Multi-objective performance optimisation for model predictive control by goal attainment

Recent studies have shown the potential of Reinforcement Learning (RL) algorithms in tuning the parameters of Model Predictive Controllers (MPC), including the weights of the cost function and unknown parameters of the MPC model. However, a framework for easy and straightforward implementation that allows training in just a few episodes and overcoming the need for imposing extra constraints as required by state-of-the-art methods, is still missing. In this study, we present two implementations to achieve these goals. In the first approach, a nonlinear MPC plays the role of a function approximator for an Expected Sarsa RL algorithm. In the second approach, only the MPC cost function is considered as the function approximator, while the unknown parameters of the MPC model are updated based on more classical system identification. In order to evaluate the performance of the proposed algorithms, first numerical simulations are performed on a coupled tanks system. Then, both algorithms are applied to the real system and their closed-loop performance and convergence speed are compared with each other. The results indicate that the proposed algorithms allow tuning of MPCs over very few episodes. Finally, also the disturbance rejection ability of the proposed methods is demonstrated.

Multivariable predictive control for vibrating structures: An application

Learning-based model predictive control has been widely applied in autonomous racing to improve the closed-loop behaviour of vehicles in a data-driven manner. When environmental conditions change, e.g., due to rain, often only the predictive model is adapted, but the controller parameters are kept constant. However, this can lead to suboptimal behaviour. In this paper, we address the problem of data-efficient controller tuning, adapting both the model and objective simultaneously. The key novelty of the proposed approach is that we leverage a learned dynamics model to encode the environmental condition as a so-called context. This insight allows us to employ contextual Bayesian optimization to efficiently transfer knowledge across different environmental conditions. Consequently, we require fewer data to find the optimal controller configuration for each context. The proposed framework is extensively evaluated with more than 3'000 laps driven on an experimental platform with 1:28 scale RC race cars. The results show that our approach successfully optimizes the lap time across different contexts requiring fewer data compared to other approaches based on standard Bayesian optimization.

The research object of this paper is single-phase PWM rectifier, the purpose is to reduce the total harmonic distortion (THD) of the grid-side current. A model predictive current control (MPCC) with fixed switching frequency and dead-time compensation is proposed. First, a combination of an effective vector and two zero vectors is used to fix the switching frequency, and a current prediction equation based on the effective vector’s optimal action time is derived. The optimal action time is resolved from the cost function. Furthermore, in order to perfect the established prediction model and suppress the current waveform distortion as a consequence of the dead-time effect, the dead-time’s influence on the switching vector’s action time is analyzed, and the current prediction equation is revised. According to the experimental results, the conclusion is that, firstly, compared with finite-control-set model predictive control, proportional-integral-based instantaneous current control (PI-ICC) scheme and model predictive direct power control (MP-DPC), the proposed MPCC has the lowest current THD. In addition, the proposed MPCC has a shorter execution time than MP-DPC and has fewer adjusted parameters than PI-ICC. In addition, the dead-time compensation scheme successfully suppresses the zero-current clamping effects, and reduce the current THD.

This paper presents a novel motion control strategy based on model predictive control (MPC) for distributed drive electric vehicles (DDEVs), aiming to simultaneously control the longitudinal and lateral motion while considering efficiency and the driving feeling. Initially, we analyze the vehicle's dynamic model, considering the vehicle body and in-wheel motors, to establish the foundation for model predictive control. Subsequently, we propose a model predictive direct motion control (MPDMC) approach that utilizes a single CPU to directly follow the driver's commands by generating voltage references with a minimum cost function. The cost function of MPDMC is constructed, incorporating factors such as the longitudinal velocity, yaw rate, lateral displacement, and efficiency. We extensively analyze the weighting parameters of the cost function and introduce an optimization algorithm based on particle swarm optimization (PSO). This algorithm takes into account the aforementioned factors as well as the driving feeling, which is evaluated using a trained long short-term memory (LSTM) neural network. The LSTM network labels the response under different weighting parameters in various working conditions, i.e., "Nor", "Eco", and "Spt". Finally, we evaluate the performance of the optimized MPDMC through simulations conducted using MATLAB and CarSim software. Four typical scenarios are considered, and the results demonstrate that the optimized MPDMC outperforms the baseline methods, achieving the best performance.

