Fractional Order Modeling of a PHWR Under Step-Back Condition and Control of Its Global Power with a Robust PI{\lambda}D{\mu} Controller

Bulk reduction of reactor power within a small finite time interval under abnormal conditions is referred to as step-back. In this paper, a 500MWe Canadian Deuterium Uranium (CANDU) type Pressurized Heavy Water Reactor (PHWR) is modeled using few variants of Least Square Estimator (LSE) from practical test data under a control rod drop scenario in order to design a control system to achieve a dead-beat response during a stepped reduction of its global power. A new fractional order (FO) model reduction technique is attempted which increases the parametric robustness of the control loop due to lesser modeling error and ensures iso-damped closed loop response with a PI{\lambda}D{\mu} or FOPID controller. Such a controller can, therefore, be used to achieve active step-back under varying load conditions for which the system dynamics change significantly. For closed loop active control of the reduced FO reactor models, the PI{\lambda}D{\mu} controller is shown to perform better than the classical integer order PID controllers and present operating Reactor Regulating System (RRS) due to its robustness against shift in system parameters.Comment: 10 pages, 11 figure

Optimum Weight Selection Based LQR Formulation for the Design of Fractional Order PI{\lambda}D{\mu} Controllers to Handle a Class of Fractional Order Systems

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.Comment: 6 pages, 5 figure

Fractional Order Fuzzy Control of Nuclear Reactor Power with Thermal-Hydraulic Effects in the Presence of Random Network Induced Delay and Sensor Noise having Long Range Dependence

This is the author accepted manuscript. The final version is available from Elsevier via the DOI in this record.Nonlinear state space modeling of a nuclear reactor has been done for the purpose of controlling its global power in load following mode. The nonlinear state space model has been linearized at different percentage of reactor powers and a novel fractional order (FO) fuzzy proportional integral derivative (PID) controller is designed using real coded Genetic Algorithm (GA) to control the reactor power level at various operating conditions. The effectiveness of using the fuzzy FOPID controller over conventional fuzzy PID controllers has been shown with numerical simulations. The controllers tuned with the highest power models are shown to work well at other operating conditions as well; over the lowest power model based design and hence are robust with respect to the changes in nuclear reactor operating power levels. This paper also analyzes the degradation of nuclear reactor power signal due to network induced random delays in shared communication network and due to sensor noise while being fed-back to the Reactor Regulating System (RRS). The effect of long range dependence (LRD) which is a practical consideration for the stochastic processes like network induced delay and sensor noise has been tackled by optimum tuning of FO fuzzy PID controllers using GA, while also taking the operating point shift into consideration

A Conformal Mapping Based Fractional Order Approach for Sub-optimal Tuning of PID Controllers with Guaranteed Dominant Pole Placement

A novel conformal mapping based Fractional Order (FO) methodology is developed in this paper for tuning existing classical (Integer Order) Proportional Integral Derivative (PID) controllers especially for sluggish and oscillatory second order systems. The conventional pole placement tuning via Linear Quadratic Regulator (LQR) method is extended for open loop oscillatory systems as well. The locations of the open loop zeros of a fractional order PID (FOPID or PI{\lambda}D{\mu}) controller have been approximated in this paper vis-\`a-vis a LQR tuned conventional integer order PID controller, to achieve equivalent integer order PID control system. This approach eases the implementation of analog/digital realization of a FOPID controller with its integer order counterpart along with the advantages of fractional order controller preserved. It is shown here in the paper that decrease in the integro-differential operators of the FOPID/PI{\lambda}D{\mu} controller pushes the open loop zeros of the equivalent PID controller towards greater damping regions which gives a trajectory of the controller zeros and dominant closed loop poles. This trajectory is termed as "M-curve". This phenomena is used to design a two-stage tuning algorithm which reduces the existing PID controller's effort in a significant manner compared to that with a single stage LQR based pole placement method at a desired closed loop damping and frequency.Comment: 23 pages, 7 figures, in press; Communications in Nonlinear Science and Numerical Simulations, 201

Variable coefficient fractional‐order PID controller and its application to a SEPIC device

The fractional-order proportional–integral–derivative (FOPID) controller has two more parameters than the integer-order proportional–integral–derivative (PID). Such characteristic makes the controller design more flexible and leads to superior performance. This study proposes a variable coefficient FOPID (VCFOPID) with optimal single step parameters, combining discrete synthesis and variable control parameters. The new algorithm is compared with previous FOPID discrete methods via several examples. Since the energy losses of the single-ended primary-inductor converter (SEPIC) cannot be ignored, the standard models are insufficient and a new model is derived using quantum-behaved particle swarm optimisation. The VCFOPID is applied to the SEPIC and both the effectiveness of the controller and the model are verified experimentally.The authors would like to thank the anonymous reviewers for their constructive comments, which greatly improved the quality of this paper. This work was supported by the National Natural Science Funds of China (nos. 61403115 and 11971032).info:eu-repo/semantics/publishedVersio

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