Generalized Predictive Control Research Articles

GPC Control of a Fractional–Order Plant: Improving Stability and Robustness

This work deals with the use of Generalized Predictive Control (GPC) with fractional order plants. Low integer–order discrete approximations will be used as models to design the controllers. The stability and robustness of the closed loop system will be studied with the Nyquist criterion. Three techniques will be proposed to enhance robustness: the improvement of the model response at low frequencies, the use of the prefilter T(z−-1), and a new recommendation to choose two of the parameters (the control horizon Nu and the error weighting sequence λ) of the GPC controller.

Generalized Predictive Control in Flying Shear Equipment

To develop and evaluate improved on-line flying-shear equipment control tasks, we introduces a Generalized Predictive Control (GPC) PID controller for positioning control of a flying-shear cutter. After successful trials and excellent regulation results, the GPC-based PID control algorithm with constraints is proved to be very robust.

Generalized Predictive Control in Fast-Rate Single-Rate and Dual-Rate Systems

This paper discusses design of Generalized Predictive Control (GPC) scheme. GPC is designed in two cases; the first is a dual-rate (DR) system, where the sampling interval of a plant output is an integer multiple of the holding interval of a control input, and the second is a fast-rate single-rate (FR-SR) system, where both the holding and sampling intervals are equal to the holding interval of the DR system. Furthermore, the relation between them is investigated, and this study gives the conditions that FR-SR and DR GPC become equivalent. To this end, a future reference trajectory of DR GPC is rewritten, and a future predictive output of the FR-SR GPC is rearranged.

Generalized Predictive Control with Online Least Squares Support Vector Machines

This paper proposes a practical generalized predictive control (GPC) algorithm based on online least squares support vector machines (LS-SVM) which can deal with nonlinear systems effectively. At each sampling period the algorithm recursively modifies the model by adding a new data pair and deleting the least important one out of the consideration on realtime property. The data pair deleted is determined by the absolute value of lagrange multiplier from last sampling period. The paper gives the recursive algorithm of model parameters when adding a new data pair and deleting an existent one, respectively, and thus the inversion of a large matrix is avoided and the memory can be controlled by the algorithm entirely. The nonlinear LS-SVM model is applied in GPC algorithm at each sampling period. The experiments of generalized predictive control on pH neutralizing process show the effectiveness and practicality of the proposed algorithm.

Generalized predictive control for improving intersample performance

AbstractThis paper proposes a design method of the Generalized Predictive Control (GPC) strategy which can take account of intersample behavior as well as sampled behavior. To this end, a discrete‐time equivalent plant model and cost function for a continuous‐time plant incorporated with zero‐order hold and discrete‐time controller are derived, and the modified discrete‐time GPC is designed. To verify the effectiveness of our proposed method, the controller is applied to a benchmark problem of a hard‐disk drive. Copyright © 2007 Institute of Electrical Engineers of Japan. Published by John Wiley & Sons, Inc.

Computationally Efficient Predictive Robot Control

Conventional linear controllers (PID) are not really suitable for the control of robot manipulators due to the highly nonlinear behavior of the latter. Over the last decades, several control methods have been proposed to circumvent this limitation. This paper presents an approach to the control of manipulators using a computationally-efficient-model-based predictive control scheme. First, a general predictive control law is derived for position tracking and velocity control, taking into account the dynamic model of the robot, the prediction and control horizons, and also the constraints. However, the main contribution of this paper is the derivation of an analytical expression for the optimal control to be applied that does not involve a numerical procedure, as opposed to most predictive control schemes. In the last part of the paper, the effectiveness of the approach for the control of a nonlinear plant is illustrated using a direct-drive pendulum, and then, the approach is validated and compared to a PID controller using an experimental implementation on a 6-DOF cable-driven parallel manipulator.

Real-time feedback control of flow-induced cavity tones—Part 1: Fixed-gain control

A generalized predictive control (GPC) algorithm was formulated and applied to the cavity flow-tone problem. The control algorithm demonstrated multiple Rossiter-mode suppression at fixed Mach numbers ranging from 0.275 to 0.38. Controller performance was evaluated with a measure of output disturbance rejection and an input sensitivity transfer function. The results suggest that disturbances entering the cavity flow are collocated with the control input at the cavity leading edge. In that case, only tonal components of the cavity wall-pressure fluctuations can be suppressed and arbitrary broadband pressure reduction is not possible with the present sensor/actuator arrangement. In the control-algorithm development, the cavity dynamics were treated as linear and time invariant for a fixed Mach number. The experimental results lend support to that treatment.

