Minimum Variance Control Law Research Articles

DBFact: A better approach to calculate the minimum variance control law for nonminimum phase MIMO systems

AbstractThis paper presents the diagonal with Blaschke products factorization (DBFact) approach to factor out multivariable time delay and nonminimum phase zeros from multi‐input multi‐output (MIMO) systems. Based on that, a new output‐order independent minimum variance (MV) control law for MIMO systems is proposed. The DBFact method is a two‐step factorization procedure, relying on the diagonal and Blaschke factorization methods. This method has the advantage of being a direct and non‐iterative procedure. This new factorization approach allows the calculation of an MV control law considering the multivariable time delay as a limiting‐performance factor and the nonminimum phase zeros and their corresponding directions. Based on the proposed MV control law, a performance benchmark is introduced, which can be calculated by the DBFact filters and routine operating data. The DBFact methodology was applied to two control structures of the linear plant model of Linde's heat integrated air separation, in which the MV control law output‐order dependency property and the suitability of the performance benchmark were evaluated. Some results were compared with those obtained by admitting the generalized interactor matrix instead of the DBFact filters. The results show the capability of the DBFact methodology to factor the nonminimum phase terms to provide a reliable MIMO controller performance benchmark and illustrate the importance of considering the nonminimum phase zeros and their actual directionality in the MV control law.

Considerations about Parameters Estimation into a Minimum Variance Control System

The starting point to design a minimum variance control law consists in identifying a linearized mathematical model (valid around an operating point) of a nonlinear process, respectively the on-line estimation of the parameters of this model. This paper presents a comparative study regarding the estimation of these parameters for the case when the process operates in open-loop, respectively the process is integrated into a closed-loop system specific to a minimum variance control. The comparison is made both analytically (for the general case) and through a validation study (by simulation) particularized for the case of an induction generator integrated into a wind energy conversion system. The main contribution of this paper consists in proving the fact that, in closed-loop (under the constraints imposed by the control law), the process parameters estimates differ from the real ones identified in open-loop (in free operating mode, without constraints). In addition, as a novelty, the paper demonstrates that, in steady-state, the process gain estimates are identical, both in closed-loop and open-loop, even though they are calculated based on different estimates of these linear model parameters. Thus, based on parameters estimates in closed-loop, the parameter estimator rather allows the estimation of the real process gain, although it does not accurately estimate the real values of the linearized model parameters (correctly estimated only in open-loop).

A New Adaptive Maximum Power Point Controller for a Photovoltaic System

Controlling extraction of maximum power from photovoltaic (PV) panels is very important for an efficient PV power system. This maximum power control can be performed by using a maximum power point tracking (MPPT) algorithm. We propose anew self-tuning based adaptive MPPT algorithm that is designed with an incremental-proportional-integral-derivative (IPID) controller. Power extraction from a PV panel is greatly influenced by external weather conditions. The IPID-controller monitors the rate of change in control signal during rapid variation in input weather conditions for maintaining stability of a PV system. The proposed adaptive MPPT controller is comprised of two components, namely, parameter estimation of the MPPT converter system and control design strategy for tuning the IPID-controller. In this paper, a recursive least square algorithm and incremental generalized minimum variance (IGMV) control law have been used for parameter estimation and tuning the gains of the IPID-controller, respectively. The efficacy of the proposed MPPT algorithm is verified on comparing its performance with that of the Perturb and observe (P&O) algorithm. From the simulation and experimental results, it is envisaged that the efficacy of the proposed adaptive MPPT control scheme exhibits superior performance as compared to P&O MPPT algorithm.

Considerations Regarding the Design of a Minimum Variance Control System for an Induction Generator

This paper presents a comparative analysis regarding a self-tuning minimum variance control system of a double-fed induction generator with load and connected to a power system through a long transmission line. A new complex nonlinear model describing this relationship between the induction generator, electrical consumer, transmission line, and power system is designed and implemented to simulate the controlled plant behavior. Starting from a simplified linear model of this complex plant, obtained through linearization of its nonlinear model around an operating point, the minimum variance control law design is performed by minimizing a cost criterion function. The main goal and also the paper novelty consists of the identification of a minimum order of this linearized model used to design a reduced order control law, which can still provide good control performance.

