Delay Handling Method in Dominant Pole Placement based PID Controller Design

This is the author accepted manuscript. The final version is available from IEEE via the DOI in this record.Time delay handling is a major challenge in dominant pole placement design due to variable number of poles and zeros arising from the approximation of the delay term. We propose a new theory for continuous time PID controller design using dominant pole placement method mapped on to the discrete time domain with an appropriate choice of the sampling time to convert the delays in to finite number of poles. The method is developed to handle linear systems, represented by second order plus time delay (SOPTD) transfer function models. The proposed method does not contain finite term approximations like various orders of Pade, for handling the time delays which may affect the number and orientation of the resulting poles/zeros. Effectiveness of the proposed method have been shown using numerical simulations on nine SOPTD test-bench processes and another six challenging processes including single, double integrators and process with zero damping.European Regional Development Fund (ERDF

Time Delay Handling in Dominant Pole Placement with PID Controllers to Obtain Stability Regions using Random Sampling

This is the author accepted manuscript. The final version is available from Taylor & Francis via the DOI in this recordThis paper proposes a new formulation of proportional-integral-derivative (PID) controller design using the dominant pole placement method for handling second order plus time delay (SOPTD) systems. The proposed method does not contain any finite term approximation like different orders of Pade for handling the time-delay term, in the quasi-polynomial characteristic equation. Rather it transforms the transcendental exponential delay term of the plant into finite number of discrete-time poles by a suitable choice of the sampling time. The PID controller has been represented by Tustin’s discretization method and the PID controller gains are obtained using the dominant pole placement criterion where the plant is discretized using the pole-zero matching method. A random search and optimization method has been used to obtain the stability region in the desired closed loop parameters space by minimising the integral squared error (ISE) criterion by randomly sampling from the stabilizable region and then these closed loop parameters are mapped on to the PID controller gains. Effectiveness of the proposed methodology is shown for nine test-bench plants with different lag to delay ratios and open loop damping levels, and the effect of choosing different sampling times, using credible numerical simulations.ESIF ERDF Cornwall New Energy (CNE