Model Predictive Controller Design of Linear Switched Reluctance Motor

The usual design procedures in model predictive control (MPC) use a rectangular type of moving horizon window. The length of the window equals the prediction horizon assumed in the algorithm. This is known to affect the closed-loop stability. The results obtained in this paper further shows that the prediction horizon also affects the numerical condition of the MPC algorithms that contain integrators. Specifically, for a large control horizon, the numerical condition of the MPC algorithm deteriorates rapidly as the prediction horizon increases. Thus, instead of a rectangular window, this paper proposes the use of an exponentially weighted moving horizon window in model predictive control design. By using a classical result in Toeplitz matrix, the paper shows that the condition number of the Hessian matrix is bounded if an appropriate exponential weight is used in the design.

Model predictive control (MPC) is used in the CO2 removal process in the Subang field to improve its control performance. MPC is used to maintain the CO2 concentration at the sweet gas output by controlling the feed gas pressure (PIC-1101), makeup water flow rate (FIC-1102), and amine flow rate (FIC-1103). The empirical model applied to MPC to represent the process model is the auto-regressive exogenous (ARX) model. The ARX model is compared with the first order plus dead time (FOPDT) model based on the root mean square error (RMSE) between the model and the actual process, then MPC parameters are tuned which include sampling time (T), prediction horizon (P) and control horizon (M) to control for the three variables. Improved control performance is measured based on the integral square error (ISE). The results show that the ARX model is the best model for the CO2 removal process with an RMSE value of 35%-91% smaller than the FOPDT model. The optimal control parameters Prediction Horizon (P), Control Horizon (M) and Sampling Time (T) in the CO2 removal process are 75, 25 and 1 on PIC-1101, 25, 10 and 1 on FIC-1102, and 30, 25 and 1 on FIC-1103. The MPC-ARX (MPC using ARX model) can improve the control performance of 33% in the servo control and 6-56% on the regulatory control. However, not all of them showed an increase in control performance improvement from previous studies even though they had used the best model (ARX). This is due to the MPC parameter setting that is not yet appropriate, so it needs to be retuning.

In this paper, constrained model predictive control (MPC) designs for a class of structured uncertain time-delay systems have been developed, where state delays as well as a random input delay have been taken into account. By replacing the control strategy with a freer one, an improved MPC design with larger initial feasible region has been developed. Furthermore, by analyzing the obtained algorithm, some useful properties of the solutions to the MPC optimization problem have been established. With these properties, a variant of the obtained algorithm with dramatically reduced number of online optimizing variables and hence the online computational burden has also been developed. However, the control performance degrades slightly. The two algorithms haven been proved to stabilize the closed loop system in the mean square sense and to guarantee the satisfaction of constraints. Finally a numeric example is given to illustrate the proposed results.

The AC/DC converter is one of the popular power electronic converters in industrial applications such as in the railway, power supply systems and electric vehicle. In this paper, a three-phase controllable rectifier is considered and its linear model is extracted. Because of MPC controllers benefits, the continuous control set model predictive controller (CCs-MPC) is designed for controlling this rectifier output DC voltage. By considering rectifier dynamic response, the suitable criteria to choice the model predictive controller parameters such as sampling time, prediction horizon and control horizon is proposed. In experimental implantation the computing burden of microcontroller is limit therefore the reaching to optimal and minimum complexity in algorithms implantation is vital problem. In other words by using these proposed criteria for selection of sample time, prediction and control horizon the tradeoff between computational burden, system performance and dynamic stability is made. When using designed MPC controller, the rectifier and grid performance such as total harmonic distribution (THD), power factor (PF) and output voltage ripple have acceptable value. This controller can eliminated the effect of heavy load change on rectifier performance which is very common problem in indusial system. Also, this controller stability guaranteed is checked by using the dual-mode method. The simulation results are validated by using MATLAB software and showing the designed controller performance.

In this paper, a model predictive control (MPC) design method is proposed for Hammerstein systems with multivariable nonlinearities. Iterative inversion is introduced such that classical linear MPC design can be used. The condition for which the numerical inversion is guaranteed to converge is derived. From this condition, the input space at which the nonlinear function is invertible can be obtained, which poses extra input constraints for MPC design. The overall constraints are transformed and approximated by a set of linear constraints by means of convex hull construction. Illustrative examples are presented to demonstrate the effectiveness of the proposed control method.