Design of a Data-Oriented Performance Driven Control System Based on the Generalized Minimum Variance Control Law

In process industries, it is necessary to maintain the user-specified control performance in order to achieve desired productivity. This paper describes a design scheme for control performance eval...

A new approach to estimate the Minimum Variance Control law for Nonminimum phase Multivariable Systems

Abstract This paper introduces a new approach to calculate the minimum variance control law, which consists of a more direct and non-iterative procedure. It is based on factorization methods that preserve the directionality of nonminimum phase factors what yields a performance index closer to the actual achievable one. The proposed methodology was carried out for different case studies and compared with those obtained from a generalized interactor matrix. The results have shown the capability of the proposed methodology to yield a suitable MIMO controller performance index.

MV Benchmark for Networked Control Systems with Random Communication Delays

Abstract This work considers the control performance assessment (CPA) of networked control systems (NCSs) with random communication delays. Two kinds of communication delays are considered simultaneously: sensor-to-controller communication delay and controller-to-actuator communication delay A closed-form solution of the linear time-variant (LTV) minimum variance (MV) control law is derived for this class of systems. Correspondingly the MV benchmark value is calculated based on the achieved output with minimum variance. These results can be used for evaluating the potential improvement of control performance for NCSs with random communication delays. Further, the proposed results are illustrated based on a numerical example.

Multiple models and neural networks based adaptive PID decoupling control of mine main fan switchover system

Mine main fan switchover system (MMFSS) consists of two main fans, which are equipped with a horizontal air door and a vertical air door, respectively. The purpose of operating MMFSS is to ensure small fluctuation of the underground airflow quantity and to guarantee safe operations of both fans simultaneously by controlling the four air doors during switchover from working to standby fan. MMFSS has time-varying dynamics under different operating conditions, strong coupling, high non-linearities and uncertainty in character, applying conventional control methods can not lead to satisfactory performances. In this study, an adaptive intelligent decoupling proportional–integral–derivative (PID) control method is proposed, where the unmodelled dynamics are estimated and compensated by neural networks, the coupling effect is eliminated by the designed decoupling compensator, and a switching mechanism among multiple models is employed to deal with the effect of time-varying dynamics. By inspiring from the generalised minimum variance control law concept, the parameters of the developed controller are determined. The stability of the close-loop system and the convergence of tracking error are examined. Finally, simulations of MMFSS show the feasibility and effectiveness of the obtained results.

Significant improvements of electrical discharge machining performance by step-by-step updated adaptive control laws

In order to obtain improved electrical discharge machining (EDM) performance, we have dedicated more than a decade to correcting one essential EDM defect, the weak stability of the machining, by developing adaptive control systems. The instabilities of machining are mainly caused by complicated disturbances in discharging. To counteract the effects from the disturbances on machining, we theoretically developed three control laws from minimum variance (MV) control law to minimum variance and pole placements coupled (MVPPC) control law and then to a two-step-ahead prediction (TP) control law. Based on real-time estimation of EDM process model parameters and measured ratio of arcing pulses which is also called gap state, electrode discharging cycle was directly and adaptively tuned so that a stable machining could be achieved. To this end, we not only theoretically provide three proved control laws for a developed EDM adaptive control system, but also practically proved the TP control law to be the best in dealing with machining instability and machining efficiency though the MVPPC control law provided much better EDM performance than the MV control law. It was also shown that the TP control law also provided a burn free machining.

Design of a Performance-Driven Controller with 1-Parameter tuning

In process industries, it is important to maintain the desired control performance in steady state because of requirement of high-quality products and energy saving. This is the main motivation in the development of a performance-driven control scheme based on the minimum variance control law. In that scheme, controller parameters are adjusted when the control performance based on the MV-Index (Minimum Variance Index) deteriorates. However, this MV-Index based tuning scheme only takes into account only controller error variance unfortunately with no regard for manipulative variable activity. To circumvent this omission, this paper describes a design of a new performance-driven control system whose control performance assessment scheme takes into account controller error variance as well as the manipulating variable variance. Furthermore, in this newly proposed scheme, controller parameters are calculated using a fictitious reference iterative tuning (FRIT) scheme which is one of the data-driven tuning scheme. The effectiveness of the proposed scheme is demonstrated by evaluation on a numerical example.

