Discrete-time Model Predictive Control Research Articles

An Improved Vehicle Path-Tracking Model Based on Adaptive Nonlinear Model Predictive Control via Online Big Bang—Big Crunch Algorithm and Artificial Neural Network

<div>In this article, a novel tuning approach is proposed to obtain the best weights of the discrete-time adaptive nonlinear model predictive controller (AN-MPC) with consideration of improved path-following performance of a vehicle at different speeds in the NATO double lane change (DLC) maneuvers. The proposed approach combines artificial neural network (ANN) and Big Bang–Big Crunch (BB–BC) algorithm in two stages. Initially, ANN is used to tune all AN-MPC weights online. Vehicle speed, lateral position, and yaw angle outputs from many simulations, performed with different AN-MPC weights, are used to train the ANN structure. In addition, set-point signals are used as inputs to the ANN. Later, the BB–BC algorithm is implemented to enhance the path-tracking performance. ANN outputs are selected as the initial center of mass in the first iteration of the BB–BC algorithm. To prevent control signal fluctuations, control and prediction horizons are kept constant during the simulations. The results showed that all AN-MPC weights are successfully tuned online and updated during the maneuvers, and the path-following performance of the ego vehicle is improved at different NATO DLC speeds using the proposed ANN + BB–BC, compared to the method where ANN is used only.</div>

Aperiodic intermittent sampling for nonlinear discrete-time event-based model predictive control

ABSTRACT In this article, an aperiodic intermittent sampling method is designed in event-based model predictive control for nonlinear discrete systems subject to external disturbances. The proposed aperiodic intermittent sampling is applied to find the appropriate triggering instant satisfying the desired sub-optimal performance. In the proposed event-based MPC, selection of the sampling instants is based on the prediction of the worst case induced by disturbances and the mapping principle with updated state feedback. With the proposed event-based MPC, the measurement frequency and the triggering rate can be reduced by sampling the system states only at certain time instants. Recursive feasibility and robust stability are established under sufficient conditions.

Hybrid continuous-discrete time control strategy to optimize thermal network dynamic storage and heat-electricity integrated energy system dynamic operation

The heat-electricity integrated energy system (HE-IES) presents a promising opportunity for increasing renewable energy generation by fully utilizing the dynamic heat storage capabilities of the thermal network (TN). However, the dynamic characteristics of the TN and the response characteristics of devices in the HE-IES present challenges to system operation and control. To address these challenges, this study proposes a novel multi-layer control strategy that divides the system based on the component response status. The first layer aims to minimize the operating costs of the HE-IES, disregarding any dynamic effects. The second layer optimizes the dynamic operation of thermal subsystems by employing a TN’s Taylor expansion model and continuous-time generalized predictive control. The third layer focuses on optimizing the power subsystem to enhance the share of renewable energy generation, using discrete-time model predictive control. To the best of our knowledge, this is the first study that utilizes continuous time models to control the dynamic operation of TNs and their thermal subsystems. Through case analysis, the proposed model achieves a 34.5% reduction in operating costs compared to a single-layer control strategy and a 2.7% reduction compared to a discrete-time multi-layer control strategy. These findings highlight the favorable economic performance of the proposed model. Additionally, the utilization of continuous-time model allows for effective capturing dynamic performance of the TN and enhances its role in system operation.

Predictive Position Control With System Constraints for PMSM Drives Based on Geometric Optimization

The system constraints (current, speed and voltage limitations) are essential for the safety control of predictive position control (PPC) method. However, online solution of model predictive control (MPC) with complex system constraints is still a challenge. In this paper, a novel discrete-time model predictive position control (DMPPC) strategy for surface permanent magnet synchronous motor (SPMSM) drive is proposed, the current, speed and position are regulated simultaneously. The optimization model of the position control system considering system constraints is formulated, the current, speed and voltage constraints are analyzed and transformed into the incremental voltage constraints. To reduce the calculation burden, a simplified method based on the geometric boundaries and cost function is proposed to solve the optimization problem, complex iterative calculations are avoided, the system constraints are well limited and less calculation time can be achieved. Finally, the proposed DMPPC method is experimentally verified and compared with a traditional iterative method and a cascade predictive position control (CPPC) method.

