speed_Control.zip\">TN114_Motor_Speed_Control_simulink.zip<\/a><a href=\"https:\/\/imperix.com\/doc\/wp-content\/uploads\/2021\/03\/TN114_Motor_Speed_Control.zip\" class=\"wp-block-file__button wp-element-button\" download>Download<\/a><\/div>\n\n\n\n<div class=\"wp-block-file\"><a href=\"https:\/\/imperix.com\/doc\/wp-content\/uploads\/2021\/03\/TN114_Motor_Speed_Control.plecs\">TN114_Motor_Speed_Control.plecs<\/a><a href=\"https:\/\/imperix.com\/doc\/wp-content\/uploads\/2021\/03\/TN114_Motor_Speed_Control.plecs\" class=\"wp-block-file__button wp-element-button\" download>Download<\/a><\/div>\n\n\n\n<h4 class=\"wp-block-heading\" id=\"TN114:Motorspeedcontrol-Cascadedcontrol.1\">Cascaded motor speed control<\/h4>\n\n\n\n<p>The figure below shows the implementation of a cascaded control structure with a Field-Oriented Control as the torque controller. A Finite State Machine (FSM) oversees the operation of the motor. In particular, the FSM receives the desired speed (in rpm) from the user and limits its variation rate to reduce the overshoot of the speed controller.<\/p>\n\n\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-large is-resized\"><img loading=\"lazy\" decoding=\"async\" width=\"522\" height=\"442\" src=\"https:\/\/imperix.com\/doc\/wp-content\/uploads\/2021\/03\/image-50.png\" alt=\"Simulink implementation of cascaded speed control\" class=\"wp-image-505\" style=\"width:392px;height:332px\" title=\"Speed and torque controllers Simulink model\" srcset=\"https:\/\/imperix.com\/doc\/wp-content\/uploads\/2021\/03\/image-50.png 522w, https:\/\/imperix.com\/doc\/wp-content\/uploads\/2021\/03\/image-50-300x254.png 300w\" sizes=\"auto, (max-width: 522px) 100vw, 522px\" \/><figcaption class=\"wp-element-caption\">Simulink implementation of cascaded motor speed control<\/figcaption><\/figure>\n<\/div>\n\n\n<h4 class=\"wp-block-heading\" id=\"TN114:Motorspeedcontrol-Speedcontroller\">Motor speed controller structure<\/h4>\n\n\n\n<p>In this application example, the speed controller is executed 100 times slower than the torque control. This way, the torque controller has enough time at its disposal to regulate the stator currents before the reference from the speed control is updated. Notice that with FOC, the torque reference must be translated into a current reference, using the equation developed in&nbsp;<a href=\"https:\/\/imperix.com\/doc\/implementation\/field-oriented-control-of-permanent-magnet-synchronous-machine\">TN111<\/a>.<\/p>\n\n\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-large is-resized\"><img loading=\"lazy\" decoding=\"async\" width=\"533\" height=\"464\" src=\"https:\/\/imperix.com\/doc\/wp-content\/uploads\/2021\/03\/image-51.png\" alt=\"Task decimation in Simulink\" class=\"wp-image-507\" style=\"width:400px;height:348px\" title=\"Speed controller Simulink model\" srcset=\"https:\/\/imperix.com\/doc\/wp-content\/uploads\/2021\/03\/image-51.png 533w, https:\/\/imperix.com\/doc\/wp-content\/uploads\/2021\/03\/image-51-300x261.png 300w\" sizes=\"auto, (max-width: 533px) 100vw, 533px\" \/><figcaption class=\"wp-element-caption\">Task decimation in Simulink<\/figcaption><\/figure>\n<\/div>\n\n\n<h4 class=\"wp-block-heading\" id=\"TN114:Motorspeedcontrol-Tuningofthespeedcontroller\">Tuning of the motor speed controller<\/h4>\n\n\n\n<p>Here is a complete numerical example of how to tune the PI of the digital speed control loop. The motor parameters are presented in the&nbsp;<em>Experimental results<\/em>&nbsp;section.