Design and Experimental Evaluation of a Performance-Driven PID Controller

[abstFig src='/00280005/01.jpg' width='300' text='Outline of the performance-driven PID control system' ] This study proposes a performance-driven control method that performs a “control performance assessment” and a “control system design” from a set of closed-loop data. The method assesses control performance based on the minimum variance control law from closed-loop data. It also calculates a control parameter that improves the control performance from the same closed-loop data by using the fictitious reference iterative tuning (FRIT) method. This method is characterized by not requiring any system model. The effectiveness of this method is verified through a numerical simulation and an application result to a temperature control unit.

Fast and stable electrical discharge machining (EDM)

In order to improve EDM performances, the most important issue is to develop a highly stable control system. As a serious defect in EDM adaptive control system by minimum-variance control law, the occasional instability deterred its full applications in industries. This paper focuses on stabilizing EDM process by establishing a new minimum-variance and pole-placement coupled control law. Based on real-time estimation of EDM process model parameters, this adaptive control system directly controls electrode discharging cycle not only to follow a specified gap state for fast machining but also to track the dynamical response of a reference model for stabilizing EDM process. Confirmation experiment demonstrates that this control system can timely adjust electrode discharging cycle in terms of different machining situations quantified as a series of varied gap states to maintain a stable and fast fabrication. The adaptive control system by this newly developed control law exhibits its superior machining ability and capability of stabilizing sparking process to those of the adaptive control system by minimum-variance control law. The adaptive system has actually theoretically and technically solved the stability issue puzzled EDM circle for decades.

A Study on Minimum Variance Benchmark under Actuator Constrains and Stochastic Disturbances

As a benchmark to assess the performance of the control loops, MV (minimum variance) has been widely used in industrial process.MV control gives the lowest achievable output variance when there is no constraint on the actuator. In this paper, it shows that MV controller is no longer optimal and the mean of the output value is non-zero when the constraint is active and the parameter of the disturbance is approaching to one. In order to achieve the lowest variance of the output value, and the mean of the output value can be approaching to zero, a new approach is proposed in this paper. The proposed method is imposing a compensation value on the constrained MV control law, meanwhile, a new performance index function is introduced. As a result, it is believed that this method is more effective to the real industrial process for systems with actuator constraints and stochastic disturbances. Simulation example demonstrates the usefulness of this method.

Control of a Weigh Feeder Based on Performance Assessment

This study discusses a design method to determine one of the design parameters in generalized minimum variance control (GMVC) law from the viewpoint of the control assessment. In this paper, a PI control law is designed based on GMVC. In addition, the control performance of the designed controller is evaluated by using a minimum variance index, and the design parameter in GMVC is automatically changed such that the control performance is optimized. In the proposed method, unknown plant parameters are estimated, and the PI control law based on GMVC is updated using estimated parameters. Finally, the effectiveness of the proposed method is shown through an experiment.

Neural Model-Based Self-Tuning PID Strategy Applied to PEMFC

This paper illustrates the benefits of a self-tuning PID strategy applied to a proton exchange membrane fuel cell system. Controller parameters are updated on-line, at each sampling time, based on an instantaneous linearization of an artificial neural network model of the process and a General Minimum Variance control law. The self-tuning PID scheme allows managing nonlinear behaviors of the system while avoiding heavy computations. The applicability, efficiency and robustness of the proposed control strategy are experimentally confirmed using varying control scenarios. In this aim, the original built-in controller is overridden and the self-tuning PID controller is implemented externally and executed on-line. Experimental results show good performance in setpoint tracking accuracy and robustness against plant/model mismatch. The proposed strategy appears to be a promising alternative to heavy computation nonlinear control strategies and not optimal linear control strategies.

Non‐linear generalised minimum variance control using unstable state‐dependent multivariable models

A non-linear generalised minimum variance (NGMV) control law is derived for systems represented by an input-output state dependent non-linear (NL) subsystem that may be open-loop unstable. The solution is obtained using a model for the multivariable discrete-time process that includes a state-dependent (NL and possibly unstable) model that links the output and any `unstructured' NL input subsystem. The input subsystem can involve an operator of a very general NL form, but this has to be assumed to be stable. This is the first NGMV control solution that is suitable for systems containing an unstable NL sub-system which is contained in the state-dependent model. The process is also assumed to include explicit common delays in input or output channels. The generalised minimum variance cost index to be minimised involves both dynamically weighted error and control signal costing terms. It may also include weighted values of the system states for greater generality. The controller derived is simple to implement considering the complexity of the system represented. If the plant is stable the controller structure can be manipulated into an internal model control form. This form of the controller is like an NL version of the Smith Predictor which is valuable for providing confidence in the solution.

