MPC for continuous piecewise-affine systems

Model predictive control (MPC) is a multi-objective control technique that can handle system constraints. However, the performance of an MPC controller highly relies on a proper prioritization weight for each objective, which highlights the need for a precise weight tuning technique. In this paper, we propose an analytical tuning technique by matching the MPC controller performance with the performance of a linear quadratic regulator (LQR) controller. The proposed methodology derives the transformation of a LQR weighting matrix with a fixed weighting factor using a discrete algebraic Riccati equation (DARE) and designs an MPC controller using the idea of a discrete time linear quadratic tracking problem (LQT) in the presence of constraints. The proposed methodology ensures optimal performance between unconstrained MPC and LQR controllers and provides a sub-optimal solution while the constraints are active during transient operations. The resulting MPC behaves as the discrete time LQR by selecting an appropriate weighting matrix in the MPC control problem and ensures the asymptotic stability of the system. In this paper, the effectiveness of the proposed technique is investigated in the application of a novel vehicle collision avoidance system that is designed in the form of linear inequality constraints within MPC. The simulation results confirm the potency of the proposed MPC control technique in performing a safe, feasible and collision-free path while respecting the inputs, states and collision avoidance constraints.

— The objective of this paper is to investigate the Model Predictive Control (MPC) strategy, analyze and compare the control effects with Proportional-Integral-Derivative (PID) control strategy in maintaining a level of spherical tank system using VFD. An advanced control method, MPC has been widely used and well received in a wide variety of applications in process control, it utilizes an explicit process model to predict the future response of a process and solve an optimal control problem with a finite horizon at each sampling instant. In this paper, an algorithm is developed for controlling the speed of the pump using VFD to maintain the level of the spherical tank system. Next, the system is modeled and linearized for analysis and design. Model is implemented in a simulation environment based on LabVIEW. Both MPC and PID control methods are tried to design the controller for the water level system in a spherical tank and compared the results in terms of peak time, settling time, overshoot, and steady-state error under various operational conditions including time delays. The results showed the advantage of MPC for dealing with the system dynamic over PID and could be designed for more complex and fast system dynamics even in presence of constraints and Reduction of power consumption by the pump due to usage of VFD for controlling level by varying the speed of the pump based on the level of the tank. Keywords: Non Linear - Spherical Tank System – Level Control – Variable Frequency Drive – PID Controller – MPC Controller – Modeling - LabVIEW. Cite this Article R. Dhanasekar, S. Vijayachitra, M. Pravin Savaridass. Controlling of Level Process in Nonlinear System Using Variable Frequency Drive. Current Trends in Information Technology. 2019; 9(1): 24–33p.

Frequency regulation balances the supply and demand of power within a power network to maintain the network's frequency about its nominal value. Using residential loads to supply frequency regulation while respecting user comfort can require costly communication infrastructure. Developing control algorithms that are resilient to communication network imperfections, e.g., delays, can allow the usage of less costly, lower reliability communication infrastructure. Previous work developed a model predictive control (MPC) approach that enables aggregations of loads to track a desired power signal despite communication delays. This work presents a novel model-reduction method to produce a minimal aggregate load model, and then uses state augmentation to include the effect of input delays. This allows the reformulation of the MPC controller into a linear controller yielding a closed-form control law that reduces online computation. We present simulations that compare the MPC and linear controllers' tracking ability given input delays. The linear controller neglects input constraints explicitly included within the MPC controller, and we characterize the impact of neglecting these constraints through simulations. The linear controller reduces the computation time by a factor of 100, but the RMS tracking error increases 11% in the cases studied.