Discussion on: “Improved MPC Design based on Saturating Control Laws”

Flexible operation of coal-fired power plants is becoming increasingly necessary for successful integration of large-scale renewable power generation into the power grid. The maximum ramp rate and the number of load cycles are generally limited by the thermal stress experienced by the boiler pressure parts, turbine metallurgy and creep and fatigue of critical thick-walled components Main steam temperature is a critical operating parameter that must be controlled within acceptable limits for safe operation. Main steam temperature deviation beyond acceptable limit has impact on boiler pressure parts and turbine material of construction due to creep and fatigue effect. Base load operating units do not require steep ramp rate and hence recommended ramping rates are kept low within the safe operating zone in comparison to the flexible operation of the units with wide range load change width. Thermal stresses are caused by the temperature changes inside the thick-walled components and turbine steam admission parameters. Hence, the quality of main steam temperature control plays a vital role in flexible operation of the coal fired units. Conventional cascaded PID temperature control loop architecture performs well at steady state condition within a limited variation of load change at low ramp rate but it acts slowly and performs poorly at transient operating conditions of flexible operation of the boiler turbine with wide range load variation and load cycle with high ramp rate and remains far from rated conditions. In this paper, a Multi-Input Multi-Output (MIMO) Non-linear Model Predictive Control (MPC) design for regulation of the main steam temperature of a Once-Through supercritical Boiler is proposed. The controller is based on a non-linear dynamic model which incorporates dynamics of the variables of interest. It has the capability to operate effectively across a wide load range while maintaining main steam temperature within acceptable limits. A notable advancement in this design of MPC is the incorporation of coal flow demand and feedwater flow demand as additional control inputs alongside primary and secondary spray flows. In simulation test cases, the MPC controller demonstrates satisfactory performance and computational efficiency.

We present an analytical and computational framework using the theory of Koopman operator to design dual-mode model predictive control (MPC) for nonlinear control systems. Dual-mode MPC incorporates stability and performance constraints in the controller and remains a challenging problem to solve for systems involving nonlinear dynamics. We exploit the spectral properties of the Koopman operator to provide a systematic approach for the design of optimal control, guaranteeing the stability of the feedback control system. The optimal cost function is also used for characterizing the maximal invariant set, which serves as the terminal set in the design of finite-horizon MPC. The finite horizon MPC relies on lifting nonlinear system dynamics using Koopman eigenfunctions to provide a linear approach for the design of MPC with state and input constraints.

This work focuses on a class of nonlinear control problems that arise when new control systems which may use networked sensors and/or actuators are added to already operating control loops to improve closed‐loop performance. In this case, it is desirable to design the pre‐existing control system and the new control system in a way such that they coordinate their actions. To address this control problem, a distributed model predictive control method is introduced where both the pre‐existing control system and the new control system are designed via Lyapunov‐based model predictive control. Working with general nonlinear models of chemical processes and assuming that there exists a Lyapunov‐based controller that stabilizes the nominal closed‐loop system using only the pre‐existing control loops, two separate Lyapunov‐based model predictive controllers are designed that coordinate their actions in an efficient fashion. Specifically, the proposed distributed model predictive control design preserves the stability properties of the Lyapunov‐based controller, improves the closed‐loop performance, and allows handling input constraints. In addition, the proposed distributed control design requires reduced communication between the two distributed controllers since it requires that these controllers communicate only once at each sampling time and is computationally more efficient compared to the corresponding centralized model predictive control design. The theoretical results are illustrated using a chemical process example. © 2009 American Institute of Chemical Engineers AIChE J, 2009

This paper presents a waypoint tracking method using model predictive control (MPC) for an autonomous driving vehicle. To solve vehicle speed variation in the MPC design, we propose a scheme using horizon-wise constant (HWC) MPC. The HWC MPC assumes that a prediction model uses a fixed parameter prediction model within a prediction horizon to resolve a parameter variation problem. To evaluate the performance of the proposed method, we performed three comparative studies with one speed variation MPC and two constant speed MPCs on a highway curve road. We verify the utility of the proposed MPC using HWC modeling and MPC using fixed velocity modeling. We have also confirmed that the proposed HWC MPC outperforms MPC at with fixed speed. The proposed controller is expected to be a solution to various parameter situations in waypoint tracking for the autonomous driving vehicle.

