Missile Attitude Control via a Hybrid LQG-LTR-LQI Control Scheme with Optimum Weight Selection

This is the author accepted manuscript. The final version is available from IEEE via the DOI in this record.This paper proposes a new strategy for missile attitude control using a hybridization of Linear Quadratic Gaussian (LQG), Loop Transfer Recovery (LTR), and Linear Quadratic Integral (LQI) control techniques. The LQG control design is carried out in two steps i.e. firstly applying Kalman filter for state estimation in noisy environment and then using the estimated states for an optimal state feedback control via Linear Quadratic Regulator (LQR). As further steps of performance improvement of the missile attitude control system, the LTR and LQI schemes are applied to increase the stability margins and guarantee set-point tracking performance respectively, while also preserving the optimality of the LQG. The weighting matrix (Q) and weighting factor (R) of LQG and the LTR fictitious noise coefficient (q) are tuned using Nelder-Mead Simplex optimization technique to make the closed-loop system act faster. Simulations are given to illustrate the validity of the proposed technique

Magnetocaloric effect and critical behavior near the paramagnetic to ferrimagnetic phase transition temperature in TbCo2-xFex

Magnetocaloric effect (MCE) in TbCo2-xFex has been studied by dc magnetization measurements.On substituting Fe in TbCo2, not only the magnetic transition temperature is tuned to room temperature, but also the operating temperature range for MCE is increased from 50 K for TbCo2 to 95 K for TbCo1.9Fe0.1. The maximum magnetic entropy change (-{\Delta}SM) for TbCo1.9Fe0.1 is found to be 3.7 J kg-1 K-1 for a 5 T field change, making it a promising candidate for magnetic refrigeration near room temperature. The temperature dependent neutron diffraction study shows a structural phase transition (from cubic to rhombohedral phase with lowering of temperature) which is associated with the magnetic phase transition and these transitions broaden on Fe substitution. To investigate the nature of the paramagnetic to ferrimagnetic phase transition, we performed a critical exponent study. From the derived values of critical exponents, we conclude that TbCo2 belongs to the 3D Heisenberg class with short-range interaction, while on Fe substitution it tends towards mean-field with long-range interaction. The derived values of critical exponents represent the phenomenological universal curve for the field dependence of {\Delta}SM, indicating that TbCo2 and TbCo1.9Fe0.1 belong to two different universality classes.Comment: 12 figure

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

LQR based improved discrete PID controller design via optimum selection of weighting matrices using fractional order integral performance index

This is the author accepted manuscript. The final version is available from Elsevier via the DOI in this record.The continuous and discrete time Linear Quadratic Regulator (LQR) theory has been used in this paper for the design of optimal analog and discrete PID controllers respectively. The PID controller gains are formulated as the optimal state-feedback gains, corresponding to the standard quadratic cost function involving the state variables and the controller effort. A real coded Genetic Algorithm (GA) has been used next to optimally find out the weighting matrices, associated with the respective optimal state-feedback regulator design while minimizing another time domain integral performance index, comprising of a weighted sum of Integral of Time multiplied Squared Error (ITSE) and the controller effort. The proposed methodology is extended for a new kind of fractional order (FO) integral performance indices. The impact of fractional order (as any arbitrary real order) cost function on the LQR tuned PID control loops is highlighted in the present work, along with the achievable cost of control. Guidelines for the choice of integral order of the performance index are given depending on the characteristics of the process, to be controlled.This work has been supported by the Dept. of Science & Technology (DST), Govt. of India under PURSE programme

Jarcho-Levin syndrome

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Stabilizing region in dominant pole placement based discrete time PID control of delayed lead processes using random sampling

