A Graphical Approach to Design Digital PI Controller for Integrator Plus Dead-Time Processes

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The aim of this paper is to present a novel graphical method to design the digital PI controller for integrator plus dead time (IPDT) model which is suitable for many processes. To start with the process and controller transfer functions are transformed from s-domain to z-domain and then the open-loop transfer function is obtained in z-domain. Then the parameters to design the controller are determined. As we need to design the digital controller in frequency domain a bilinear transformation of z-domain to w-domain is used. Let us determine the stability region by combination the traditional D-partition technique and graphical technique in the controller parameters plane. Then sketch the loci of constant stability margins, such as the gain and phase margins, gain and phase crossover frequencies and Smith’s vector margin in the parameter space. Also, it will be proven that by varying the coefficients of PI controller one can achieve the gain crossover frequency in the interval [0, ωA max] and the phase crossover frequency in the interval [0, ωB max), where ωA max and ωB max are determined by the parameters of process. By sketching the two loci of indices and obtaining their intersection point, one can approach to desired closed-loop systems specifications. Finally some examples are given to demonstrate the effectiveness of the proposed method.
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Digital PI Controller; Bilinear Transformation; Industrial Processes Plus Dead Time; Frequency Domain; Phase and Gain Margin; Phase and Gain Crossover Frequency; Smith’s Vector Margin

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