Multi-step Predictive Control Research Articles

Generalized Correntropy Predictive Control for Waste Heat Recovery Systems Based on Organic Rankine Cycle

Organic Rankine cycle (ORC) is one of the most promising technologies to recover energy from low temperature waste heat. The heat sources usually experience fluctuations in temperature and mass flow rate, which makes it difficult to obtain satisfactory control performances of ORC systems. In this paper, a single neuron adaptive multi-step predictive control scheme is developed for an ORC based waste heat recovery (WHR) system with non-Gaussian disturbances. Since the non-Gaussian disturbances existed in WHR system follow heavy-tailed distribution, generalized correntropy is adopted as the performance index to characterize the system uncertainties. The weights of the single neuron controller are updated by optimizing the performance function. The whole implementation procedures of the proposed control strategy for the WHR are presented. As a contrast, the performances of the minimum error entropy (MEE) based controller and the mean square error (MSE) based controller are also tested. The proposed control scheme is confirmed to be more effective through simulations.

Restricted structure predictive control for linear and nonlinear systems

ABSTRACT An optimal predictive control algorithm is introduced for the control of linear and nonlinear discrete-time multivariable systems. The controller is specified in a ‘restricted structure’ form involving a set of given linear transfer-functions and a set of gains that minimise a Generalised Predictive Control (GPC) cost-index. The set of functions can be chosen as proportional, integral and derivative terms, however, a wide range of controller structures is possible. This is referred to as Restricted-Structure GPC control. The multi-step predictive control cost-function is novel, since it includes weightings on the ‘low-order’ controller gains and the rate of change of gains. This considerably improves the numerical computations ensuring critical inverse computations cannot lead to a singular matrix. It also provides the option of adding soft or hard constraints on the controller gains which provides additional flexibility for control design. The ability to include a plant model that can include a general nonlinear operator is also new for restricted structure control solutions. The low-order controller provides a potential improvement in robustness, since it is often less sensitive to plant uncertainties. The simple controller structure also enables relatively unskilled staff to retune the system using familiar tuning terms, and provides a potentially simpler QP problem for the constrained case.

Multi-Step Model Predictive Control Based on Online Support Vector Regression Optimized by Multi-Agent Particle Swarm Optimization Algorithm

As optimization of parameters affects prediction accuracy and generalization ability of support vector regression (SVR) greatly and the predictive model often mismatches nonlinear system model predictive control, a multi-step model predictive control based on online SVR (OSVR) optimized by multi-agent particle swarm optimization algorithm (MAPSO) is put forward. By integrating the online learning ability of OSVR, the predictive model can self-correct and adapt to the dynamic changes in nonlinear process well.

Model Predictive Control for DC–DC Boost Converters With Reduced-Prediction Horizon and Constant Switching Frequency

The implementation of multistep direct model predictive control (MPC) for dc–dc boost converters overcomes the well-known issue of nonminimum phase behavior. However, it can lead to a high computational burden depending on the prediction horizon length. In this paper, a simple and computationally efficient MPC method for dc–dc boost converters is proposed. The key novelty of the presented control strategy lies in the way dynamic references are handled. The control strategy is capable of providing suitable references for the inductor current and the output voltage, without requiring additional control loops. Moreover, this reference design allows the predictive controller to be implemented with a single-step prediction horizon. Thus, a significant reduction in the required real-time calculations executed in the control hardware is achieved. To obtain constant switching frequency, the power switch commutation instants within a sampling period are considered as control inputs. Therefore, the predictive controller is formulated as a continuous control set MPC. Additionally, the proposed formulation is able to deal with different operation modes of the converter without changing the controller structure. Finally, an observer is used to dynamically modify the reference to provide robustness to system parameter uncertainties. Simulation and experimental results show an accurate tracking of dynamic inductor current and output voltage references, while respecting the restrictions on maximum inductor current levels of the converter.

A Multi-step Output Feedback Robust MPC Approach for LPV Systems with Bounded Parameter Changes and Disturbance

This paper considers a multi-step output feedback robust model predictive control (OFRMPC) approach for the linear parameter varying (LPV) systems with bounded changes of scheduling parameters and bounded disturbance. Less conservative bounds of future estimation error sets and system parametric uncertain sets are predicted by considering bounded changes of scheduling parameters in LPV systems. In the multi-step OFRMPC approach, an optimization problem is solved to obtain a sequence of controller gains, which considers predictions of future bounds of estimation error sets and system parametric uncertain sets. The optimized sequence of controller gains corresponding to a sequence of Lyaponov matrices have less constraint conditions and also introduce more degree of freedom for the optimization. The proposed multi-step OFRMPC guarantees robust uniform ultimately bounded of the estimation error and robust stability of the observer system. A numerical example is given to demonstrate the effectiveness of the approach.