This paper presents the comparative study of Model Predictive Controller (MPC) with PID Controller implemented for flow control loop in LABVIEW. Classical PID controller is mostly used in process instrumentation yet tuning of PID controller is the crucial part to be dealt with. Moreover, changes in the parameters of the loop components affects the tuning of the controller, hence over a period of time retuning of PID controller is required. On the other hand MPC controller works on the process model which predicts and optimizes the process performance. Here, Flow control loop performance was studied for MPC and PID controller. MPC worked on 1st order state space system model and PID was tuned using Internal Model Control (IMC) method. The result of implementation shows that, MPC controller performs much better than PID controller. Set point of with less settling time and zero peak overshoot was observed in MPC whereas PID has comparatively more settling time and peak overshoot.

In power system operation and control, automatic generation control (AGC) scheme is used to maintain the balance in between the net generation and the total load in a system by supplying sufficient power with good quality. Controller plays an important role in AGC scheme. This paper presents a control scheme based on model predictive control (MPC) concept for multiarea power system in deregulated scenario. For guaranteed stability each area controller is designed independently. MPC controller is designed in such a way that for any load perturbation, generators can regulate the real power output to settle down deviations in frequency and tie line power exchange at desired values. The proposed MPC control scheme has been implemented for deregulated two area thermal power system. The performance of MPC controller is also checked for 75 bus Indian power system. Various load conditions has been considered to evaluate the performance of controller. The results and performance analysis are presented to justify the robustness & effectiveness of control scheme. The comparative performance analysis of MPC scheme and conventional proportional integral controller (PID) control is also presented.

Path-tracking control is a crucial process for autonomous vehicles, ensuring that the vehicle drives safely along the reference path, and the suitable controller parameters ensure the accuracy and stability of this process. To enhance the adaptability of traditional path-tracking controller parameters, this paper proposes an adaptive model predictive control (MPC) controller based on a preview-based PID controller and deep deterministic policy gradient (DDPG) algorithm to achieve adaptive tuning of the controller parameters. Starting with the design of the dynamics tracking error model of the vehicle and the MPC controller. Based on the actor-critic reinforcement learning architecture, the DDPG agent is designed to tune the prediction horizon and weight matrix of the MPC controller. A preview-based PID controller is proposed to improve the efficiency and stability of reinforcement learning and compensate for the error in vehicle modeling. The improved algorithm performance is verified through the simulation scenarios of high-speed lane changing and accelerated overtaking scenarios constructed by MATLAB/Simulink. The results show that the improved algorithm significantly improves the adaptive ability of the traditional MPC controller to time-varying conditions and achieves higher tracking accuracy and stability.

Cascade control of effluent nitrate and ammonium in an activated sludge process

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.

Model predictive control (MPC) is an advanced control that has found widespread use in industries, particularly in process industries like oil refining and petrochemicals. Although the basic premise behind MPC is easy to comprehend, its inner workings are still generally viewed or regarded as too advanced for actual plant operator understanding. This lack of understanding is exposed when MPC performance deteriorates sometime after commissioning, as is often the case in some commercially operated process plants. Currently operators might have difficulty over reasoning about MPC performance degradation and formulating steps to investigate the cause. A tool is described that aims to make MPC more transparent to the operators. Commonly reported causes of MPC performance degradation are discussed and ways in which the operator can recognise them when they occur are outlined. Issues that are addressed include: making the set of controlled variables to be used for a given set of manipulated variables simpler and clearer; ways to recognise when a MPC controller is performing poorly and to identify the source of performance deterioration. An aim is to determine under what instances the operator can return the MPC performance to previous levels or request for specialist support or simply switch the MPC off. A goal is to avoid the kind of often reported situation where the operator gets worried that the controller is deteriorating and ends up taking knee jerk actions that cause further problems in MPC. At the top of the maintenance tool hierarchy is the trends comparison group, where MPC reference graphical performance trends are compared with actual graphical performance trends counterpart. If any abnormality is observed in these trends, the operator is encouraged to choose an option from a list of preliminary diagnostic questions contained in a group below trends comparison group, which best describes the observed abnormality. Each abnormality is associated with a list of suspected causes. When a suspected cause is chosen from the associated list, the operator is led to the symptoms investigation window, which contains scripts detailing steps for systematic examination of each symptom, with a view to either rejecting or confirming the suspicion. Assisted in the investigation are four background information windows: the virtual plant without MPC window, the virtual plant with MPC window, the transfer function matrix window and steady state gain, relative gain array (RGA) and relative weight array (RWA) window. The windows contain information and guidance that the operator might refer to from time to time during symptom investigation. Development of the maintenance tool is still at the design stage. The key components described have been research implementing MPC on three nonlinear process models, a continuous stirred tank reactor (CSTR), an evaporator process and a fluid catalytic cracking unit (FCCU). Case studies representing different MPC degradation scenarios are simulated, followed by a systematic procedure for diagnosing, isolating and recovering from such degradation, based on assumed operator’s perspective and expert’s technical reasoning. The knowledge gained from the case studies is used to develop an outline of a vision for a data-driven model predictive maintenance tool to help the operator make sensible judgements about performance degradation, the form and direction of diagnosis and fault isolation, and possibly, the recovery procedure.

