Amitava Gupta

Saptarshi Das, Suman Saha, Shantanu Das et al.

In this paper, a comparative study is done on the time and frequency domain tuning strategies for fractional order (FO) PID controllers to handle higher order processes. A new fractional order template for reduced parameter modeling of stable minimum/non-minimum phase higher order processes is introduced and its advantage in frequency domain tuning of FOPID controllers is also presented. The time domain optimal tuning of FOPID controllers have also been carried out to handle these higher order processes by performing optimization with various integral performance indices. The paper highlights on the practical control system implementation issues like flexibility of online autotuning, reduced control signal and actuator size, capability of measurement noise filtration, load disturbance suppression, robustness against parameter uncertainties etc. in light of the above tuning methodologies.

Saptarshi Das, Indranil Pan, Shantanu Das et al.

A novel fractional order (FO) fuzzy Proportional-Integral-Derivative (PID) controller has been proposed in this paper which works on the closed loop error and its fractional derivative as the input and has a fractional integrator in its output. The fractional order differ-integrations in the proposed fuzzy logic controller (FLC) are kept as design variables along with the input-output scaling factors (SF) and are optimized with Genetic Algorithm (GA) while minimizing several integral error indices along with the control signal as the objective function. Simulations studies are carried out to control a delayed nonlinear process and an open loop unstable process with time delay. The closed loop performances and controller efforts in each case are compared with conventional PID, fuzzy PID and PIλDμ controller subjected to different integral performance indices. Simulation results show that the proposed fractional order fuzzy PID controller outperforms the others in most cases.

Suman Saha, Saptarshi Das, Ratna Ghosh et al.

Phase shaping using fractional order (FO) phase shapers has been proposed by many contemporary researchers as a means of producing systems with iso-damped closed loop response due to a stepped variation in input. Such systems, with the closed loop damping remaining invariant to gain changes can be used to produce dead-beat step response with only rise time varying with gain. This technique is used to achieve an active step-back in a Pressurized Heavy Water Reactor (PHWR) where it is desired to change the reactor power to a pre-determined value within a short interval keeping the power undershoot as low as possible. This paper puts forward an approach as an alternative for the present day practice of a passive step-back mechanism where the control rods are allowed to drop during a step-back action by gravity, with release of electromagnetic clutches. The reactor under a step-back condition is identified as a system using practical test data and a suitable Proportional plus Integral plus Derivative (PID) controller is designed for it. Then the combined plant is augmented with a phase shaper to achieve a dead-beat response in terms of power drop. The fact that the identified static gain of the system depends on the initial power level at which a step-back is initiated, makes this application particularly suited for using a FO phase shaper. In this paper, a model of a nuclear reactor is developed for a control rod drop scenario involving rapid power reduction in a 500MWe Canadian Deuterium Uranium (CANDU) reactor using AutoRegressive Exogenous (ARX) algorithm. The system identification and reduced order modeling are developed from practical test data. For closed loop active control of the identified reactor model, the fractional order phase shaper along with a PID controller is shown to perform better than the present Reactor Regulating System (RRS) due to its iso-damped nature.

Indranil Pan, Saptarshi Das, Amitava Gupta

The issues of stochastically varying network delays and packet dropouts in Networked Control System (NCS) applications have been simultaneously addressed by time domain optimal tuning of fractional order (FO) PID controllers. Different variants of evolutionary algorithms are used for the tuning process and their performances are compared. Also the effectiveness of the fractional order PIλDμ controllers over their integer order counterparts is looked into. Two standard test bench plants with time delay and unstable poles which are encountered in process control applications are tuned with the proposed method to establish the validity of the tuning methodology. The proposed tuning methodology is independent of the specific choice of plant and is also applicable for less complicated systems. Thus it is useful in a wide variety of scenarios. The paper also shows the superiority of FOPID controllers over their conventional PID counterparts for NCS applications.

Saptarshi Das, Basudev Majumder, Anindya Pakhira et al.

Rational approximation of fractional order (FO) differ-integrators via Continued Fraction Expansion (CFE) is a well known technique. In this paper, the nominal structures of various generating functions are optimized using Genetic Algorithm (GA) to minimize the deviation in magnitude and phase response between the original FO element and the rationalized discrete time filter in Infinite Impulse Response (IIR) structure. The optimized filter based realizations show better approximation of the FO elements in comparison with the existing methods and is demonstrated by the frequency response of the IIR filters.

Saptarshi Das, Shantanu Das, Amitava Gupta

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 PIλDμ 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 PIλDμ 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.

Sayan Saha, Saptarshi Das, Anish Acharya et al.

The paper investigates nonlinear system identification using system output data at various linearized operating points. A feed-forward multi-layer Artificial Neural Network (ANN) based approach is used for this purpose and tested for two target applications i.e. nuclear reactor power level monitoring and an AC servo position control system. Various configurations of ANN using different activation functions, number of hidden layers and neurons in each layer are trained and tested to find out the best configuration. The training is carried out multiple times to check for consistency and the mean and standard deviation of the root mean square errors (RMSE) are reported for each configuration.