In this study, model predictive control (MPC) of the three‐phase split capacitor (TPSC) distribution static compensator (DSTATCOM) using VlseKriterijumska Optimizacija I Kompromisno Resenje (VIKOR) method is proposed. Power quality improvement using MPC involves the selection of switching state which minimises the difference between reference and actual DSTATCOM currents. However, the limitation of MPC is higher switching frequency and limitation of TPSC DSTATCOM is voltage divergence of dc‐link capacitors. To alleviate these problems, one constraint is to suppress the voltage divergence and the other is to reduce the switching frequency is included in the cost function using weighting factors. Optimal selection of switching state for minimisation of a multi‐constraint cost function is depending on the weighting factor; however, its tuning is a challenging task. In this study, the simplification of weighting factor tuning is achieved using the VIKOR method and it further selects the optimal switching state based on a specific measure of closeness to the ideal solution and multi‐criteria ranking index. The advantages of the proposed work are compensation of power quality issues, balance the dc‐link voltages, switching frequency reduction of inverter and simplification of weighting factor tuning. Finally, the proposed work is evaluated using simulation and experimental studies.

This paper compares two torque control methodologies, namely Field Oriented and Model Predictive ones, for monitoring Interior Permanent Magnet Motor (IPMM) over a wide speed range. IPMM magnetic saturation and cross coupling effects are taken into consideration, increasing significantly the precision of the developed controllers. Maximum Torque per Ampere (MTPA) and Field Weakening (FW) operating modes below and above the rated speed, respectively, are considered for an Electric Vehicle (EV) application. In the Field Oriented Control (FOC) case, this is achieved by implementing convenient Look-Up Tables (LUT) and PI controllers, while in the Model Predictive Control (MPC) case it is obtained via a particular cost function. Moreover, in the MPC case, an additional power loss tracking factor is introduced in the cost function, in order to minimize the total motor losses over the entire drive cycle. The proposed control techniques are evaluated under both steady state and dynamic conditions, illustrating the relative advantages of MPC in terms of robustness and dynamic behavior.

Model predictive control (MPC) is one of the most used optimization-based control strategies for large-scale systems, since this strategy allows to consider a large number of states and multi-objective cost functions in a straightforward way. One of the main issues in the design of multi-objective MPC controllers, which is the tuning of the weights associated to each objective in the cost function, is treated in this work. All the possible combinations of weights within the cost function affect the optimal result in a given Pareto front. Furthermore, when the system has time-varying parameters, e.g., periodic disturbances, the appropriate weight tuning might also vary over time. Moreover, taking into account the computational burden and the selected sampling time in the MPC controller design, the computation time to find a suitable tuning is limited. In this regard, the development of strategies to perform a dynamical tuning in function of the system conditions potentially improves the closed-loop performance. In order to adapt in a dynamical way the weights in the MPC multi-objective cost function, an evolutionary game approach is proposed. This approach allows to vary the prioritization weights in the proper direction taking as a reference a desired region within the Pareto front. The proper direction for the prioritization is computed by only using the current system values, i.e., the current optimal control action and the measurement of the current states, which establish the system cost function over a certain point in the Pareto front. Finally, some simulations of a multi-objective MPC for a real multivariable case study show a comparison between the system performance obtained with static and dynamical tuning .

In this paper, using the two control methods of model predictive control (MPC), model predictive current control (MPCC) and model predictive torque control (MPTC) is applied to the control system of permanent magnet synchronous motor(PMSM). The algorithms are based on the minimization of different cost functions, and the corresponding optimal voltage vector can be obtained. Comparison of the dynamic and steady state performance of the tested PMSM with MPCC and MPTC is elaborated. The delay compensation is considered to reduce the fluctuation of current and torque, in order to reduce the computational burden by using a single vector, comparison of two methods in the speed control system of dynamic and steady-state performance and speed tracking performance and resistance to load disturbance. The simulation results show that both MPCC and MPTC can be well applied to the PMSM driving systems with good speed tracking performance. However the MPCC can achieve less harmonics in the stator currents, and consequently the circular flux linkage trajectory is smoother, while the MPTC shows advantages in smaller ripples in the mechanical torque.

To improve the accuracy of tracking unmanned vehicles on known trajectories, two optimised model predictive control (MPC) trajectory tracking control systems are designed based on the adaptive compensation and robust control of a radial basis function (RBF) neural network. Based on the traditional MPC trajectory tracking controller and the local approximation characteristics of the RBF neural network, the proposed RBF compensation–MPC control system is designed to compensate for the inaccuracy in the MPC prediction model arising from modelling errors. The results show that this method can achieve a root mean square error of less than 0.3703 m for the lateral position. Subsequently, to suppress the error generated by the RBF neural network and reduce the degree of vehicle sideslip, the error is considered to be external interference, and the anti-interference characteristic of the RBF robust control is incorporated into the RBF robust-MPC control system. Following the re-optimisation of the RBF robust control, the root mean square error of the lateral position is set within 0.2352 m. The results of a MATLAB/Carsim joint simulation show that using the RBF robust control can improve the tracking accuracy of the traditional MPC controller compared with RBF compensation control, while simultaneously improving the driving stability of the vehicle.