To improve the load frequency control (LFC) performance of power systems incorporating virtual power plants (VPPs) while reducing network resource consumption, a model predictive control (MPC) method based on a mixed time/event-triggered mechanism (MTETM) is proposed. This mechanism integrates an event-triggered mechanism (ETM) with a time-triggered mechanism (TTM), where ETM avoids unnecessary signal transmission and TTM ensures fundamental control performance. Subsequently, for the LFC system incorporating VPPs, a state hard constrained MPC problem is formulated and transformed into a “min-max” optimisation problem. Through linear matrix inequalities, the original optimisation problem is equivalently transformed into an auxiliary optimisation problem, with the optimal control law solved via rolling optimisation. Theoretical analysis demonstrates that the proposed auxiliary optimisation problem possesses recursive feasibility, whilst the closed-loop system satisfies input-to-state stability. Finally, validation through case studies of two regional power systems demonstrates that the MPC approach based on MTETM outperforms the ETM-based MPC approach in terms of control performance while maintaining a triggering rate of 33.3%. Compared with the TTM-based MPC algorithm, the MTETM-based MPC method reduces the triggering rate by 66.7%, while maintaining nearly equivalent control performance. Consequently, the results validate the effectiveness of the MTETM-based MPC approach in conserving network resources while maintaining control performance.

Heat exchangers are expedients used to transfer of heat energy from one medium to other while preventing the two from mixing. Heat exchangers are hired in a selection of domestic, commercial, and industrial applications, such as air conditioning, power production, refrigeration, process industry, and manufacturing industry. A larger variation in the temperature affects property of non-Newtonian fluids, thus affects the uniform heat transfer process. This paper is primarily to deal the response analysis of different controllers that is regulating the outlet temperature of fluid inside the PHE is proposed. The cold fluid flow is highly influenced on the hot water temperature, the research work mainly focuses on controlling cold fluid flow. In order to attain the precise model of the system, a mathematical model by first principle methods and process history based methods were used. A PI, PID and Model Predictive Controller (MPC) are known for its better control action of the system. The controller’s performance analysed such as PI, PID and MPC controller to adjust the temperature of hot fluid outlet to a required setpoint. Performance criteria analysis value for various controllers are PI, PID and MPC. It is understood that MPC controller results lower value of performance measures compared to other controllers, this implies that it could track the setpoint by rejecting the external disturbances with less settling time and moderate oscillation. The transient performance and the error criteria of the controllers are investigated and the best controller to regulate the temperature is found out. It is found out that the MPC controller outperforms PI and PID controller from the results of simulation.

