Nonlinear Generalized Predictive Control Research Articles

Improved nonlinear generalized model predictive control for robustness and power enhancement of a DFIG-based wind energy converter

Many studies have been made on the double-fed induction generator wind turbine system (DFIG-WTS) in recent decades due to its power management capability, speed control operation, low converter cost, and minimized energy losses. In contrast, induction machine control is a more complex task because of its multivariable and nonlinear nature. In this work, a new robust nonlinear generalized predictive control (RNGPC) is developed to maximize the extracted energy from the wind without the use of aerodynamic torque measurements or an observer. The aim of the predictive control is to produce an anticipated impact by employing explicit knowledge of the present condition. By revisiting the cost function of the conventional nonlinear generalized predictive control (NGPC), which is based on Taylor series expansion, in that way, the resilience of the system is improved. An integral action is included in the nonlinear predictive controller. As a result, if the closed loop system is stable, the suggested controller totally eliminates the steady state error, even if unknown perturbations and mismatched parameters are present. The output locating error’s convergence to the source is utilized to show the locked system’s stability. Simulation results demonstrate and verify the efficiency, the good performance, and robustness of this proposed control technique.

Multivariable generalized predictive control of reactive distillation column process for biodiesel production

Most industrial control systems consist of a significant number of control loops. Generally, large processes are divided into many interconnected subsystems affecting each other, thus creating multivariable systems known as multiple–input multiple–output (MIMO) process. Generalized Predictive Control (GPC) based control algorithm is most suitable for MIMO systems. In this study, multivariate nonlinear (NL) GPC and discrete–time PID control of calcium oxide catalyst–packed reactive distillation (RD) column used for biodiesel production from waste cooking oil were investigated. Temperatures of reaction and reboiler sections were controlled by using non–decoupled and decoupled MIMO NLGPC and discrete–time MIMO PID algorithms. Feed flow rate with constant molar ratio and reboiler heat duty parameters were selected as manipulating variables. All recommended control methods, except for non-decoupled MIMO NLGPC, have been found to perform satisfactorily reference tracking and disturbance rejection in RD column. Consequently, the best control results were obtained in the decoupled MIMO NLGPC.

Stability improvement of large-scale power systems in the presence of wind farms by employing HVDC and STATCOM based on a non-linear controller

In this paper, a non-linear generalized predictive control (NGPC) has been used for the stability analysis in a hybrid power system consisting of series and parallel compensators in the presence of wind farms. In this system, STATCOM has been used as a parallel compensator for improving reactive power of the wind farm, and HVDC is employed to improve damping of transmission line connected to the power system. The proposed method is based on two internal and external control loops. The internal control loop is used to apply the switching signals suitable for the rotor-side converter in DFIG, HVDC’s converter, and the STATCOM inverter. In the external control loop, a disturbance observer has been employed to estimate the aerodynamic torque and to control the wind turbine’s speed. The aim of designing the observer is to evaluate the robustness of the controller under the changes of internal parameters of the system. The simulations have been implemented in the MATLAB software in different scenarios on a large-scale power system with 16 machines and 68 buses.

One Layer Nonlinear Economic Closed-Loop Generalized Predictive Control for a Wastewater Treatment Plant

The main scope of this paper is the proposal of a new single layer Nonlinear Economic Closed-Loop Generalized Predictive Control (NECLGPC) as an efficient advanced control technique for improving economics in the operation of nonlinear plants. Instead of the classic dual-mode MPC (model predictive controller) schemes, where the terminal control law defined in the terminal region is obtained offline solving a linear quadratic regulator problem, here the terminal control law in the NECLGPC is determined online by an unconstrained Nonlinear Generalized Predictive Control (NGPC). In order to make the optimization problem more tractable two considerations have been made in the present work. Firstly, the prediction model consisting of a nonlinear phenomenological model of the plant is expressed with linear structure and state dependent matrices. Secondly, instead of including the nonlinear economic cost in the objective function, an approximation of the reduced gradient of the economic function is used. These assumptions allow us to design an economic unconstrained nonlinear GPC analytically and to state the NECLGPC allow for the design of an economic problem as a QP (Quadratic Programing) problem each sampling time. Four controllers based on GPC that differ in designs and structures are compared with the proposed control technique in terms of process performance and energy costs. Particularly, the methodology is implemented in the N-Removal process of a Wastewater Treatment Plant (WWTP) and the results prove the efficiency of the method and that it can be used profitably in practical cases.