Utilizing diverse mix of energy storage for LFC performance enhancement of a microgrid: A novel MPC approach

Integration of highly fluctuating renewable energy source (RES)-based distributed generation units (DGUs) and a low inertia of an islanded microgrid (MG), resulting from absence of direct coupling between the various DGUs and the MG, can stimulate severe frequency deviation problems. In such a scenario implementation of the energy storage units (ESUs) becomes imperative. Consequently, this paper examines the impact of diverse mix of two widely employed ESUs namely electric vehicle (EV) battery and superconducting magnetic energy storage (SMES) on the dynamic responses of an islanded MG. A novel discrete-time Laguerre functions-based intelligent model predictive control (LiMPC) approach is administered as a secondary controller. Realization of the Laguerre functions-based MPC approach, as compared to the classical MPC approach, reduces the number of parameters to be optimized and simultaneously downsizes the computational time of the control vector trajectory. Simulation results clearly validate the potency of the energy storage-based LiMPC approach, when both the ESUs are engaged, in improving the dynamic responses of the MG and simultaneously satisfying the load frequency control (LFC) requirements. A maximum percentage improvement of 41.91% in peak overshoot and 51.98% in peak undershoot of the dynamic responses, and 94.93% in the performance index value is observed. Furthermore, the superiority of the suggested control approach over a few widely used control approaches is shown. Finally, the robustness to parametric modifications of the proposed LiMPC approach is verified.

Modelling and Simulation of 1 MW Grid-Connected PV System Regulated by Sliding Mode Control, Model Predictive Control and PI Control

The design and modeling of a 1 MW grid-connected multistage PV system consisting of four equal power rated PV arrays are presented. Two nonlinear control methods, namely sliding mode control and discrete time model predictive control with finite switching states are adopted as the current control scheme of the inverter together with the parameter update for the LCL filter for each control mode. The proposed controllers are based on coordinate transformation of the variables and use decoupling to improve control performance. The dynamic and steady-state performances of these controllers have been thoroughly evaluated and compared with the conventional decoupled PI current control scheme in Matlab Simulink environment under fixed and changing weather conditions. It is observed that the performances of the controller schemes are satisfactory and they give almost similar steady-state performances under given test conditions, although there are little changes observed during system starting.

Nonlinear Model Predictive Control with Terminal Cost for Autonomous Vehicles Trajectory Follow

This paper presents a nonlinear model predictive control with terminal cost (NMPC–WTC) algorithm and its open/closed-loop system analysis and simulation validation for accurate and stable path tracking of autonomous vehicles. The path tracking issue is formulated as an optimal control problem. In order to improve the squeezing phenomenon of traditional NMPC, a discrete-time nonlinear model predictive controller with terminal cost is then designed, in which the state error of last step is augmented. The cost function of NMPC–WTC consists of two parts: (1) the traditional NMPC cost function responding to tracking errors and controller output, and (2) the augmented terminal cost. The algorithm was implemented on CasADi numerical optimization framework, which is free, open-source and developed for nonlinear optimization. The open-loop and closed-loop simulation results are then presented to demonstrate the improved performance in tracking accuracy and stability compared to traditional model predictive controller.

Discrete-Time Model Predictive Controller Using Laguerre Functions for Active Flutter Suppression of a 2D wing with a Flap

In this paper, a discrete-time model predictive controller using Laguerre orthonormal function-based (LMPC) for active flutter suppression of a two-dimensional wing with a flap is presented. In this work, a linear mathematical state-space model for the pitch, plunge, and flap degrees of freedom under unsteady aerodynamics is derived and used to determine the linear flutter velocity and frequency of the parameters of a selected experimental wing. To verify the model, the open-loop simulation results are compared to an experimental study using the same wing from the literature. The state-space system is then discretized and LMPC with a Kalman filter is designed and tuned using the MATLAB® simulation environment at a selected speed in the linear flutter region. The predictive control advantage of dealing with input constraints in a systematic manner is explored through a quantitative analysis of the response of both constrained and unconstrained LMPC controllers. The results indicate that theoretically both cases can give excellent performance. However, the input trajectory generated by the unconstrained LMPC is very aggressive in a way that it is considered impractical when compared to the physical limits of an experimental actuator from the literature. The potential of LMPC to achieve a reasonable performance at a significantly lower computational cost compared to the classical model predictive controller (MPC) is investigated by measuring the time required by the same computer to compute the control trajectory for both controllers. The data suggest that LMPC requires remarkably low computational power, which makes it an excellent choice for fast aeroelastic applications.