Real-time feedback control of flow-induced cavity tones—Part 2: Adaptive control

An adaptive generalized predictive control (GPC) algorithm was formulated and applied to the cavity flow-tone problem. The algorithm employs gradient descent to update the GPC coefficients at each time step. Past input–output data and an estimate of the open-loop pulse response sequence are all that is needed to implement the algorithm for application at fixed Mach numbers. Transient measurements made during controller adaptation at fixed Mach number revealed that the controller coefficients converged to a steady state in the mean, and this implies that adaptation can be turned off at some point with no degradation in control performance. The control algorithm demonstrated multiple Rossiter mode suppression at fixed Mach numbers of 0.275, 0.32, and 0.38, provided the plant model was updated for each Mach number. However, as in the case of fixed-gain GPC, the adaptive GPC was limited by spillover in sidebands around the suppressed Rossiter modes. The algorithm was also able to maintain suppression of multiple cavity tones as the freestream Mach number was varied over a modest range (0.275–0.29). Beyond this range, stable operation of the control algorithm was not possible due to the fixed plant model in the algorithm.

CARMA-model-based j-step-ahead prediction for MIMO systems

The single-input single-output (SISO) j-step-ahead predictor for generalized predictive control (GPC) controllers was traditionally derived using the polynomial approach through the Diophantine equations. An equivalent version of the predictor in a state-space form is available in the literature. In this paper, a z-domain analysis of the multiple input multiple output (MIMO) extension of the state-space predictor is carried out, and then an MIMO j-step-ahead predictor in polynomial form based on the controlled autoregressive moving average model is derived. The predictor enables us to simplify the GPC algorithm design for multivariable systems. In the SISO case the predictor is just the traditional GPC predictor, therefore this paper gives rigorous proof of the equivalence between the traditional GPC predictor and the state-space predictor.

Constrained predictive control based on T-S fuzzy model for nonlinear systems

Abstract A constrained generalized predictive control (GPC) algorithm based on the T-S fuzzy model is presented for the nonlinear system. First, a Takagi-Sugeno (T-S) fuzzy model based on the fuzzy cluster algorithm and the orthogonal least square method is constructed to approach the nonlinear system. Since its consequence is linear, it can divide the nonlinear system into a number of linear or nearly linear subsystems. For this T-S fuzzy model, a GPC algorithm with input constraints is presented. This strategy takes into account all the constraints of the control signal and its increment, and does not require the calculation of the Diophantine equations. So it needs only a small computer memory and the computational speed is high. The simulation results show a good performance for the nonlinear systems.

Output power leveling of wind turbine generators using pitch angle control for all operating regions in wind farm

AbstractEffective utilization of renewable energies such as wind energy instead of fossil fuels is desirable. Wind energy is not constant and windmill output is proportional to the cube of the wind speed, which causes the generated power of wind turbine generators (WTGs) to fluctuate. In order to reduce the output power fluctuation of wind farms, this paper presents an output power leveling control strategy for a wind farm based on both the average wind farm output power and the standard deviation of the wind farm output power, a cooperative control strategy for WTGs, and pitch angle control using a generalized predictive controller (GPC) in all WTG operating regions. Simulation results using an actual detailed model for wind farm systems show the effectiveness of the proposed method. © 2007 Wiley Periodicals, Inc. Electr Eng Jpn, 158(4): 31– 41, 2007; Published online in Wiley InterScience (www.interscience. wiley.com). DOI 10.1002/eej.20448

GPC Robust Design Using Linear and/or Bilinear Matrix Inequalities*

This article proposes an integrated methodology for the robust design of a generalized predictive controller (GPC) based on linear and/or bilinearmatrix inequalities (LMIs/ BMIs). Firstly, a GPC formulation in state space which incorporates a full rank observer to estimate the on-line states is presented. It is then shown that the poles of such an observer are equivalent to the roots of filter polynomials Tj(z−1) in a GPC Input/Output (I/O)formulation, which implies that these poles inherit the robustness effect associated with filter polynomial roots. In this way, we obtain closed-loop robust stability conditions and closedloop robust ∞ -norm bounding conditions for the design of a GPC, based on LMIs and/or BMIs. These conditions take into account linear fractional (LFR) plant uncertainty. This type of uncertainty also contains affine dependence as a particular case, and can represent any matrix rational function. Finally, the robust GPC parameters are optimally obtained using a multiobjective genetic algorithm (GA). This integrated methodology is applied, as an example, to themultiobjectivemaximization of an uncertainty range and ∞ -norm minimization in a benchmark plant: the twomass-spring mechanical system.

