Multistep Model Predictive Control Research Articles

Control of discrete-time nonlinear systems via finite-step control Lyapunov functions

In this work, we establish different control design approaches for discrete-time systems, which build upon the notion of finite-step control Lyapunov functions (fs-CLFs). The design approaches are formulated as optimization problems and solved in a model predictive control (MPC) fashion. In particular, we establish contractive multi-step MPC with and without reoptimization and compare it to classic MPC. The idea behind these approaches is to use the fs-CLF as running cost. These new design approaches are particularly relevant in situations where information exchange between plant and controller cannot be ensured at all time instants. An example shows the different behavior of the proposed controller design approaches.

Enabling Multistep Model Predictive Control for Transient Operation of Power Converters

Recently, an efficient multistep direct model predictive control (MPC) scheme for power converters has been proposed. It relies on the Sphere Decoding Algorithm (SDA) to solve the associated long-horizon optimal control problem. Since the SDA evaluates only a small number of candidate solutions to find the optimal one, a significant reduction in the average computational burden can be achieved compared to the basic exhaustive search approach. However, this is only true during steady-state operation. In fact, the SDA still requires a large execution time during transients. This paper shows that if not properly addressed, the dynamic performance of the system may be degraded, which clearly limits its practical application. To mitigate this issue, which particularly arises during transients, an efficient preconditioning approach for the SDA is proposed. This approach ensures that only a small number of candidate solutions are evaluated during both steady-state, and transients. This allows the multistep direct MPC to become a viable control alternative for power converters operating at low semiconductor switching frequencies, e.g., below 450 Hz. The proposal is validated using a grid-connected three-level converter as a case study. Both processor-in-the-loop simulations, and experimental results on a scaled-down 2.24 kVA laboratory setup are presented.

Performance Analysis of Long Horizon Predictive Control with Modified Sphere Decoding Algorithm

Abstract The complexity of the optimization problem arises in multistep model predictive control for power electronics as they are discrete by nature and have predefined control actions given as integer control variables. Generally, Sphere Decoding Algorithm (SDA) is used to solve the optimization problem. In this paper, we present an SDA with an Evolutionary Optimization attitude (EO) to simplify the complex exhaustive search that is brought by the long prediction horizon. The presented technique reconstructs a smaller search area from a large search area which decreases the number of candidate solutions. The performance of the optimization algorithm is evaluated through statistical analysis and computation burden.

Multi-step model predictive current control of permanent-magnet synchronous motor

The traditional model predictive current control (MPCC) strategy has the advantages of a fast dynamic response and flexible constraint conditions. However, this strategy only determines the optimal voltage vector in a period rather than in multiple periods, which may result in a large current ripple. To solve the above problem, this paper proposes a multi-step MPCC strategy of permanent-magnet synchronous motor. In the proposed multi-step MPCC strategy, the optimal voltage vector and the sub-optimal voltage vector are considered simultaneously. The current response in the next period is predicted on the basis of the optimal and the sub-optimal voltage vectors, respectively. To ensure the optimality of the selected voltage vector in two control periods, the current responses of the two control periods are contrasted. Compared with the traditional MPCC strategy, simulation and experimental results show that the proposed multi-step MPCC strategy can effectively reduce the current ripple and improve the steady-state performance without increasing the switching frequency.

On the Impact of Transients on Multistep Model Predictive Control for Medium-Voltage Drives

In medium-voltage drives, multistep model predictive control (MPC) can lower the total harmonic distortion of the stator currents and thereby reduce losses and improve efficiency. However, from the point of view of implementation, there is still uncertainty as to whether transients have a major adverse effect on achieving this improved steady-state performance. The time-varying nature of machine drives, initialization of the optimization process, and limited computational resources are identified as key factors. This paper analyzes the link between these key factors in detail, thus a suitable reformulation and selective initialization approach is designed to enable the deterministic use of multistep finite-control-set MPC irrespective of the drive system conditions. Guidelines to select the prediction horizon, weighting factor, and minimum switching frequency considering the control platform limitations are presented. The significant impacts of transients on the design and experimental validation, covering several drive conditions, are evaluated in a scaled-down three-level induction machine drive switching at 350 Hz. This paper is accompanied by a video demonstrating the real-time implementation of multistep MPC.

Multi-step output feedback predictive control for uncertain discrete-time T–S fuzzy system via event-triggered scheme

This paper addresses a synthesis approach of multi-step event-triggered output feedback model predictive control (OFMPC) for uncertain discrete-time Takagi–Sugeno (T–S) fuzzy system with bounded disturbance. An event-triggered scheme, which aims at reducing the redundant signal transmission, is designed to determine whether the current measured output should be released or not. The parameter-dependent output feedback predictive controller is presented by minimizing the upper bound of an infinite horizon quadratic objective function respecting input constraint. Based on this result, an additional optimization problem to tighten the bound of the state error is provided, which is of crucial importance on the control performance. The overall multi-step predictive control approach, which parameterizes the infinite horizon control moves into a sequence of output feedback laws, offers more degrees of freedom for optimization and leads to better control performance with the increase of the switching horizon. Simulation results of a continuous stirred tank reactor (CSTR) system are given to demonstrate the effectiveness of the provided techniques.