A discrete-time linear model predictive control for motion planning of an autonomous vehicle with adaptive cruise control and obstacle overtaking

Motion planners for autonomous driving improve traffic safety through collision-free motion generation along the path. However, conventional motion planners render passengers uncomfortable as a result of jerky motion. To overcome this, we propose a model predictive control (MPC) based motion planner that not only ensures safety but also improves driving comfort. The proposed planner generates path tracking and collision-free maneuvers to ensure safety, and improve driving comfort by minimizing acceleration and jerk. Collision-free maneuvers include vehicle following and overtaking. The target speed is determined by comprehensively considering path tracking performance improvement and whether overtaking is possible. The speed of the vehicle is controlled by considering longitudinal acceleration and jerk minimization. The steering command is determined by considering both path tracking error reduction, and lateral acceleration and jerk minimization. In cases where vehicle overtaking is required and during high-speed driving conditions, the consideration of lateral acceleration and jerk minimization increases to improve driving comfort. The proposed planner is formulated as a convex optimization problem. The effectiveness of the proposed planner was evaluated in path tracking and collision avoidance simulations. The simulation results confirm that the proposed planner ensures vehicle safety through lane keeping and collision avoidance, and improves driving comfort.

Practical implementable controller design with guaranteed asymptotic stability for nonlinear systems

Establishing the stability of model predictive control formulation is challenging. Using a combination of the terminal cost term and the terminal inequality constraint i.e. terminal set results in nominal asymptotic stability. Larger terminal set results in shorter minimum prediction horizon length required for feasibility from identical initial condition. Current work presents novel linear quadratic Gaussian regulator based approach for the terminal set characterization for the discrete time model predictive control scheme. Proposed approach provides large degrees of freedom in the form of additive matrices as tuning parameters for enlarging the terminal sets as against a single scalar for the literature approaches. Efficacy of the novel approach is demonstrated using a benchmark four tank system. It was observed that the average computation time reduces to significantly when compared to the approaches from the literature for identical initial conditions. This makes the controller design suitable for practical implementation.

Fast Online Optimization for Terrain-Blind Bipedal Robot Walking With a Decoupled Actuated SLIP Model.

We present an online optimization algorithm which enables bipedal robots to blindly walk over various kinds of uneven terrains while resisting pushes. The proposed optimization algorithm performs high-level motion planning of footstep locations and center-of-mass height variations using the decoupled actuated spring-loaded inverted pendulum (aSLIP) model. The decoupled aSLIP model simplifies the original aSLIP with linear inverted pendulum (LIP) dynamics in horizontal states and spring dynamics in the vertical state. The motion planning can be formulated as a discrete-time model predictive control (MPC) problem and solved at a frequency of 1 kHz. The output of the motion planner is fed into an inverse-dynamics–based whole body controller for execution on the robot. A key result of this controller is that the feet of the robot are compliant, which further extends the robot’s ability to be robust to unobserved terrain variations. We evaluate our method in simulation with the bipedal robot SLIDER. The results show that the robot can blindly walk over various uneven terrains including slopes, wave fields, and stairs. It can also resist pushes of up to 40 N for a duration of 0.1 s while walking on uneven terrains.