Fault Detection and Control of Process Systems

This paper develops a stochastic hybrid model-based control system that can determine online the optimal control actions, detect faults quickly in the control process, and reconfigure the controller accordingly using interacting multiple-model (IMM) estimator and generalized predictive control (GPC) algorithm. A fault detection and control system consists of two main parts: the first is the fault detector and the second is the controller reconfiguration. This work deals with three main challenging issues: design of fault model set, estimation of stochastic hybrid multiple models, and stochastic model predictive control of hybrid multiple models. For the first issue, we propose a simple scheme for designing faults for discrete and continuous random variables. For the second issue, we consider and select a fast and reliable fault detection system applied to the stochastic hybrid system. Finally, we develop a stochastic GPC algorithm for hybrid multiple-models controller reconfiguration with soft switching signals based on weighted probabilities. Simulations for the proposed system are illustrated and analyzed.

A novel algorithm of constrained multivariable fuzzy generalised predictive control for non-linear systems

A constrained multivariable Generalised Predictive Control (GPC), which is based upon the T-S fuzzy model, is proposed for a class of non-linear systems. The proposed method can deal with the case of rate and amplitude constraints for the control signal with a way different from the classical constrained multivariable GPC, so the computation burden cut down with a degree and the control scheme can be used in the high speed sampled control systems. The simulation results demonstrate the effectiveness of the proposed algorithm.

A PRACTICAL APPROACH TO PREDICTIVE CONTROL FOR NONLINEAR PROCESSES

This paper presents a Model Predictive Control (MPC) Technique for Nonlinear Systems. The algorithm is based on a new interpretation of the procedure used by traditional linear predictive controllers, like Dynamic Matrix Control (DMC) and Generalized Predictive Controller (GPC), to compute the predictions. The proposed technique requires no specific model structure, treating equally models based on neural networks, difference equations or ordinary difference equation systems. Comparisons to other techniques are presented in the paper applying the algorithm to nonlinear systems available in literature. The main advantages of the proposed approach are: (i) it makes no use of iterative algorithms, (ii) the control action can be obtained by the same methods used in linear MPCs and (iii) any type of nonlinear model can be used.

HIGHER-ORDER GENERALIZED 2D PREDICTIVE ITERATIVE LEARNING CONTROL SCHEMES

In this paper, based on the prediction control performances defined over one cycle or multiple cycles, two higher-order ILC schemes have been developed by extending the Generalized Predictive Control (GPC) method to the two-dimensional (2D) system. The dynamics of the ILC system along time and cycle is taken as a 2D system, and the proposed designs integrate optimally the design and the combination of a time-wise GPC scheme and a cycle-wise ILC scheme in 2D sense. The simulations show the feasibility and effectiveness of the proposed algorithms.

Multivariable Decoupling Predictive Control Based on QFT Theory and Application in CSTR Chemical Process

A novel method of incorporating generalized predictive control (GPC) algorithms based on quantitative feedback theory (QFT) principles is proposed for solving the feedback control problem of the highly uncertain and cross-coupling plants. The quantitative feedback theory decouples the multi-input and multi-output (MIMO) plant and is also used to reduce the uncertainties of the system, stabilize the system, and achieve tracking performance of the system to a certain extent. Single-input and single-output (SISO) generalized predictive control is used to achieve performance with higher performance. In GPC, the model is identified on-line, which is based on the QFT input and the plant output signals. The simulation results show that the performance of the system is superior to the performance when only QFT is used for highly uncertain MIMO plants.

MIMO Generalized Predictive Control for a Hydroelectric Power Station

In this paper, the approach of generalized predictive control (GPC) is applied to a multivariable model of the Dinorwig pumped-storage hydroelectric power station. The response of the system with constrained predictive control is compared with the classic PI controller as currently implemented. The results show that GPC offers significantly better performance across the plant's operating range. It is shown that fixed-parameter, constrained GPC produces a faster primary response when the station is operating with a single unit while preserving stability as the operating conditions change when multiple units are online

Generalized predictive control applied to a pH neutralization process

In this work, generalized predictive control (GPC) was applied to a pH neutralization process. The process consists of a continuous flow tubular reactor. The process stream is a water solution of acetic acid and the titrating stream is a water solution of sodium hydroxide. The aim of the control is to keep the pH value at a given set point value when the process is subjected to variations in feed flowrate. The use of polynomial autoregressive integral moving average with external input (ARIMAX) model related with pH and base flowrate was emphasized. The model parameters were determined by using Bierman and Genetic algorithms. The λ weighting was varied in order to achieve optimal GPC performance. The efficiency of the GPC was observed by calculating the integral of the square of the error (ISE) and the integral of the absolute value of the error (IAE) from experimental results.

Neural generalized prediction control with modified performance index

The objective of this paper is to improve the dynamic response and reduction in sluggishness in neural generalized predictive control (NGPC) with a modified performance index. A comparative study has been made between NGPC and a modified NGPC. The simulation results show that there is further significant improvement in the dynamic response using the modified NGPC.