Deterministic vs. stochastic performance assessment of iterative learning control for batch processes

The performance assessment of linear time‐invariant batch processes when iterative learning control (ILC) is implemented has been discussed. Previous literatures show that conventional performance assessment cannot be directly applied to batch processes due to the nature of batch operations. Chen and Kong have suggested a new method to assess the control performance of batch processes using optimal ILC as the benchmark. In their work, ILC controllers are assumed to affect either stochastic or deterministic performance but without considering their interaction. This work elaborates the controllers effects on both stochastic and deterministic control performance of batch processes. It is shown that the optimal solution based on the minimum variance control law has a trade‐off between deterministic and stochastic performance, which can be shown by a trade‐off curve. Furthermore, a method is proposed to estimate this curve from routine operating data, against which the performance of ILC controllers can be assessed. Simulation studies are conducted to verify the proposed method. © 2012 American Institute of Chemical Engineers AIChE J, 59: 457–464, 2013

Recursive Gauss–Seidel algorithm for direct self‐tuning control

SUMMARYA recursive algorithm based on the use of Gauss–Seidel iterations is introduced to adjust the parameters of a self‐tuning controller for minimum phase and a class of nonminimum phase discrete‐time systems. The proposed algorithm is called the Recursive Gauss–Seidel (RGS) algorithm and is used to update the controller parameters directly. The use of the RGS algorithm with a generalized minimum variance control law is also given for nonminimum phase systems, and a forgetting factor is used to track the time‐varying parameters. Furthermore, the overall stability of the closed‐loop system is proven by using the Lyapunov stability theory. Using computer simulations, the performance of the RGS algorithm is examined and compared with the widely used recursive least squares algorithm.Copyright © 2011 John Wiley & Sons, Ltd.

Tapping the energy storage potential in electric loads to deliver load following and regulation, with application to wind energy

This paper develops new methods to model and control the aggregated power demand from a population of thermostatically controlled loads, with the goal of delivering services such as regulation and load following. Previous work on direct load control focuses primarily on peak load shaving by directly interrupting power to loads. In contrast, the emphasis of this paper is on controlling loads to produce relatively short time scale responses (hourly to sub-hourly), and the control signal is applied by manipulation of temperature set points, possibly via programmable communicating thermostats or advanced metering infrastructure. To this end, the methods developed here leverage the existence of system diversity and use physically-based load models to inform the development of a new theoretical model that accurately predicts – even when the system is not in equilibrium – changes in load resulting from changes in thermostat temperature set points. Insight into the transient dynamics that result from set point changes is developed by deriving a new exact solution to a well-known hybrid state aggregated load model. The eigenvalues of the solution, which depend only on the thermal time constant of the loads under control, are shown to have a strong effect on the accuracy of the model. The paper also shows that load heterogeneity – generally something that must be assumed away in direct load control models – actually has a positive effect on model accuracy. System identification techniques are brought to bear on the problem, and it is shown that identified models perform only marginally better than the theoretical model. The paper concludes by deriving a minimum variance control law, and demonstrates its effectiveness in simulations wherein a population of loads is made to follow the output of a wind plant with very small changes in the nominal thermostat temperature set points.

GMV control of non-linear continuous-time systems including common delays and state-space models

A non-linear generalized minimum variance control law is proposed for the control of non-linear continuous-time multivariable systems with common delays on input and output channels. The quadratic cost index involves both error and control signal costing terms. The solution for the control law is obtained using a non-linear operator representation of the plant and a linear state-equation model for the disturbance and reference models. The reference and disturbance models are represented by linear subsystems. However, the plant model can be in a very general non-linear operator form, which could involve state-space, transfer operators or non-linear function look up tables. The structure of the system and criterion is chosen so that a simple controller structure and solution is obtained. The controller obtained is simple to implement, particularly in one form, which might be considered to be a state-space version of a non-linear Smith predictor. The results are related to those for discrete-time systems but the presence of the transport delay terms complicates the solution rather more in the continuous-time case.