A detailed dynamic model for the poly(ethylene terephthalate) (PET) solid-state polymerization (SSP) process is employed for the design of an advanced control scheme based on model predictive control (MPC). The original model of the reactor, consisting of a system of 16 time-dependent partial differential equations in two spatial coordinates, is simplified by contracting the radial direction. Such a reduced model is then incorporated into an MPC methodology. The overall control scheme is simulated to verify its reliability by maintaining the reactor temperature and the final intrinsic viscosity (IV) of the outlet PET resin constant. The validation of the resulting control loop composed of the MPC controller and the SSP unit is performed through the use of a detailed model that substitutes for the real plant. Control parameters such as the prediction and control horizons and the sampling time are tested and optimized. Control performances in response to unmeasured disturbance and set-point variations are i...

This work investigates the event‐driven model predictive control problem for perturbed nonlinear systems with input and state constraints. Firstly, a new event‐driven triggering condition, considering the gradient and accumulation of the error between the optimal and actual states at adjacent moments with a state‐dependent relative threshold is designed with a guaranteed positive inter‐event time to avoid Zeno behaviour. Secondly, an error gradient and accumulation type event‐driven model predictive control framework is designed based on the new triggering condition and the dual‐mode strategy, for effectively reducing the calculation and communication burden of the model predictive control controller while ensuring desired control performance. Furthermore, the feasibility and the input‐to‐state practical stability (ISpS) of gradient and accumulation‐type event‐driven model predictive control are rigorously guaranteed theoretically. At last, the simulation results are provided to validate the this algorithm.

The need for cost-effective fuel economy improvements has driven the introduction of automatic transmissions with an increasing number of gear ratios. Incorporation of interlocking dog clutches in these transmissions decreases package space and increases efficiency, as compared to conventional dry or wet clutches. Unlike friction based clutches, interlocking dog clutches require very precise rotational speed matching prior to engagement. Precise engine speed control is therefore critical to maintaining high shift quality. This research focuses on controlling the engine speed during a gearshift period by manipulating throttle position and combustion phasing. Model predictive control (MPC) is advantageous in this application since the speed profile of a future prediction horizon is known with relatively high confidence. The MPC can find the optimal control actions to achieve the designated speed target without invoking unnecessary actuator manipulation and violating hardware and combustion constraints. This research utilizes linear parameter varying (LPV) MPC to control the engine speed during the gearshift period. Combustion stability constraints are considered with a control oriented covariance of indicated mean effective pressure model (COV of IMEP). The proposed MPC engine speed controller is validated with a high-fidelity 0-dimensional engine model with crank angle resolution. Four case studies, based on simulation, investigate the impact of different MPC design parameters. They also demonstrate that the proposed MPC engine controller successfully achieves the speed reference tracking objective while considering combustion variation constraints.

This paper deals with the design and the robustness analysis of a model predictive control (MPC) for the position tracking of primary flight movables driven by electro-mechanical actuators. This study is, in particular, focused on a rotary electro-mechanical actuator (EMA) by UMBRAGROUP, employing a patented mechanical transmission based on a differential ball-screw mechanism characterized by a huge gear ratio. To obtain a baseline reference, conventional PID regulators were initially optimized by using multi-objective cost functions based on tracking accuracy, load disturbance rejection, and power consumption. The position regulator was then replaced by an MPC regulator, designed to balance performance, computational resources, and safety constraints. A nonlinear physics-based simulation model of the EMA, entirely developed in the Matlab–Simulink environment and validated with experiments, was used to compare the two control strategies. The simulation results in both the time and frequency domains highlight that the MPC solution provides faster and more accurate position tracking, improved dynamic stiffness, and reduced power absorption. Finally, the robustness against model uncertainties of the MPC was addressed by imposing random and combined deviations of model parameters from the nominal values (via Monte Carlo analysis). The results demonstrate that the implementation of MPC control laws could enhance the stability and the reliability of EMAs, thus supporting their application for safety-critical flight control functions.

An adaptive-prediction-horizon model prediction control-based path tracking controller for a four-wheel independent control electric vehicle is designed. Unlike traditional model prediction control with fixed prediction horizon, this paper devotes to satisfy the varied path tracking demand by adjusting online the prediction horizon of model prediction control according to its effect on vehicle dynamic characteristics. Vehicle dynamic stability quantized with the vehicle sideslip-feature phase plane is preferentially considered in the prediction horizon adjustment. For stability during switching prediction horizon and for robustness during path tracking, the numerical problem inherent in the adaptive-prediction-horizon model prediction control is analysed and solved by introducing exponentially decreasing weight. Subsequently, the desired motion for path tracking with the four-wheel independent control electric vehicle is realized with a hierarchical control structure. Simulation results finally illustrate the effectiveness of the proposed method.