An Improved Model Predictive Fast Frequency Control for Power System Stability Against Unknown Time-Delay Switch Attack

A modern power grid is a cyber-physical system, which are vulnerable to cyber attacks. A recently found attack, the time-delay switch attack (TDSA), is made by inserting time delays into communication channels. A TDSA can be highly destructive to a power system as it can lead to instability. This paper presents a novel model predictive control (MPC) for fast frequency controller in a power system which can effectively mitigate the unknown TDSA. The MPC recently has received great attentions to be applied as FFC in a power system. Most of the MPC design are based on discrete-time model, whose future plant behaviour is calculated through iteration, rather than convolution. Nevertheless, one crucial step in the derivation of discrete-time MPC (DTMPC) is to capture the control trajectory over a finite prediction horizon. This imposes a challenge in designing a DTMPC to counteract the time-delay with unknown time length. Thus, a continuous-time MPC (CTMPC) is proposed to deal with TDSA. To overcome the unknown time delay, we synthesize an accurate time-delay estimator and sequential state predictor (SSP), are designed to accurately estimate and effectively counteract the unknown and random TDSA. All presented case studies are based on a real Taipower system and justification of the effectiveness of the proposed method was verified.

Online Foot Location Planning for Gait Transitioning Using Model Predictive Control

This paper proposes an online uniform foot location planning method (UPMPC) based on model predictive control (MPC) for solving the problem of large posture changes during gait transitioning. This method converts the foot location planning into a discrete-time MPC problem. The core part of the method is to complete the planning of the foot location based on the linear inverted pendulum (LIP) model and the simplified robot dynamics model. By unifying the input foot location at each time step, the solution time is shortened. The final simulation experiment compares the results of using the UPMPC and foot location planning method with heuristic function (HF) for gait transitioning, respectively. This result demonstrates that the UPMPC can complete the gait transitioning task and adapt to large changes in posture during gait transitioning. In addition, the results also show the good performance of UPMPC in fixed gait.

A model predictive controller for precision irrigation using discrete lagurre networks

The increasing demand for water is depleting the natural water resources worldwide. One of the major consumers of water is the agricultural industry. Traditional means of irrigation results in a lot of water wastage due to which the notion of precision irrigation was introduced using embedded devices. Many of the existing techniques for precision irrigation produce either sub-optimal results or have high computational complexity not suitable for low cost and simple embedded devices such as Raspberry-Pi (RPi). To solve this issue, this paper presents a precision irrigation technique based on discrete time model predictive control (MPC). To reduce the computational complexity of the proposed techniques, the use of Laguerre functions to approximate the control horizon is proposed. Using simulations in MATLAB, the results shows that the proposed technique can approximate the behavior of a discrete linear quadratic regulator with sufficient accuracy. The experimental results in a greenhouse environment, show that the proposed that the proposed technique can reduce water consumption by 30% over a period of 21 days. Moreover, a performance analysis of the proposed technique is presented to show that the proposed technique has significantly lower the computational complexity as compared to other conventional MPC techniques, i.e., it results in a computational complexity at least three time lower than existing techniques. Thus, the proposed precision irrigation control technique can be an attractive choice for real time agricultural application.

Adaptive Learning-Based Observer With Dynamic Inversion for the Autonomous Flight of an Unmanned Helicopter

This article presents the development of an autonomous flight control system for a small-scale unmanned helicopter based on an online adaptive learning-based observer and model predictive control (MPC). The adaptive learning-based observer provides an approximate dynamic inversion for solving the coupled dynamic problem. The discrete-time MPC (DMPC) uses a prediction process to obtain a stable model. The Laguerre function, a state observer, and a recursive learning algorithm were integrated into DMPC, the core of the flight control system. Exponential data weighting was adopted to increase the stability of the designed flight control system. By integrating these approaches, an adaptive learning-based flight control system, which consists of the pitch, roll, yaw, and heave controllers, is presented to evaluate the stability and performance of the proposed autonomous flight control system of an unmanned helicopter. Moreover, an adaptive controller based on neural approximation for yaw motion is used to improve the performance of yawing control of the helicopter. In order to validate the feasibility of the proposed method, a hardware-in-the-loop simulation was performed in real time. The system included an embedded system, a self-developed users interface, and the X-plane flight simulator. The simulation results showed that the flight control system was able to maintain the position and the attitude of the helicopter in hover mode under the influence of wind gust and disturbance. The proposed method had better performance than a robust control system, in both ideal and disturbed environments.

