Robust Output Feedback MPC for Linear Systems via Interpolation Technique

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

Stabilization of max-plus-linear systems using model predictive control: The unconstrained case

This paper presents the application of the model predictive control (MPC) technique for controlling the speed of the induction motor drive. Vector control principle has been used for decoupling between motor speed and rotor flux. A simple model of induction motor is employed in the MPC structure so as to minimize the computational load. The MPC controller design is taken into account the effect of uncertainty due to motor parameters variation and load disturbance could be reduced. The effectiveness of the proposed scheme has been successfully verified through simulations. The performance of the system including the MPC controller is compared with the corresponding one using the traditional PI controller. The results proved that the induction motor with the MPC speed controller has superior transient response, and good robustness in face of uncertainties including load disturbance. Moreover, accurate tracking performance has been achieved.

— 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.

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 popularity of model predictive control (MPC) is mainly founded on its easy implementation and its ability to consider state and input constraints. For future applications in safety-critical systems, however, it is necessary to provide formal guarantees of safety despite disturbances and measurement noise. In this paper, we include reachability analysis in an MPC approach to obtain provably safe controllers which are easy to implement. We consider continuous-time, nonlinear systems affected by disturbances and measurement noise. In contrast to most existing techniques, we explicitly consider the computation time and guarantee the satisfaction of state and input constraints despite the previously-mentioned disturbances. We use a novel type of dual mode MPC, which does not require the computation of Lyapunov functions. We demonstrate the applicability of our approach with a numerical example of a chemical reactor, where we show the advantages of our approach compared to existing MPC.

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 .

Frequency Domain Tuning Method for Unconstrained Linear Output Feedback Model Predictive Control

Explicit Model Predictive Control (MPC) is an attractive control strategy, especially when one aims at a fast, computationally less demanding implementation of MPC. Although leading to a fast implementation of optimization-based control, the main downside of explicit MPC is its high complexity in terms of memory occupancy, which often limits practical applicability of such a control methodology. Therefore in this paper we propose to obtain simple explicit MPC controllers that provide guarantees of recursive satisfaction of input and state constraints. The task is accomplished by optimizing, off-line, the parameters of the feedback law such that an integrated square error between the optimal, but complex controller and its simpler replacement is minimized. We show that the task can be formulated as a quadratic optimization problem which always yields an admissible solution. In this way, suboptimality of simple feedbacks with respect to their complex optimal counterparts is significantly mitigated.

Model Predictive Control (MPC) has the advantage of including constraints into the optimization. By combining MPC with Feedback Linearization (FBL) it is possible to use linear, discrete time MPC algorithms with nonlinear models. This way the constraints on the control systems, thrusters and aerodynamic surface deflections, and on the attitude of the vehicle can be integrated into the controller synthesis. The main disadvantage of this type of controller is the lack of robustness when uncertainties enter the system. This paper therefore improves the nominal FBL-MPC controller by replacing the Quadratic Programming algorithm with a minmax MPC technique involving Linear Matrix Inequalities. Uncertainties on the nonlinear aerodynamic coecients are used as a source of disturbances. By mapping these uncertainties to a linear state space model as used by the MPC controller, a polytopic set of uncertainty models is created that can be used by the min-max algorithm to minimize the performance cost over the worst case model from the uncertainty set. This approach will be illustrated using a model of the X-38 re-entry vehicle flying along a predefined trajectory with active input and state constraints. The results show that the robustness is improved significantly when compared to the nominal controller with the same uncertainties.

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

A stabilizing output feedback model predictive control algorithm is proposed for linear systems with input constraints. Dual mode control strategy is adopted: the state observer, linear feedback controller and terminal constraint set are pre-computed; if the state is contained in terminal constraint set, linear feedback controller is used; otherwise a linear control structure with free vector is used, and control law can be obtained by solving an Second Order Cone Programming (SOCP) problem. The system with bounded disturbance is considered and bounded stability is shown. Simulations results show the effectiveness of the control algorithm.

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.

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.

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.