{"id":21953,"date":"2025-01-04T00:25:28","date_gmt":"2025-01-04T00:25:28","guid":{"rendered":"https:\/\/liquidinstruments.com\/?p=21953"},"modified":"2025-08-29T04:41:00","modified_gmt":"2025-08-29T04:41:00","slug":"constructing-feedback-control-loops","status":"publish","type":"post","link":"https:\/\/liquidinstruments.com\/application-notes\/constructing-feedback-control-loops\/","title":{"rendered":"Feedback control: constructing feedback control loops","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 css=””]<\/p>\n

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

Part 2 of our series<\/a> on frequency-domain control demonstrates how one can construct feedback control loops using the block-diagram approach discussed previously. Please see Part 1<\/a> for an introduction to the mathematical representation of our control loops. We will analyze these loops and discover how they can track a changing set point or mitigate disturbances. As an example, we will look at disturbances arising from the loop sensor itself.<\/p>\n

Part 1 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 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. In Part 4<\/a> 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 Part 6<\/a> with the study of the PID controller<\/a>. This common control architecture is generally considered from a time-domain point-of-view; we illustrate the complementary frequency-domain representation.<\/p>\n

2.2 Open loop<\/h2>\n

Let us begin our foray into the world of control systems<\/a> by considering the frequency control system of Figure 2.1. Such a diagram could represent the tuning input of a voltage-controlled oscillator (VCO), laser, or motor (in which case we\u2019d think of frequency as rotation rate or speed). The system to be controlled is often called the plant.<\/p>\n

\"Open<\/p>\n

Figure 2.1: An open-loop frequency control system. H(s)<\/em>, with dimensions of Hz\/V, describes the transfer function of the system\u2019s tuning input. In response to a set-point<\/em> input of Xsp<\/sub>, the output frequency is \\(X_{freq}\\), i.e. \\(X_{freq}(s)=H(s)X_{sp}(s)\\).<\/span><\/p>\n

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Ideally, one could simply fix the input voltage based on the desired output frequency, varying it as necessary. Unfortunately, real-world <\/span>disturbances <\/span><\/i>render this approach unfeasible. We divide disturbances into <\/span>input <\/span><\/i>and <\/span>output <\/span><\/i>categories as shown in (see Figure <\/span>2.2<\/span>).<\/span><\/p>\n

\"Input<\/p>\n

Figure 2.2: Input and output disturbances, di and do respectively, perturb the system. This necessitates action on our part to maintain the desired output. Note that in the interest of brevity and readability, we henceforth omit dimensions and independent variables.<\/p>\n

Under closed-loop control, the effect of input and output disturbances can be quite different and the distinction between them relatively subtle. Considering the dimensions of the disturbance and whether it should be filtered by the transfer function in question usually removes any uncertainty.<\/p>\n

2.3<\/b> Feedforward<\/b><\/h2>\n

A simple approach to combatting a disturbance would be to:<\/p>\n