Saptarshi Das, Sayan Saha, Ayan Mukherjee et al.

Gain and order scheduling of fractional order (FO) PIλDμ controllers are studied in this paper considering four different classes of higher order processes. The mapping between the optimum PID/FOPID controller parameters and the reduced order process models are done using Radial Basis Function (RBF) type Artificial Neural Network (ANN). Simulation studies have been done to show the effectiveness of the RBFNN for online scheduling of such controllers with random change in set-point and process parameters.

Saptarshi Das, Indranil Pan, Shantanu Das et al.

Genetic Algorithm (GA) has been used in this paper for a new Nyquist based sub-optimal model reduction and optimal time domain tuning of PID and fractional order (FO) PIλDμ controllers. Comparative studies show that the new model reduction technique outperforms the conventional H2-norm based reduced order modeling techniques. Optimum tuning rule has been developed next with a test-bench of higher order processes via Genetic Programming (GP) with minimum value of weighted integral error index and control signal. From the Pareto optimal front which is a trade-off between the complexity of the formulae and control performance, an efficient set of tuning rules has been generated for time domain optimal PID and PIλDμ controllers.

Basudev Majumder, Saptarshi Das, Indranil Pan et al.

This paper analyzes a nuclear reactor power signal that suffers from network induced random delays in the shared data network while being fed-back to the Reactor Regulating System (RRS). A detailed study is carried out to investigate the self similarity of random delay dynamics due to the network traffic in shared medium. The fractionality or selfsimilarity in the network induced delay that corrupts the measured power signal coming from Self Powered Neutron Detectors (SPND) is estimated and analyzed. As any fractional order randomness is intrinsically different from conventional Gaussian kind of randomness, these delay dynamics need to be handled efficiently, before reaching the controller within the RRS. An attempt has been made to minimize the effect of the randomness in the reactor power transient data with few classes of smoothing filters. The performance measure of the smoothers with fractional order noise consideration is also investigated into.

Suman Saha, Saptarshi Das, Ratna Ghosh et al.

Phase curve of an open loop system is flat in nature if the derivative of phase with respect to frequency is zero. With a flat phase curve, the corresponding closed-loop system exhibits an iso-damped property i.e. maintains constant overshoot with the change of gain and with other parametric variations. In recent past application, fractional order (FO) phase shapers have been proposed by contemporary researchers to achieve enhanced parametric robustness. In this paper, a simple Routh tabulation based methodology is proposed to design an appropriate FO phase shaper to achieve phase flattening in a control loop, comprising a system, controlled by a classical PID controller. The method is demonstrated using MATLAB simulation of a second order DC motor plant and also a first order with time delay system.

Ayan Mukherjee, Anindya Pakhira, Saptarshi Das et al.

The paper presents a Stateflow based network test-bed to validate real-time optimal control algorithms. Genetic Algorithm (GA) based time domain performance index minimization is attempted for tuning of PI controller to handle a balanced lag and delay type First Order Plus Time Delay (FOPTD) process over network. The tuning performance is validated on a real-time communication network with artificially simulated stochastic delay, packet loss and out-of order packets characterizing the network.

Saptarshi Das, Kaushik Halder, Amitava Gupta

This paper derives new formulations for designing dominant pole placement based proportional-integral-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 non-dominant 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. 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.

Saptarshi Das, Indranil Pan, Shantanu Das et al.

Genetic Algorithm (GA) has been used in this paper for a new approach of sub-optimal model reduction in the Nyquist plane and optimal time domain tuning of PID and fractional order (FO) PIλDμ controllers. Simulation studies show that the Nyquist based new model reduction technique outperforms the conventional H2 norm based reduced parameter modeling technique. With the tuned controller parameters and reduced order model parameter data-set, optimum tuning rules have been developed with a test-bench of higher order processes via Genetic Programming (GP). The GP performs a symbolic regression on the reduced process parameters to evolve a tuning rule which provides the best analytical expression to map the data. The tuning rules are developed for a minimum time domain integral performance index described by weighted sum of error index and controller effort. From the reported Pareto optimal front of GP based optimal rule extraction technique a trade-off can be made between the complexity of the tuning formulae and the control performance. The efficacy of the single-gene and multi-gene GP based tuning rules has been compared with original GA based control performance for the PID and PIλDμ controllers, handling four different class of representative higher order processes. These rules are very useful for process control engineers as they inherit the power of the GA based tuning methodology, but can be easily calculated without the requirement for running the computationally intensive GA every time. Three dimensional plots of the required variation in PID/FOPID controller parameters with reduced process parameters have been shown as a guideline for the operator. Parametric robustness of the reported GP based tuning rules has also been shown with credible simulation examples.