Dominant Time Constant-Based IMC-PIDA Controller Synthesis for Third-Order Plus Time Delay Systems

This paper presents a new approach of physically realizable Internal Model Control (IMC) based PIDA control framework tailored for Third Order Plus Time Delay (TOPTD) systems. Standard PID controllers lack the structural degrees of freedom to effectively compensate for the complex pole zero dynamics of high order plants resulting in compromised transient performance and limited disturbance rejection. We propose a systematic method that overcomes these limitations through two primary mechanisms. First the derivative and acceleration terms are augmented with first order low pass filters ensuring properness and inherent attenuation of high frequency measurement noise. Second, a deterministic tuning strategy is introduced wherein the IMC filter time constant γ is analytically set to the plants dominant open loop time constant τdom. This approach of (γ=τdom) guarantees robust stability margins (1.4≤Ms≤2.0) without iterative numerical optimization. A rigorous frequency domain analysis guides the selection of the derivative filter constant λ to balance causality with phase margin preservation. Furthermore a multiplicative gain correction factor is derived to address steady state inaccuracies arising in model reduction. Further we provide a mathematical proof demonstrating that this correction guarantees zero steady state error for both step and impulse inputs irrespective of the reduction algorithm employed. Extensive validation on three industrial benchmarks, including a high gain overdamped process, a precision sun tracker, and a bagasse fired boiler with significant dead time confirms the methods superiority. The proposed framework results in a robust, high performance controller suitable for direct industrial deployment.