A nonlinear generalized predictive control for pumped storage unit

In this paper, the control problem of pumped storage unit (PSU) has been studied. A nonlinear generalized predictive control (NGPC) method has been applied to design the controller for a PSU. The NGPC controller is designed based on instantaneous linearization model of the control system, and the parameters of the linearized model are identified online by the recursive least square method (RLSM). Besides, in order to minimize the modelling error on initial state, a prior-knowledge learning method has been proposed to get the initial parameters for control model estimation. To verify the effectiveness of the NGPC controller, we chose a pumped-storage hydropower plant in China as the experimental subject and the simulation experiments respect to the control system are designed. The processes of start-up and speed disturbance under no-load condition have been simulated to testify the robustness and efficiency of the NGPC controller. Comparative experiments have been conducted, while the NGPC controller, a PID controller and a fractional order PID (FOPID) controller have been compared. Experimental results show that the designed NGPC could effectively restrain the oscillation of rotational speed in different working conditions of PSU and demonstrates higher robustness and stability than both the PID and FOPID controllers.

Model-based Predictive and Backstepping controllers for a state coupled four-tank system with bounded control inputs: A comparative study

This paper investigates the problem of global tracking control design for a state coupled four-tank liquid level system with bounded control inputs. For this MIMO system׳s dynamics, motivated by a desire to provide precise liquid level control, two radically different control approaches are presented and compared: the nonlinear generalized predictive control (NGPC) and the Backstepping control. First, an analytical solution of the NGPC is developed based on the nominal model. Then, a nonlinear Backstepping controller is designed in order to ensure globally asymptotical stabilization for this nonlinear system. To ensure a suitable basis for their comparison, the two different control methods are designed and verified with the same test setup under the control input saturation imposed by the system’s actuators. To highlight the efficiency and applicability of the proposed control schemes, simulation as well as experimental results are provided and discussed.

Real time simulation of nonlinear generalized predictive control for wind energy conversion system with nonlinear observer

In order to make a wind power generation truly cost-effective and reliable, an advanced control techniques must be used. In this paper, we develop a new control strategy, using nonlinear generalized predictive control (NGPC) approach, for DFIG-based wind turbine. The proposed control law is based on two points: NGPC-based torque-current control loop generating the rotor reference voltage and NGPC-based speed control loop that provides the torque reference. In order to enhance the robustness of the controller, a disturbance observer is designed to estimate the aerodynamic torque which is considered as an unknown perturbation. Finally, a real-time simulation is carried out to illustrate the performance of the proposed controller.

Adaptive interconnected observer-based sensorless non-linear generalised predictive control for IMs with parameters tuning

The combination of the non-linear generalised predictive control (NGPC) and the adaptive interconnected observer (AIO) is considered for the design of the output feedback predictive controller. Since the induction motors (IMs) are intensively used in applications requiring high dynamic performance, the algorithm developed is potentially useful for a fully decoupling in speed and flux magnitude regulation. Indeed, in a first step the state-feedback controller is given, which stems from the approximation of the output tracking error in the receding horizon by its Taylor-series expansion is given. In a second step, the AIO property is exploited in order to avoid the problem of parameters uncertainly and state unavailability during the drive motor, with realising a suitable tracking of trajectories for the system output. This results in a sensorless control of the induction motors, whose rotor and stator resistances, the load torque, the rotor flux and mechanical speed are simultaneously recovered by profiting only from the measurements of the stator current. Effectiveness of the proposed observers and the performance of the controller are confirmed by simulation results.

Online-SVR-compensated nonlinear generalized predictive control for hypersonic vehicles

This paper is concerned with the problem of hypersonic vehicle (HSV) attitude control system in uncertain flight conditions. The problem can be expressed as the adaptive robust control for a class of uncertain nonlinear systems. Based on the description of the aerodynamic structure and the model of flight control system of a certain kind of HSV, the ideal nonlinear generalized predictive control (NGPC) law based on uncertain nonlinear model is raised first to optimize the receding-horizon criterion of tracking errors. Then the online support vector regression (SVR) is employed to identify the uncertain item in the ideal control law. It is the compensating part of the controller. In addition, the stability of the close-loop system is analyzed using the Lyapunov method. The developed control strategy is well-implemented in this HSV attitude control system, and the simulation results compared with both nominal NGPC and RBF neural network disturbance observer show the good robustness and disturbance attenuation ability of this strategy and demonstrate the efficiency of online SVR algorithm.

Adaptive recurrent-functional-link-network control for hypersonic vehicles with atmospheric disturbances

The controller design for a near-space hypersonic vehicle (NHV) is challenging due to its plant uncertainties and sensitivity to atmospheric disturbances such as gusts and turbulence. This paper first derives 12 states equations of NHVs subjected to variable wind field, and presents a novel recurrent neural network (RNN) control method for restraining atmospheric disturbances. The method devises a new B-spline recurrent functional link network (BRFLN) and combines it with the nonlinear generalized predictive control (NGPC) algorithm. Moreover, the proportional-derivative (PD) correction BRFLN is proposed to approximate atmospheric disturbances in flight. The weights of BRFLN are online tuned by the adaptive law based on Lyapunov stability theorem. Finally, simulation results show a satisfactory performance for the attitude tracking of the NHV in the mesosphere, and also illustrate the controller’s robustness to wind turbulence.