Multistep Model Predictive Control for Cascaded H-Bridge Inverters: Formulation and Analysis

In this paper, a suitable long prediction horizon (multistep) model predictive control (MPC) formulation for cascaded H-bridge inverters is proposed. The MPC is formulated to include the full steady-state system information in terms of output current and output voltage references. Generally, basic single-step predictive controllers only track the current references. As a distinctive feature, the proposed MPC also tracks the control input references, which in this case is designed to minimize the common-mode voltage (CMV). This allows the controller to address both output current and CMV targets in a single optimization. To reduce the computational effort introduced by a long prediction horizon implementation, the proposed MPC formulation is transformed into an equivalent optimization problem that can be solved by a fast sphere decoding algorithm. Moreover, the benefits of including the control input references in the proposed formulation are analyzed based on this equivalent optimization problem. This analysis is key to understand how the proposed MPC formulation can handle both control targets. Experimental results show that the proposal provides an improved steady-state performance in terms of current distortion, inverter voltages symmetry, and CMV.

Multistep Model Predictive Control With Current and Voltage Constraints for Linear Induction Machine Based Urban Transportation

In order to improve the working performance of linear metro, the multistep model predictive control (MMPC) is applied to linear induction machine (LIM) in this paper. However, due to the maximum current and voltage limitations, the optimal problem of multistep model predictive control (MMPC) becomes difficult to handle in practice. For simplifying the optimal problem of an MMPC with constraints, first, the optimal problem of MMPC is solved off-line, with the assumption that the input voltage of the LIM is continuous without limitations. And, the expression of current constraint is expressed by voltage variables through the mathematical model of the LIM to simultaneously consider both the voltage and current limitations. Then, according to the solved optimal value without constraints, one iterative algorithm is proposed to search a suboptimal value, which satisfies both the current and voltage limitations. Finally, the proposed strategy is applied to two 3-kW arc induction motors to verify its effectiveness.

A fast multi-step prediction and rolling optimization excitation control method for multi-machine power system

A fast multi-step prediction and rolling optimization excitation control method for multi-machine power system

Experimental Speedup and Stability Validation for Multi-Step MPC

In this paper, we propose a multi-step model predictive control (MPC) scheme without stabilizing constraints and/or costs. Within this work, a relaxed Lyapunov inequality is employed to verify asymptotic stability of the MPC closed loop. To this end, prior work is adapted to a trajectory based setting. The approach works for shorter prediction horizons in comparison to single-step MPC, but requires to stay in open loop for longer periods of time. We propose a technique to mitigate this drawback during runtime of the algorithm such that we benefit from the inherent robustness of single-step MPC. Then, we present a prime experimental validation of the proposed control scheme on a skid-steering mobile robot and show that the computational effort is significantly reduced.

Computationally efficient multi‐step direct predictive torque control for surface‐mounted permanent magnet synchronous motor

The multi-step direct model predictive control (M-DMPC) could reduce the switching frequency and improve the efficiency of the motor drive system while ensuring good steady and dynamic performance. However, the conventional M-DMPC, which uses the exhaustive optimisation method is with exponential time complexity, so it is difficult to realise in a short sample period. This study proposes a multi-step direct predictive torque control (M-DPTC) algorithm for two-level voltage source inverter fed surface-mounted permanent magnet synchronous motor (SPMSM) drive system. In the proposed algorithm, first, in order to reduce computation time in multi-step predictive process, a simplified multi-step predictive model is established. Compared with the complex operations, like square root and trigonometric function used in the conventional predictive model, only look-up table and addition operation are utilised in the proposed model for multistep prediction. Second, compared with the exhaustive searching method, the proposed optimisation method avoids the exploration of all possible switching sequences and has logarithmic time complexity. Combining the above two measures, the proposed M-DPTC can be achieved in a relatively shorter sample period. Simulation and experimental results for a 6-kW SPMSM are presented to validate the proposed algorithm.

