Sequential synthesis of PID controllers based on LQR method

Abstract

totales del petróleo intemperizados en suelos y sedimentos (Biodegradation modeling of sludge bioreactors of total petroleum hydrocarbons weathering in soil and sediments)

Analytical and hybrid-neuro-differential approaches for describing contaminant removal from aqueous systems

“…In addition, state-space formulations such as that given in Eqs. ( 21) to ( 23) can be applied to design popular linear controllers, such as PI or PID ones, by using well-known state-space methods for LTI representations and further examine their stability, performance, and robustness (Hernández-Osorio et al, 2020).…”

Optimal Identification and Metaheuristic PID Control of a Two-Tank System

“…Over the years, the PID tuning methods evolved from empirical (Ziegler-Nichols [7,8], Cohen-Coon) and analytical (internal model, pole placement, gain-phase margin [9]) to adaptive and optimization-based [5]. Unlike the empirical and analytical methods that provide weak or only satisfying performance, the optimization techniques applied to PID tuning yield good performance (disturbance rejection, set-point tracking) and robustness [4,10,11]. Therefore, in recent decades, the problem of designing an optimal PID controller that drives the systems into a desired behavior has increasingly captured the interest of the automatic control community.…”

“…For example, one can mention the methods to synthesize Linear Quadratic Regulators of H-infinity controllers (with the help of the Linear Matrix Inequality optimization procedure) [11,17]. This approach has been successfully employed to design multivariable and multiloop PID controllers implemented either in continuous time [10,11] or in discrete time [18]. Nevertheless, this approach involves an elaborated mathematical foundation and complex algorithms [12].…”

Stochastic LQR optimal control with white and colored noise: Dynamic programming technique

“…Moreover, LQR optimal control is used in situations where no linear dynamic becomes linear around fix points through Taylor expansion, Tang et al (2012); Prasad et al (2011). Some applications can be found in Hernández-Osorio et al (2019); Rojas et al (2016); Razmjooy et al (2016); López et al (2011);Sam et al (2000); Seekhao et al (2020); Ahmad et al (2020)…”