This is the final version. Available on open access from Elsevier via the DOI in this recordData availability: Data will be made available on request.Handling time delays in industrial process control is a major challenge in the dominant pole placement based design of proportional-integral-derivative (PID) controllers due to variable number of zeros and poles which may arise from the Pade approximation of the exponential delay terms in the characteristic polynomials used for stability analysis. This paper proposes a new concept for designing PID controllers with a derivative filter using dominant pole placement method mapped onto the discrete time domain with a suitable choice of the sampling time to convert the continuous time time-delays into finite number of discrete time poles. Here, the continuous-time plant and the filtered PID controller have been discretized using the pole-zero matching method for handling linear dynamical systems, represented by the first order plus time delay with zero (FOPTDZ) transfer function models of the open-loop system under control. We use a swarm intelligence based global optimization method as a sampler to discover the approximate the pattern of the stabilizable region in the controller parameter as well as the design specification space while also satisfying the analytical conditions for pole placement given as higher order polynomials. Simulations on test-bench plants with open-loop stable, unstable, integrating, low-pass, high-pass characteristics have been presented in order to demonstrate the validity and effectiveness of the proposed control design method.European Regional Development Fund (ERDF

Comparative study on sorption characteristics of coal seams from Barakar and Raniganj formations of Damodar Valley Basin, India

The methane retention mechanism in coal seams is markedly different from those of conventional gas reservoirs. Methane remains mainly as physically adsorbed molecules on micropore surface. Chemical and petrographic compositions of coal are the measures of maturity and type of organic matter that control the methane sorption characteristics of the coal. 99% of Indian coal occurrences are contributed by lower Gondwana sequences housed in two major geologic formations, younger Raniganj and older Barakar. The Raniganj Formation is best exposed in Raniganj Sub-basin and Barakar Formation is best exposed in Jharia Sub-basin of Damodar Valley. Present work attempts a systematic investigation on comparative account of methane sorption characteristics of coals from Raniganj Formation of Raniganj Sub-basin and Barakar Formations of Jharia Sub-basin in relation to their chemical composition and petrographic makeup. Chemical analyses shows that moisture, ash, volatile matter and fixed carbon varies between 2.5 and 4.6%, 10.0–27.2%, 38.8–40.2% (dmmf) and 59.8–61.2% (dmmf), respectively for Raniganj coals and, 0.5–1.1%, 16.7–32.9%, 20.7–22.0% (dmmf) and 78.0–79.3% (dmmf), respectively for Barakar coals. Carbon content is distinct for the suites of coal, 79.2–85.4% and 85.6–92.0% for Raniganj and Barakar coals, respectively. The vitrinite reflectance for the Raniganj coals ranges 0.53–0.72% and the Barakar coals ranges 1.09–1.23%. Based on the chemical composition and vitrinite reflectance value Raniganj coals belongs to high volatile bituminous type, whereas Barakar coals belongs to high to medium volatile bituminous type. Such variation in composition and maturity is mainly attributed to the variation in precursor organic matter as well as the basinal and thermal history of the sub-basins under consideration. H/C atomic ratio of the Raniganj and Barakar coals varies between 0.65 and 0.80 and 0.51–0.72 and O/C atomic ratio varies between 0.05 and 0.13 and 0.01–0.07, respectively. Coals of both the Raniganj and Barakar formations are mostly of kerogen Type-III with Raniganj coals falling in wet gas maturity stage approaching early-thermogenic methane generation whereas Barakar coals falling in condensate gas stage approaching peakthermogenic methane generation. The Langmuir volume ranges from 9.3–21.8 cc/g (daf) for Raniganj coals and 21.1–29.1 cc/g (daf) for Barakar coals. Sorption capacity for the set of coals shows a strong rank dependency and increase with corresponding increase in rank down the stratigraphic column. Methane sorption capacity shows positive relationship with carbon content and vitrinite reflectance, and negative relationship with moisture content, ash and volatile matter. Moisture effect is more prominent in low rank Raniganj coals. The adsorption capacity shows a strong positive relation with vitrinite content and a moderate negative relation with inertinite content for both the Raniganj and Barakar coals, which may be attributed to dominancy of micropores in vitrinites with rank enhancement. The multiple regression analysis shows that the moisture is the main predictor of the VL, and the interaction of moisture with ash and reflectance mainly control the sorption capacity. A predictive model equation is developed for determination of sorption for Damodar basin coals from carbon, ash and moisture data