SMDO-Based NGPC Control for Uncertain Nonlinear Systems

As the velocity of near-space vehicle (NSV) is hypersonic, the system should be influenced by strong disturbance and uncertainty. It is difficult to design the flight control system. Nonlinear Generalized Predictive Control (NGPC) method is investigated based on the mechanism model. However, the control performance of NGPC method based on nominal model will be degraded for uncertain systems. Therefore, concerning about a class of uncertain nonlinear systems, the ideal NGPC law based on uncertain model is raised first in this paper. Then a sliding mode disturbance observer (SMDO) is designed to estimate the compound disturbance which includes internal uncertainty, modeling error, and external disturbance. On the other hand, the outputs of SMDO are integrated with nominal NGPC law to eliminate the hybrid disturbance. Furthermore, the stability of the close-loop system is analyzed using the Lyapunov method. Finally, the developed control strategy is used in a hypersonic NSV attitude control system, and simulation results show good robustness and disturbance attenuation ability of this strategy.

Generalized delta rule (GDR) algorithm with generalized predictive control (GPC) for optimum temperature tracking of batch polymerization

The generalized delta rule (GDR) algorithm with generalized predictive control (GPC) control was implemented experimentally to track the temperature on a set point in a batch, jacketed polymerization reactor. An equation for optimal temperature was obtained by using co-state Hamiltonian and model equations. To track the calculated optimal temperature profiles, controller used should act smoothly and precisely as much as possible. Experimental application was achieved to obtain the desired comparison. In the design of this control system, the reactor filled with styrene–toluene mixture is considered as a heat exchanger. When the reactor is heated by means of an immersed heater, cooling water is passed through the reactor-cooling jacket. So the cooling water absorbs the heat given out by the heater. If this is taken into consideration, this reactor can be considered to be continuous in terms of energy. When such a mixing chamber was used as a polymer reactor with defined values of heat input and cooling flow rate, system can reach the steady-state condition. The heat released during the reaction was accepted as a disturbance for the heat exchanger. Heat input from the immersed heater is chosen as a manipulated variable. The neural network model based on the relation between the reactor temperature and heat input to the reactor is used. The performance results of GDR with GPC were compared with the results obtained by using nonlinear GPC with NARMAX model. The reactor temperature closely follows the optimal trajectory. And then molecular weight, experimental conversion and chain lengths are obtained for GDR with GPC.

Non-linear generalised predictive control of a jacketed well mixed tank as applied to a batch process—A polymerisation reaction

The purpose of this study is to control the temperature of a well mixed jacketed tank under set-point changes with the use of non-linear generalised predictive control (NLGPC) system. Firstly, perturbations were given to the cooling flow rates so as to investigate the dynamic behaviour of the process. The emphasis was put on the use of polynomial non-linear autoregressive moving average with external input (NARIMAX) model related with tank temperature and heat input for non-linear control. The second part of the study deals with the presentation of identification algorithm for the construction of polynomial NARIMAX and autoregressive moving average with external input (ARIMAX) models. A pseudo random binary sequence (PRBS) signal was utilised as a forcing function in order to determine the parameters of the models. Levenberg–Marquardt algorithm was applied in the estimation of relevant parameters of NARIMAX model. Similar studies were performed for the ARIMAX model using Bierman algorithm. Next linear and non-linear models with generalised predictive control (GPC) algorithm were applied to test the performance of the available control in response to disturbances. Finally the results from NLGPC were compared with linear generalised predictive control (LGPC) to see the efficiency of the batch control system.

OPTIMAL TEMPERATURE CONTROL IN A BATCH POLYMERIZATION REACTOR USING NONLINEAR GENERALIZED PREDICTIVE CONTROL

The application of Non-Linear Generalized Predictive Control (NLGPC) to the free radical solution polymerization of styrene in a jacketed batch reactor has been realized. The dynamic behavior of polymerization reactor is modelled and simulated for control purposes. The optimal temperature policies for minimum time, desired conversion and molecular chain length were obtained at different initiator concentrations by applying the optimal control theory which is based on the Hamiltonian principle. The polynomial Nonlinear auto Regressive Integrated Moving Average with external input (NARIMAX) model is used to relate the reactor temperature with heat input for nonlinear control algorithm. The linear (ARIMAX) and nonlinear (NARIMAX) models are utilized in the GPC algorithm for comparison. A Pseudo Random Binary Sequence (PRBS) signal was employed to operate the system. The model parameters are evaluated by using Levenberg Marquart Method. The NLGPC, Linear Generalized Predictive Control (LGPC) and standard PID controllers are applied experimentally to the polymerization reactor by using on-line computer control system. The performance of NLGPC control system was compared with LGPC and standard PID controller. It is concluded that the NLGPC control gives much better performance than the other.