<\/p>\n\n\n\n<p>The tuning of the inner loop of the cascaded control is detailed in&nbsp;<a href=\"https:\/\/imperix.com\/doc\/implementation\/field-oriented-control-of-permanent-magnet-synchronous-machine\">TN111<\/a>. As a reminder:<\/p>\n\n\n\n<p>$$(6) \\qquad \\left\\{ \\begin{array}  \\displaystyle T_{tot,inner-loop} &amp;= 75 \\,\\text{\u00b5s}\\\\ \\displaystyle K_{p,inner-loop} &amp;= 80.95 \\,\\Omega\\\\ \\displaystyle K_{i,inner-loop} &amp;= 22675.7 \\,\\Omega\\,\\text{s}^{-1} \\end{array} \\right. $$<\/p>\n\n\n\n<p>The first step is to identify the transfer function of the speed controller:<\/p>\n\n\n\n<p>$$(7) \\qquad H_2 (s) = \\frac{1}{s \\space J_m} = \\frac{1}{s \\space T_{2}} = \\frac{1}{s \\space 2.9 \\times 10^{-4} \\,\\text{kg} \\,\\text{m}^2} $$<\/p>\n\n\n\n<p>The determination of the delays along the control chain of a cascaded control is explained in&nbsp;<a href=\"https:\/\/imperix.com\/doc\/help\/discrete-control-delay\">PN142<\/a>. In this Simulink implementation, the outer-loop was chosen to the&nbsp;N=100&nbsp;times slower than the inner-loop. Consequently, the various delays are:<\/p>\n\n\n\n<p>$$(8) \\qquad \\left\\{ \\begin{array} \\displaystyle T_{sens} \\approx 0 \\\\[5pt] \\displaystyle T_{ctrl} = N \\times T_s = \\cfrac{100}{20 \\, \\text{kHz}} = 5 \\,\\text{ms}\\\\[5pt] \\displaystyle T_{PWM} = \\cfrac{T_{sw}}{2} = \\cfrac{1}{2 \\times 20 \\, \\text{kHz}} = 25 \\,\\text{\u00b5s} \\end{array}\\right.$$<\/p>\n\n\n\n<p>The total delay of the outer-loop is then the sum of the small time constants:<\/p>\n\n\n\n<p>$$(9) \\qquad T_{tot} = T_{sens} + T_{ctrl} + T_{PWM} = 5.025 \\,\\text{ms} $$<\/p>\n\n\n\n<p>According the&nbsp;<em>symmetrical optimum<\/em>&nbsp;criterion, the parameters of the PIs are computed as:<\/p>\n\n\n\n<p>$$(10) \\qquad \\left\\{\n\\begin{array}\n\\displaystyle T_n &amp;= 4 \\space T_{tot} = 20.1 \\,\\text{ms}\\\\[5pt]\n\\displaystyle T_i &amp;= 8 \\space \\frac{T_{tot}^2}{T_2} = 0.697 \\,(\\text{N}\\,\\text{m})^{-1} \\\\[5pt]\n\\displaystyle K_p &amp;= T_n \\space \/ \\space T_i = 0.029 \\, \\text{N}\\,\\text{m}\\,\\text{s}\\\\[5pt]\n\\displaystyle K_i &amp;= 1 \\space \/ \\space T_i = 1.43 \\,\\text{N}\\,\\text{m}\n\\end{array} \\right. $$<\/p>\n\n\n\n<h3 class=\"wp-block-heading\" id=\"TN114:Motorspeedcontrol-Experimentalresults\"><span class=\"ez-toc-section\" id=\"Experimental-results\"><\/span>Experimental results<span class=\"ez-toc-section-end\"><\/span><\/h3>\n\n\n\n<p>The experimental setup consists of a PMSM supplied by voltage source inverter controlled by a&nbsp;<a href=\"https:\/\/imperix.com\/products\/control\/bbox\/\">B-Box prototyping controller<\/a>. The FOC control is implemented using the&nbsp;<a href=\"https:\/\/imperix.com\/software\/acg-sdk\/\">graphical programming of 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 a brake to generate a load torque.<\/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\">\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\">Electric motor drive est bench with inverter 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\">\n<figure class=\"wp-block-image 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>\n<\/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<h3 class=\"wp-block-heading\" id=\"TN114:Motorspeedcontrol-Machineparameters\"><span class=\"ez-toc-section\" id=\"Motor-parameters\"><\/span>Motor parameters<span class=\"ez-toc-section-end\"><\/span><\/h3>\n\n\n\n<p>The motor speed controller was validated on a <a href=\"https:\/\/acim.nidec.com\/en\/motors\/leroy-somer\/Products\/servomotors\">Unimotor fm<\/a> Permanent Magnets Synchronous Motor (PMSM) 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 that encircles the stator winding<\/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\">Physical parameters of motor: Control techniques 095U2B300BACAA100190<\/figcaption><\/figure>\n\n\n\n<h3 class=\"wp-block-heading\" id=\"TN114:Motorspeedcontrol-Testconditions\"><span class=\"ez-toc-section\" id=\"Test-conditions\"><\/span>Test conditions<span class=\"ez-toc-section-end\"><\/span><\/h3>\n\n\n\n<ul class=\"wp-block-list\">\n<li>Load torque: 2 Nm (PMSM with resistors as load)<\/li>\n\n\n\n<li>DC link voltage: 500 V<\/li>\n\n\n\n<li>Inverter: 4x PEB8032 (one leg for braking chopper)<\/li>\n\n\n\n<li>Interrupt 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>Torque control technique: Field-Oriented Control (FOC)<\/li>\n<\/ul>\n\n\n\n<h3 class=\"wp-block-heading\" id=\"TN114:Motorspeedcontrol-Results\"><span class=\"ez-toc-section\" id=\"Results\"><\/span>Results<span class=\"ez-toc-section-end\"><\/span><\/h3>\n\n\n\n<p>The tracking performance of the motor speed controller was validated experimentally by applying a speed reference step from 0 to 1500 rpm. The experiment was performed twice, with two different rate limits on the speed reference.