Performance analysis of robust stable PID controllers using dominant pole placement for SOPTD process models

This is the author accepted manuscript. The final version is available from Elsevier via the DOI in this recordThis paper derives new formulations for designing dominant pole placement based proportionalintegral-derivative (PID) controllers to handle second order processes with time delays (SOPTD). Previously, similar attempts have been made for pole placement in delay-free systems. The presence of the time delay term manifests itself as a higher order system with variable number of interlaced poles and zeros upon Pade approximation, which makes it difficult to achieve precise pole placement control. We here report the analytical expressions to constrain the closed loop dominant and nondominant poles at the desired locations in the complex s-plane, using a third order Pade approximation for the delay term. However, invariance of the closed loop performance with different time delay approximation has also been verified using increasing order of Pade, representing a closed to reality higher order delay dynamics. The choice of the nature of non-dominant poles e.g. all being complex, real or a combination of them modifies the characteristic equation and influences the achievable stability regions. The effect of different types of non-dominant poles and the corresponding stability regions are obtained for nine test-bench processes indicating different levels of open-loop damping and lag to delay ratio. Next, we investigate which expression yields a wider stability region in the design parameter space by using Monte Carlo simulations while uniformly sampling a chosen design parameter space. The accepted data-points from the stabilizing region in the design parameter space can then be mapped on to the PID controller parameter space, relating these two sets of parameters. The widest stability region is then used to find out the most robust solution which are investigated using an unsupervised data clustering algorithm yielding the optimal centroid location of the arbitrary shaped stability regions. Various time and frequency domain control performance parameters are investigated next, as well as their deviations with uncertain process parameters, using thousands of Monte Carlo simulations, around the robust stable solution for each of the nine test-bench processes. We also report, PID controller tuning rules for the robust stable solutions using the test-bench processes while also providing computational complexity analysis of the algorithm and carry out hypothesis testing for the distribution of sampled data-points for different classes of process dynamics and non-dominant pole types.KH acknowledges the support from the University Grants Commission (UGC), Govt. of India under its Basic Scientific Research (BSR) schem

Transformation of LQR weights for Discretization Invariant Performance of PI/PID Dominant Pole Placement Controllers

This is the author accepted manuscript. The final version is available from Cambridge University Press via the DOI in this record.Linear quadratic regulator (LQR), a popular technique for designing optimal state feedback controller is used to derive a mapping between continuous and discrete-time inverse optimal equivalence of proportional integral derivative (PID) control problem via dominant pole placement. The aim is to derive transformation of the LQR weighting matrix for fixed weighting factor, using the discrete algebraic Riccati equation (DARE) to design a discrete time optimal PID controller producing similar time response to its continuous time counterpart. Continuous time LQR-based PID controller can be transformed to discrete time by establishing a relation between the respective LQR weighting matrices that will produce similar closed loop response, independent of the chosen sampling time. Simulation examples of first/second order and first-order integrating processes exhibiting stable/unstable and marginally-stable open-loop dynamics are provided, using the transformation of LQR weights. Time responses for set-point and disturbance inputs are compared for different sampling time as fraction of the desired closed-loop time constant.University Grants Commission (UGC), Government of IndiaESIF ERDF Cornwal

Optimum Weight Selection Based LQR Formulation for the Design of Fractional Order PIλDμ Controllers to Handle a Class of Fractional Order Systems

This is the author accepted manuscript. The final version is available from IEEE via the DOI in this record.A weighted summation of Integral of Time Multiplied Absolute Error (ITAE) and Integral of Squared Controller Output (ISCO) minimization based time domain optimal tuning of fractional-order (FO) PID or PI{\lambda}D{\mu} controller is proposed in this paper with a Linear Quadratic Regulator (LQR) based technique that minimizes the change in trajectories of the state variables and the control signal. A class of fractional order systems having single non-integer order element which show highly sluggish and oscillatory open loop responses have been tuned with an LQR based FOPID controller. The proposed controller design methodology is compared with the existing time domain optimal tuning techniques with respect to change in the trajectory of state variables, tracking performance for change in set-point, magnitude of control signal and also the capability of load disturbance suppression. A real coded genetic algorithm (GA) has been used for the optimal choice of weighting matrices while designing the quadratic regulator by minimizing the time domain integral performance index. Credible simulation studies have been presented to justify the proposition

Understanding the evolution of catalytically active multi-metal sites in a bifunctional high-entropy alloy electrocatalyst for zinc–air battery application

Zinc–air batteries are known for high theoretical energy density and environmental friendliness. The successful commercial utilization of rechargeable zinc–air batteries is limited by unstable electrochemical interfaces and sluggish kinetics with poor round-trip efficiency. In this study, we report a nanocrystalline high entropy alloy (HEA) comprising Cu–Co–Mn–Ni–Fe (CCMNF) prepared by casting-cum-cryomilling method. This multi-component HEA embodies multiple catalytically active sites with diverse functionalities, thus enhancing the electrochemical redox reactions, e.g., oxygen reduction (ORR) and oxygen evolution reaction (OER). The bifunctional electrocatalytic performance of this HEA is comparable to that of standard catalysts, RuO2 and Pt/C, as evidenced by low overpotential requirements towards OER and ORR. The HEA was tested for use in the air electrode catalyst in the zinc–air battery, where it performed stable oxygen electrocatalysis that was durable over 1045 charging–discharging cycles for ∼90 hours of continuous operation. The microstructural analysis of HEA at different time scales (0, 24, 87 h) during the zinc–air battery operation suggested a dynamic participation of multiple metal active sites on the catalyst surface. Detailed studies revealed that despite leaching in harsh alkaline operation conditions, the synergistic electronic interactions between the component metal sites sustained good electrocatalytic performance and promoted oxygen electrocatalysis through the modification of electronic and chemical properties

Understanding the multiple magnetic structures of the intermetallic compound NdMn1.4Co0.6Si2

Magnetic phases for the intermetallic compound NdMn1.4Co0.6Si2 have been investigated at various temperatures by dc magnetization, neutron diffraction and neutron depolarization. Our study shows multiple magnetic phase transitions with temperature (T) over 1.5-300 K. In agreement with dc-magnetization and neutron depolarization results, the temperature dependence of the neutron diffraction patterns shows five distinct regions with different magnetic phases. These temperature regions are (i) T >= 215 K, (ii) 215 K > T >= 50 K, (iii) 50 K > T >= 40 K, (iv) 40 K > T > 15 K, and (v) T =< 15 K. The corresponding magnetic structures are paramagnetic, commensurate collinear antiferromagnetic (AFM-I), incommensurate AFM (AFM-II), mixed ferromagnetic and AFM (FM+AFM-II), and incommensurate AFM (AFM-II), respectively.Comment: 26 pages, 10 figure

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

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

Polarization entangled photon-pair source based on a type-II PPLN waveguide emitting at a telecom wavelength

We report the realization of a fiber coupled polarization entangled photon-pair source at 1310 nm based on a birefringent titanium in-diffused waveguide integrated on periodically poled lithium niobate. By taking advantage of a dedicated and high-performance setup, we characterized the quantum properties of the pairs by measuring two-photon interference in both Hong-Ou-Mandel and standard Bell inequality configurations. We obtained, for the two sets of measurements, interference net visibilities reaching nearly 100%, which represent important and competitive results compared to similar waveguide-based configurations already reported. These results prove the relevance of our approach as an enabling technology for long-distance quantum communication.Comment: 13 pages, 4 figures, to appear in New Journal of Physic