{"id":21889,"date":"2025-01-04T00:30:01","date_gmt":"2025-01-04T00:30:01","guid":{"rendered":"https:\/\/liquidinstruments.com\/?p=21889"},"modified":"2025-08-29T04:40:59","modified_gmt":"2025-08-29T04:40:59","slug":"loop-shaping-frequency-domain-tuning","status":"publish","type":"post","link":"https:\/\/liquidinstruments.com\/application-notes\/loop-shaping-frequency-domain-tuning\/","title":{"rendered":"Loop shaping: frequency domain tuning","gt_translate_keys":[{"key":"rendered","format":"text"}]},"content":{"rendered":"

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In this series, we provide a practical reference for designing and debugging loops by presenting a short introduction to feedback control as encountered in the frequency domain.<\/p>\n\n <\/div>\n <\/div>\n

\n Get the frequency control guide<\/span><\/a>\n Control systems solutions<\/span><\/a>\n \n \n <\/div>\n <\/div>\n <\/div>[vc_column_text]<\/p>\n

4.1<\/b> Introduction<\/b><\/h2>\n

All properties of a loop are determined by its open-loop transfer function (OLTF), labeled <\/span>G, <\/span><\/i>and it is this quantity that we must modify in order to achieve the required performance objectives. However, the transfer functions of the plant and sensor are generally fixed, with the only available degrees of freedom found in the controller. We thus tune the controller transfer function <\/span>C<\/span><\/i>, to modify the OLTF. Frequency-domain tuning of this type is often termed <\/span>loop shaping<\/span><\/i><\/a>.<\/span><\/p>\n

Part 1<\/a> establishes the definition of a transfer function and provides the components from which one can construct control loop block diagrams to model elaborate systems. In Part 2<\/a> we demonstrate how feedback control systems can be used to suppress disturbances or track a process set point. The complications associated with noisy sensors are also discussed. Unlike open-loop systems, devices under feedback control have the potential to become unstable and there is tension between performance and robustness. Ultimately, delays in signal propagation can impose the most stringent limit. These issues are treated in Part 3<\/a>. In the frequency domain, most parameters of a feedback system can be linked to its open-loop transfer function. Here in Part 4 we explain how to measure this important quantity and provide a list of functions often used in shaping it. Part 5<\/a> describes one method of avoiding actuator saturation and, in doing so, introduces ideas useful to the treatment of multiple actuators. Our series concludes in  with the study of the PID controller. This common control architecture is generally considered from a time-domain point-of-view; we illustrate the complementary frequency-domain representation.<\/p>\n

4.2<\/b> Design principles<\/b><\/h2>\n

Based on the discussions in the previous parts of this series<\/a>, the design rules are as follows:<\/span><\/p>\n