Hybrid Model Predictive Control of DC–DC Boost Converters With Constant Power Load

This article presents a hybrid model predictive controller to ensure dc microgrid stability and enhance the performance of dc-dc boost converters interfaced with constant power loads (CPLs) in a hybrid system. Hybrid systems are dynamic systems with both continuous current mode and discontinuous current mode states. The main purpose in this article is to develop an advanced control technique for voltage regulation and stabilization of the converters in the presence of CPLs due to serious stability concerns, without considering the accurate modelling information of the system. In this regard, an automatic model, considering different modes of operation induced by semiconductor switches in dc-dc boost converters and highly non-linear nature of CPL is employed to design the proposed control approach. The non-linear CPL connected directly to a dc-dc boost converter is utilized to define an optimal tracking control problem by minimizing a finite-prediction horizon cost function, which is known as a finite control set MPC. The proposed controller, which is implemented in both continuous and discontinuous current modes, accounts for the regulation of output voltage within the predefined range. The effectiveness of the proposed hybrid model predictive control is verified using a comparative evaluation with discrete-time averaged model predictive control, continuous control set MPC, and the conventional PI control under experimental conditions. The results authenticate an improved dynamic performance, which can be applied to practical dc microgrids with CPLs.

Discrete-time MPC for switched systems with applications to biomedical problems

This paper studies switched systems in which the manipulated control action is the time-depending switching signal. To control the switched systems means to select an autonomous system - at each time step - among a given finite family. Even when this selection can be done by solving a Dynamic Programming (DP) problem, such a solution is often difficult to apply, and state/control constraints cannot be explicitly considered. In this work a new set-based Model Predictive Control (MPC) strategy is proposed to handle switched systems in a tractable form. The optimization problem at the core of the MPC formulation consists in an easy-to-solve mixed-integer optimization problem, whose solution is applied in a receding horizon way. Applications to schedule therapies in viral infection and cancer treatments are studied. The numerical results suggest that the proposed strategy outperforms the schedule for available treatments.

Model Predictive Control with a Relaxed Cost Function for Constrained Linear Systems

The Model Predictive Control technique is widely used for optimizing the performance of constrained multi-input multi-output processes. However, due to its mathematical complexity and heavy computation effort, it is mainly suitable in processes with slow dynamics. Based on the Exact Penalization Theorem, this paper presents a discrete-time state-space Model Predictive Control strategy with a relaxed performance index, where the constraints are implicitly defined in the weighting matrices, computed at each sampling time. The performance validation for the Model Predictive Control strategy with the proposed relaxed cost function uses the simulation of a tape transport system and a jet transport aircraft during cruise flight. Without affecting the tracking performance, numerical results show that the execution time is notably decreased compared with two well-known discrete-time state-space Model Predictive Control strategies. This makes the proposed Model Predictive Control mainly suitable for constrained multivariable processes with fast dynamics.

Parameters Estimation and Auto-Tuning of a Discrete-Time Model Predictive Speed Controller of Induction Motor Drives by ANFIS Controller

Parameters Estimation and Auto-Tuning of a Discrete-Time Model Predictive Speed Controller of Induction Motor Drives by ANFIS Controller

Non-PDC Interval Type-2 Fuzzy Model Predictive Microclimate Control of a Greenhouse

Greenhouse climate control is known as a challenging task since it is characterized by the strong interaction among the involved variables, the time-varying uncertainties, and the external disturbances that severely affect its internal environment. In this paper, a discrete-time fuzzy model predictive control approach of a greenhouse is investigated. An interval type-2 (IT2) Takagi–Sugeno fuzzy model is employed to represent the nonlinear dynamics of the plant subject to parameter uncertainties, which are effectively captured by interval membership functions. To design the fuzzy model predictive controller, an optimization problem which minimizes a quadratic cost function respecting the input and state constraints is formulated and solved at each sampling instant in the prediction time horizon. By introducing a non-parallel distributed compensation (non-PDC) design concept and based on the non-quadratic Lyapunov function, less conservative conditions are developed in terms of linear matrix inequality to guarantee the stability analysis. Simulation results illustrate the effectiveness of the proposed control approach in leading to promote a comfortable greenhouse microclimate for the growth of the crops.