Non‐linear predictive generalised minimum variance state‐dependent control

A non-linear predictive generalised minimum variance control algorithm is introduced for the control of nonlinear discrete-time state-dependent multivariable systems. The process model includes two different types of subsystems to provide a variety of means of modelling the system and inferential control of certain outputs is available. A state dependent output model is driven from an unstructured non-linear input subsystem which can include explicit transport delays. A multi-step predictive control cost function is to be minimised involving weighted error, and either absolute or incremental control signal costing terms. Different patterns of a reduced number of future controls can be used to limit the computational demands.

An Increment-Type Multi-Step Predictive and Multi-Step Control Algorithm of Single-Variable Systems

In this paper, an increment-type multi-step predictive and multi-step control algorithm of single-variable systems based on Laguerre function approximate model is presented, and then the stability of this algorithm is analyzed. Additionally, simulation of this algorithm had been done to investigate performance, the results show that the controlling quality of this algorithm is fairly good.

A multi-step robust model predictive control scheme for polytopic uncertain multi-input systems

Model predictive control (MPC) has attracted wide attention in process industries with its ability to handle constrained multivariable processes. Computational complexity can become a limiting factor when MPC is applied to large-scale systems with fast sampling times. In this paper, a control scheme known as multi-step robust MPC is presented for polytopic uncertain multi-input systems. Only one or several state feedback laws are optimized at each time interval to reduce computational complexity. A set invariance condition for polytopic uncertain systems is identified and the invariant set is determined by solving a linear matrix inequality (LMI) optimization problem. Based on the set invariance condition, a min-max multi-step robust MPC scheme is proposed. Numerical simulations show the effectiveness of the proposed scheme.

Offset‐free multistep nonlinear model predictive control under plant–model mismatch

SUMMARYA multistep nonlinear model predictive control (MPC) framework is developed to achieve steady‐state offset‐free control in the presence of plant–model mismatch. Our formulation explicitly accounts for the effect of plant–model mismatch by involving the output feedback error, which is expressed as the difference between the measured process output and the predicted model output at the previous sampling instance, in the multistep model recursive prediction. The proposed scheme is capable of improving the performance of nonlinear MPC, because the plant–model mismatch is effectively compensated through the recursive prediction propagation. We prove that this formulation is able to remove the steady‐state error to achieve offset‐free control. The proposed nonlinear MPC framework is applied to a highly nonlinear two‐input two‐output continuous stirred tank reactor, in comparison with other MPC implementations. The results obtained demonstrate that the proposed technique outperforms some existing popular MPC schemes and can realise offset‐free control even under significant plant–model mismatch and unmeasured disturbances. Copyright © 2012 John Wiley & Sons, Ltd.

State-space approach to nonlinear predictive generalised minimum variance control

A nonlinear predictive generalised minimum variance control algorithm is introduced for the control of nonlinear discrete-time multivariable systems. The plant model is represented by the combination of a very general nonlinear operator and also a linear subsystem which can be open-loop unstable and is represented in state-space model form. The multi-step predictive control cost index to be minimised involves both weighted error and control signal costing terms. The solution for the control law is derived in the time domain using a general operator representation of the process. The controller includes an internal model of the nonlinear process, but because of the assumed structure of the system, the state observer is only required to be linear. In the asymptotic case, where the plant is linear, the controller reduces to a state-space version of the well-known GPC controller.

Polynomial approach to non-linear predictive generalised minimum variance control

A relatively simple approach to non-linear predictive generalised minimum variance (NPGMV) control is introduced for non-linear discrete-time multivariable systems. The system is represented by a combination of a stable non-linear subsystem where no structure is assumed and a linear subsystem that may be unstable and modelled in polynomial matrix form. The multi-step predictive control cost index to be minimised involves both weighted error and control signal costing terms. The NPGMV control law involves an assumption on the choice of cost-function weights to ensure the existence of a stable non-linear closed-loop operator. A valuable feature of the control law is that in the asymptotic case, where the plant is linear, the controller reduces to a polynomial matrix version of the well known generalised predictive control (GPC) controller. In the limiting case when the plant is non-linear and the cost-function is single step the controller becomes equal to the polynomial matrix version of the so-called non-linear generalised minimum variance controller. The controller can be implemented in a form related to a non-linear version of the Smith predictor but unlike this compensator a stabilising control law can be obtained for open-loop unstable processes.