<\/p>\n\n\n\n<p>At first, the&nbsp;rate limiter&nbsp;was set to 100000 rpm\/s. As shown below, the PMSM is unable to accelerate at this rate because the speed controller hits its upper saturation limit (1.1 pu of the nominal torque). Additionally, the tuning from the&nbsp;<em>symmetrical optimum<\/em>&nbsp;criterion leads to an overshoot of 21%.<\/p>\n\n\n\n<p>For the second run, the reference variation was limited to 5000 rpm\/s. In this case, the speed control is able to follow the acceleration of the speed reference. Since the control uses a 1<sup>st<\/sup>&nbsp;order PI controller, it is not able to completely eliminate the tracking error during the ramp. However, this has the advantage that the mechanical stress on the motor is also reduced since the control does not abruptly apply a high torque at startup. What&#8217;s more, the overshoot is also reduced to only 4.7%. The only drawback compared to the first experiment is the&nbsp;prolonged&nbsp;settling time of 0.4 s, compared to 0.3 s.<\/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-52.png\" alt=\"Speed tracking results of motor speed control\" class=\"wp-image-508\" title=\"Speed tracking performance\" srcset=\"https:\/\/imperix.com\/doc\/wp-content\/uploads\/2021\/03\/image-52.png 800w, https:\/\/imperix.com\/doc\/wp-content\/uploads\/2021\/03\/image-52-300x113.png 300w, https:\/\/imperix.com\/doc\/wp-content\/uploads\/2021\/03\/image-52-768x288.png 768w\" sizes=\"auto, (max-width: 800px) 100vw, 800px\" \/><\/figure>\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-53.png\" alt=\"Speed motor control, torque reference and estimation\" class=\"wp-image-509\" title=\"Motor torque control\" srcset=\"https:\/\/imperix.com\/doc\/wp-content\/uploads\/2021\/03\/image-53.png 800w, https:\/\/imperix.com\/doc\/wp-content\/uploads\/2021\/03\/image-53-300x113.png 300w, https:\/\/imperix.com\/doc\/wp-content\/uploads\/2021\/03\/image-53-768x288.png 768w\" sizes=\"auto, (max-width: 800px) 100vw, 800px\" \/><\/figure>\n\n\n\n<p>The choice of the speed reference rate limitation is a trade-off between the settling time and the mechanical stress induced by a sudden change of the torque.<\/p>\n\n\n\n<h2 class=\"wp-block-heading\" id=\"TN114:Motorspeedcontrol-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] Slobodan N. Vukosavi\u0107 ,&#8221;Digital Control of Electrical Drives&#8221;, Springer, 2007, ISBN 978-0-387-25985-7<\/p>\n\n\n\n<p>[2] 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<\/p>\n","protected":false},"excerpt":{"rendered":"<p>This technical note explains how to implement speed control for an electric motor. First, the note introduces the general operating principles of motor speed control,&#8230;<\/p>\n","protected":false},"author":8,"featured_media":3037,"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":[104],"provided-results":[108],"related-products":[50,32,166,114,111],"guidedreadings":[60,119],"tutorials":[131,124],"user-manuals":[],"coauthors":[62],"class_list":["post-423","post","type-post","status-publish","format-standard","has-post-thumbnail","hentry","category-implementation","tag-motor-drives","software-environments-plecs","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-direct-torque-control-of-a-permanent-magnet-synchronous-motor","tutorials-field-oriented-control"],"acf":[],"yoast_head":"<!-- This site is optimized with the Yoast SEO plugin v27.4 - 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