This thesis addresses the design of optimization-based control laws for the case where convergence to a desired set-point, minimization of an arbitrary performance index, or a combination of the two, is the desired objective. The results are developed within the sample-data Model Predictive Control (MPC) framework considering constrained nonlinear continuous-time time-varying dynamical systems. For a given time sampling, a sample-data MPC control strategy consists of i) choosing among all future finite horizon predictions of state and input trajectories of the system the one that minimizes the given performance index, ii) applying the optimal input trajectory to the system until a new time sample is reached, and iii) iterating this process. The performance index is chosen to describe the specific control problem under consideration. In a classic Tracking-MPC framework, where the main goal is to steer the state of the system to a desired steady-state, the performance index is properly chosen to penalize the distance from the current state to a desired one. In order to capture more complex control objectives, in recent years a growing attention has been dedicated to a new class of controllers that goes under the name of Economic-MPC. Here, the term economic is used to stress the fact that the performance index is a general index of interest that we wish to minimize, e.g., economic, which does not denote the distance to a desired set point. This setting makes full use of the potentialities of optimization-based control strategies. Although, it comes with disadvantages. In fact, by choosing an arbitrary performance index, it is difficult to predict, and therefore certify, the evolution of the closed-loop system, which could potentially manifest undersirable behaviors. This thesis provides analysis and certification of a variety of closed-loop behaviors stemming from the use Economic-MPC controllers. A set of tools for design of provably correct MPC controllers is provided for the case where the performance index is of the Tracking-MPC type, purely economic, or a combination of the two. The results focus the certification of both closed-loop economic performance and closed-loop state evolution. The proposed strategies are applied to a range of motion control problems for underactuated vehicles. An MPC controller for Trajectory-Tracking and Path-Following with convergence guarantees is first proposed and then extended, using the results presented on Economic-MPC, to address the control problems of distributed formation keeping, energy efficient trajectory-tracking, and target-following through highly observable trajectories.

The model predictive control (MPC) framework, a very popular controller design method in the process industry, is extended to transfer coordination in railway systems. In fact, the proposed approach can also be used for other systems with both hard and soft synchronization constraints, such as logistic operations. The main aim of the control is to optimally recover from delays by breaking connections (at a cost). In general, the MPC control design problem for railway systems leads to a nonlinear, nonconvex optimization problem. Computing an optimal MPC strategy using an extended linear complementarity problem is demonstrated. Also presented is an extension with an extra degree of freedom to recover from delays by letting some trains run faster than usual (again at a cost). The resulting extended MPC railway problem can also be solved using an extended linear complementarity problem.

Unmanned logistics vehicle (ULV) realize the automation and intelligence of cargo transportation, which improves the efficiency, cost-effectiveness and safety of logistics and distribution, while the trajectory tracking control of ULV is the key technology to ensure their safe and efficient delivery of goods. In order to solve the trajectory tracking problem of ULV in the process of delivering goods, this paper proposes a model predictive control (MPC) method based on event-triggered and fuzzy adaptive optimization parameters. Firstly, the dynamics model of the ULV is established. Secondly, an event-triggered mechanism is introduced to establish ET-MPC, while a disturbance observer is designed considering the external disturbance and the controller calculation discarding the nonlinear term. Thirdly, the advantages of fuzzy control and MPC algorithms are integrated, and the four important parameters in the MPC controller are adaptively optimized by fuzzy control, and the improved MPC control strategy is designed. Finally, the CarSim-Matlab/Simulink co-simulation platform and the experimental vehicle platform are constructed to verify the effectiveness of the improved MPC trajectory tracking controller proposed in this paper. The results show that the improved MPC control strategy can reduce the computation time of the controller, and the total number of triggering times of the controller is reduced by 46.44% compared with the classical MPC, which reduces the computational complexity of the controller and improves the accuracy and smoothness of the trajectory tracking of the ULV.

This paper proposes a time-lag model predictive control (MPC) method to solve the problem of communication delay in networked automatic generation control (AGC). The method uses the optimum weighting method to predict delay and the time-lag dynamic state equation of interconnected grid as the MPC prediction model. Then the deviation of predicted output is added to the objective function of rolling optimization in MPC method. The backup suboptimal control command from MPC controller can handle the loss of data packet in networked AGC. The correctness of the proposed method is verified by dynamic simulation.