In this article, sensorless finite control set model predictive speed control of induction motor using adaptive full-order observer is proposed. Firstly, finite control set model predictive speed control is introduced. It is composed of direct speed control and model predictive control, which gets over the limitations of cascaded structure and obtains high dynamics response. Due to lack of speed loop, stator flux linkage, rotor speed and stator current are taken as the control targets in the cost function. Then, adaptive full-order observer is used to estimate rotor speed and stator flux linkage to improve the reliability and keep the system cost down. Finally, the simulation results indicate that the proposed method has well dynamic performance in the wide speed range.

Stability is perhaps the most important property of controllers. A stable controller performs its task reliably in any circumstance; however, an unstable controller may cause system failure with dramatic effects. Unstable controllers in an active vibration control (AVC) system may even cause structural failure. Stability can be guaranteed and studied in traditional control systems by inspecting the location of the closed-loop poles of the transfer function, or equivalently the magnitude of the eigenvalues of the state matrix. Unfortunately, the constrained model predictive control (MPC) law is nonlinear and it cannot be expressed in a closed form. Considering the cost function as a Lyapunov function is the key to understand the stability of the constrained MPC strategy. As long as the cost function is monotonically decreasing, the control process remains stable. It can be proved that the condition for this is to ensure the feasibility of the input sequence from the current time up to infinity. Fortunately, this seemingly formidable task can be implemented with a finite number of optimization variables. An additional constraint checking horizon in infinite horizon cost dual-mode constrained MPC ensures stability and feasibility. The series of additional constraints to ensure stability also allocate a special region of state-space called the region of attraction and its subset, the target set. For an optimal MPC strategy with maximum performance, these have a complex polyhedral shape. In the interest decreasing complexity and increasing computational speeds, these sets can be simplified to low complexity hypercubes or a hyperellipsoids. This chapter reviews the stability properties of the constrained MPC control law, how it can be guaranteed at all times, introduces the reader to maximal invariant target sets and some of its simplified approximations.

The objective of this paper is to introduce with a quaternion orientation based quadrotor that can be controlled by Model Predictive Control (MPC). As MPC offers promising performance in different industrial applications, quadrotor can be another suitable platform for the application of MPC. The present study consistently adopts unit quaternion approach for quadrotor orientation in order to avoid any axes overlapping problem, widely known as singularity problem whereas Euler angle orientation approach is unable to resolve so. MPC works based on the minimal cost function that includes the attitude error and consequently, the cost function requires quaternion error in order to proceed with process of MPC. Therefore, the main contribution of this study is to introduce a newly developed cost function for MPC because by definition, quaternion error is remarkably different from the attitude error of Euler angle. As a result, a unit quaternion based quadrotor with MPC can ascertain a smooth singularity-free flight that is influenced by model uncertainty. MATLAB and Simulink environment has been used to validate the cost function for quaternion by simulating several trajectories.

A model predictive control (MPC) system has been developed for application to the condensate recycle process of a 300 MW cogeneration power station of the East-West Power Plant, Gyeonggido, Korea. Unlike other industrial processes where MPC has been predominantly applied, the operation mode of the cogeneration power station changes continuously with weather and seasonal conditions. Such characteristic makes it difficult to find the process model for controller design through identification. To overcome the difficulty, process models for MPC design were derived for each operation mode from the material balance applied to the pipeline network around the concerned process. The MPC algorithm has been developed so that the controller tuning is easy with one tuning knob for each output and the constrained optimization is solved by an interior-point method. For verification of the MPC system before process implementation, a process simulator was also developed. Performance of the MPC was investigated first with a process simulator against various disturbance scenarios.

A successful implementation of Model Predictive Control (MPC) requires appropriately tuned parameters. This paper presents a novel tuning approach based on Artificial Neural Network (ANN). To build the data learning base of the ANN, we adopted the Particle Swarm Optimisation (PSO) method, and we used the reliable algorithm, Online Sequential Extreme-Learning-Machine (OS-ELM) to learn the ANN. The objective of this work is to show that good tuning of MPC parameters makes it possible to reach closed-loop stability and ensure robustness against disturbances and sensor noises, without using robustification approaches in addition to MPC. The effectiveness of our approach is brought to light by comparing the obtained performances to other MPC tuning approaches without disturbances, and also to a robustified Generalized Predictive Control (GPC) using Youla parametrisation in the presence of disturbances.