Adaptive peak seeking control of a proton exchange membrane fuel cell

The primary aim of operating any fuel cell (PEMFC) system is to produce the power/electricity at maximum efficiency. The cell voltage/current manipulation appear to be the most suitable choice for controlling the power density. However, the power density exhibits a highly nonlinear and complex dynamic relationship with respect to the cell voltage. Since the process output variable (i.e. power density) itself is the objective function for the optimization, there exists a singularity at the optimum operating condition. In addition, the location of the optimum operating point changes with time due to the occurrence of variety of disturbances and/or changes in the operating conditions. Thus, the need to operate the PEMFC at its peak power density and track the shifting optimum turns out to be a challenging control problem. The task of on-line optimizing control of PEMFC poses difficulties in real time control due to its fast dynamics and it is impractical to employ a mechanistic model for locating the changing optimum on-line. In this context the adaptive optimizing control scheme developed by Bamberger and Isermann (1978) [1] appears interesting. Their scheme is based on on-line adaptation of a nonlinear black box time series models and facilitates analytical computation of changing optimum. Recently, Bedi et al. (2007) [2] have developed a closed form multi-step predictive control law under nonlinear internal model control framework using a black-box nonlinear model and employed it for peak power control in PEMFC. From the viewpoint of PEMFC operation, this nonlinear IMC controller meets the demand on the fast computations as a closed form solution is obtained for the nonlinear control problem at each time step. In this work, we propose to develop an adaptive optimizing control scheme, which combines the attractive features of the on-line optimization approach proposed by Bamberger and Isermann (1978) [1] and closed form control law developed by Bedi et al. (2007) [2]. We demonstrate the effectiveness of the proposed adaptive optimizing scheme by conducting simulation studies on the distributed an along-the-channel model of PEMFC. Analysis of the simulation results indicate that the proposed adaptive optimizing control scheme satisfactorily tracks the shifting optimum operating point in the face of changing unmeasured disturbances

Predictive control of a class of bilinear systems based on global off-line models

A new multi-step adaptive predictive control algorithm for a class of bilinear systems is presented. The structure of the bilinear system is converted into a simple linear model by using nonlinear support vector machine (SVM) dynamic approximation with analytical control law derived. The method does not need on-line parameters estimation because the system’s internal model has been transformed into an off-line global model. Compared with other traditional methods, this control law reduces on-line parameter estimating burden. In addition, its overall linear behavior treating method allows an analytical control law available and avoids on-line nonlinear optimization. Simulation results are presented in the article to illustrate the efficiency of the method.

Multi-step predictive control with TDBP method for pneumatic position servo system

This paper presents a new multi-step predictive controller based on neural networks and researches the adaptability of the predictive controller for a pneumatic position servo system which has some typical characteristics of non-linearity and time-varying. A diagonal recurrent neural network (DRNN) is used to predict the system output of the multi-step ahead directly. According to the intrinsic defects of a back-propagation (BP) algorithm that cannot update network weights incrementally, a new hybrid learning algorithm combining the temporal differences (TD) method with the BP algorithm to train the DRNN is put forward. A three-layer feedforward BP neural network is used as a non-linear rolling optimal controller to realize the optimization of control input of the next step according to a single-value predictive control algorithm to simplify computation. Simulation and experimental results indicate that the proposed predictive controller is suitable for real-time control of a pneumatic position servo system because of its characteristics of a simple algorithm, fast calculation of the control input and good tracking effects.

Dynamic recurrent radial basis function network model predictive control of unstable nonlinear processes

A multistep model predictive control (MPC) strategy based on dynamically recurrent radial basis function networks (RBFNs) is proposed for single-input single-output (SISO) control of uncertain nonlinear processes. The control system consists of two automatically configured RBFNs, a trained network representing the plant model and a network with on-line learning to function as controller. The automatic configuration and learning of the networks is carried out by using a hierarchically self-organizing learning algorithm. This control strategy is structurally simple and computationally efficient since a single output node of each RBFN is configured to provide multistep predictions for plant output and controller. The performance of the proposed RBFNMPC strategy is evaluated by applying to two unstable nonlinear chemical processes, a chemical reactor and a biochemical reactor, and also a stable polymerization reactor. Further, the results of the RBFNMPC is compared with similar RBFN model based control strategies and also with well tuned PID/PI controller. The results show the better performance of the proposed RBFNMPC for the control of open-loop unstable nonlinear processes that exhibit multiple steady-state behavior.