Experimental evaluation of predictive temperature control for a batch reactor system

A nonlinear generalized predictive control (NLGPC) algorithm developed by Katende and Jutan (1996) is tested on a nonlinear batch reactor system by carrying out a number of experiments and comparing its performance with other control strategies. This experimental setting allows a more practical comparison of the relative merits of these controllers. The NLGPC is shown to outperform the constrained self-tuning PID (STPID) controller by Katende and Jutan (1993), and the generalized minimum variance (GMV) controller by Clarke and Gawthrope (1975). It is also shown to have better performance than the well-known generalized predictive control (GPC) algorithm by Clarke et al. (1987). The advantage of the NLGPC over the other controllers is attributed to its adaptive nature and use of nonlinear process models in its design.

Nonlinear PID Predictive Controller

A class of nonlinear PID controllers is derived for nonlinear systems using a nonlinear generalised predictive control (NGPC) approach. First, the disturbance decoupling ability of the NGPC is discussed. For a nonlinear system where the disturbance cannot be decoupled, a nonlinear observer is designed to estimate the offset. By selecting the nonlinear gain function in the observer, it is shown that the closed-loop system under optimal generalised predictive control with the nonlinear observer is asymptotically stable. It is pointed out that this composite controller is equivalent to a nonlinear controller with integral action. As a special case, for a nonlinear system with a low relative degree, the proposed nonlinear controller reduces to a nonlinear PI or PID predictive controller, which consists of a nonlinear PI or PID controller and a prediction controller. The design method is illustrated by an example nonlinear mechanical system.

Nonlinear generalised predictive control and optimal dynamical inversion control

Abstract This paper addresses nonlinear Generalised Predictive Control (GPC) for nonlinear mechanical systems and its relationship with dynamical inversion control. First continuous-time generalised predictive control for nonlinear systems is developed and the stability of the closed-loop systems is shown. It is pointed out that the dynamical inversion control is a special case of continuous-time nonlinear GPC. This result also provides an optimal design method for dynamical inversion control in term of the generalised predictive control performance index. The nonlinear GPC developed is successfully applied to the control of a two-link robotic manipulator.

Quadratic Nonlinear Predictive Control

Generalized predictive control (GPC) has been well-accepted in the chemical process industries because of its adaptive nature and ease of tuning. Nevertheless, the GPC structure is based on linear models, which can be a limitation for highly nonlinear processes often found in the chemical industry. A nonlinear generalized predictive control (NLGPC) algorithm was developed by Katende and Jutan (IEEE ACC Proceedings, Session FP10, Seattle, WA, 1995; Ind. Eng. Chem. Res. 1996, 35, 3539) and compared favorably to the standard GPC; however, the computational burden could be excessive in some cases. In this paper two quadratic forms of the NLGPC are developed on the basis of a second-order Hammerstein model structure and different criterion functions. These second-order models allow for simple on-line implementation and lay the basis for analytical evaluation of the algorithms. In this paper, simulation of sample problems are carried out and the effect of each criterion function used in the nonlinear controller...

Non-linear generalized predictive control (NLGPC) applied to muscle relaxant anaesthesia

The well-known generalized predictive control (GPC) algorithm is used to derive a discrete-time non-linear predictive controller for muscle relaxant anaesthesia, which has a Wiener structure representation, and which normally exhibits strong non-linearities as well as varying dead-time and lag dynamics owing to patient-topatient variability. The proposed controller minimizes the GPC quadratic performance index, taking into account the non-linear output predictions obtained using predictions of the linear part inferred using the inverse of the non-linear function. The minimization problem is solved using robust numerical search methods such as the golden section search method when NU= 1, the modified simplex method of Nelder-Mead when NU > 1 or genetic algorithms. Moreover, variations in the model dynamics are estimated using a recursive least-squares (RLS) estimation algorithm. The proposed scheme is shown to be superior to the linear GPC algorithm even in the case of significant mismatch between the assumed model nonlinearity and that of the actual system. The work forms the validation basis for future clinical trials on humans in operating theatre conditions.

Generalized Predictive Control System Design Based on Non-Linear Identification by Using Hammerstein Model

Two types of new adaptive generalized predictive control (GPC) system design methods are proposed for a class of non-linear systems described by Hammerstein model. These methods consist of two parts, that is, non-linear system identification part and GPC design one. Since Hammerstein model is a serial connection of static non-linear block and dynamic linear one; firstly we identify each characteristics based on observed input-output data. Then, two types of GPC design methods are applied to the identified model. One method is based on decomposition of the system to non-linear part and linear one. The GPC is designed for the latter part and actual input is computed in consideration of the former part. The other method strictly designs the GPC for the whole non-linear system by using the optimization technique. Effectiveness of the methods is examined through numerical examples.