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

Stabilizing regions of dominant pole placement for second order lead processes with time delay using filtered PID controllers

This is the final version. Available from Public Library of Science via the DOI in this record. Data Availability Statement: All relevant data are within the paper.In order to handle second order lead processes with time delay, this paper provides a unique dominant pole placement based filtered PID controller design approach. This method does not require any finite term approximation like Pade to obtain the quasi-polynomial characteristic polynomial, arising due to the presence of the time delay term. The continuous time second order plus time delay systems with zero (SOPTDZ) are discretized using a pole-zero matching method with specified sampling time, where the transcendental exponential delay terms are converted into a finite number of poles. The pole-zero matching discretization approach with a predetermined sampling period is also used to discretize the continuous time filtered PID controller. As a result, it is not necessary to use any approximate discretization technique, such as Euler or Tustin, to derive the corresponding discrete time PID controller from its continuous time counterpart. The analytical expressions for discrete time dominant pole placement based filtered PID controllers are obtained using the coefficient matching approach, while two distinct kinds of non-dominant poles, namely all real and all complex conjugate, have been taken into consideration. The stabilizable region in the controller and design parameter space for the chosen class of linear second order time delay systems with lead is numerically approximated using the particle swarm optimization (PSO) based random search technique. The efficacy of the proposed method has been validated on a class of SOPTDZ systems including stable, integrating, unstable processes with minimum as well as non-minimum phase zeros.European Regional Development Fun