Model Predictive Voltage Control Based on Finite Control Set With Computation Time Delay Compensation for PV Systems

For the conservativeness and computational delay of the traditional finite control set model predictive control (FCS-MPC), a multi-step model predictive voltage control method based on finite control set (FCS-MMPVC) with delay compensation method is proposed in this paper, and the proposed method is validated on a three-level three-phase voltage source PV inverter. In each control cycle, the 27 voltage vectors for inverters are evaluated on line based on predictive model to obtain the optimal and suboptimal switching state. The selected switching state is optimal in two control cycle with the proposed method. Considering that the time spent in the actual sampling and calculation process cannot be ignored, the delay compensation is added in FCS-MMPVC algorithm. The simulation and experimental results show that the proposed method has good stability and reliability. Compared with the traditional FCS-MPC algorithm, the proposed method can reduce the difference significantly between the output voltage and the reference under the unbalanced and non-linear load, and the output voltage quality of the inverter is improved.

Asymmetrical Multi-Step Direct Model Predictive Control of Nine-Switch Inverter for Dual-Output Mode Operation

Nine-Switch Inverter (NSI) is composed of two conventional inverters with three common switches. Two sets of three phase ac loads can be connected to the outputs of NSI and independently controlled without any undesirable interaction. In conventional multi-step Model Predictive Control (MPC) of a nine-switch inverter, the prediction steps of both load stages must be equal. Unfortunately, this results in losing the freedom of selecting independent prediction horizon for individual loads. To overcome this problem, a novel asymmetrical multi-step direct model predictive control method is presented in this paper. The proposed method finds two independent optimum solutions for each load to match with their utilization profile. It is assumed that two individual loads are controlled by two separate virtual inverters, and two separate model predictive control problems with their own prediction steps are solved to identify optimum control actions. The control calculations are performed in a Cyclone IV Field Programmable Gate Array (FPGA) by using a pipelined architecture. The system stability is analyzed using Lyapunov stability method. To highlight the effectiveness of introduced strategy, mathematical proof for controlling two separate loads with an asymmetrical prediction step is validated in experimentally.

Band-Based Multi-Step Predictive Torque Control Strategy for PMSM Drives

The multi-step model predictive control can effectively reduce the switching frequency of inverter and improve the efficiency of motor drive system. However, the conventional multi-step model predictive control algorithm is difficult to implement in a short sampling period because of high computational complexity. In this paper, a band-based multi-step predictive torque control (BM-PTC) strategy for permanent magnet synchronous motor (PMSM) drives is proposed. On the one hand, the simplified multi-step prediction model for tracking errors of torque and stator flux is derived, and the method of reducing candidate switching sequences by band constraints is proposed, thus the computational complexity of multi-step prediction can be significantly reduced. On the other hand, the steady-state control mode and transient-state control mode are designed respectively to ensure that the system has good steady-state and dynamic performance under low switching frequency. Based on a 6-kW PMSM, the feasibility and effectiveness of the proposed strategy are verified by experiments. The proposed strategy can reduce the switching frequency by more than 37% while ensuring high performance.

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.

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.

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.

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.

Sensitivity-based multistep MPC for embedded systems

In model predictive control (MPC), an optimization problem is solved every sampling instant to determine an optimal control for a physical system. We aim to accelerate this procedure for fast systems applications and address the challenge of implementing the resulting MPC scheme on an embedded system with limited computing power. We present the sensitivity-based multistep MPC, a strategy which considerably reduces the computing requirements in terms of floating point operations (FLOPs), compared to a standard MPC formulation, while fulfilling closed- loop performance expectations. We illustrate by applying the method to a DC-DC converter model and show how a designer can optimally trade off closed-loop performance considerations with computing requirements in order to fit the controller into a resource-constrained embedded system.

A Novel Multi‐Step Model Predictive Control for Multi‐Input Systems

AbstractIn this paper, a novel control scheme, known as multi‐step model predictive control (MPC), is presented for multi‐input systems. To reduce computational complexity, only one or several control inputs are optimized at each time interval. A multi‐step MPC scheme for nominal multi‐input systems is presented. A set invariance condition for polytopic uncertain systems is identified, and the invariant set is determined by solving a linear matrix inequality optimisation problem. Based on the set invariance condition, a min‐max multi‐step robust MPC algorithm is proposed for the polytopic uncertain systems. Two examples are carried out to demonstrate the effectiveness of the proposed algorithms.

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.