Miroslav Fikar

Clipping-Based Complexity Reduction in Explicit MPC

The idea of explicit model predictive control (MPC) is to characterize optimal control inputs as an explicit piecewise affine (PWA) function of the initial conditions. The function, however, is often too complex and either requires too much processing power to evaluate on-line, or consumes a prohibitive amount of memory. The paper focuses on the memory issue and proposes a novel method of replacing a generic continuous PWA function by a different function of significantly lower complexity in such a way that the simple function guarantees the same properties as the original. The idea is based on eliminating regions of the PWA function over which the function attains a saturated value. An extensive case study is presented which confirms that a significant reduction of complexity is achieved in general.

A Flexible and Configurable Architecture for Automatic Control Remote Laboratories

In this paper, we propose a novel approach in hardware and software architecture design for implementation of remote laboratories for automatic control. In our contribution, we show the solution with flexible connectivity at back-end, providing features of multipurpose usage with different types of experimental devices, and fully configurable client side application at front-end. The physical setup and communication principles of hardware architecture are based on two types of devices: the programmable logic controllers and industrial network routers. The user interface of client application is designed as a Web page, powered by optimized JavaScript, using the sophisticated on-the-fly content generation. To prove the suitability of the architecture, we compare it with other existing approaches of remote laboratory design. We evaluate their benefits and weaknesses, especially in terms of expense, implementation difficulty, and versatility of usage. In this paper, we also show a detailed example of remote laboratory implementation based on new architecture for thermo-optical educational system and provide three other examples of developed remote laboratories. Evaluation of remote laboratory usage and its benefits is provided to demonstrate the learning value of proposed architecture in education process.

Automatic code generation for real-time implementation of Model Predictive Control

Model Predictive Control (MPC) is a proven control concept with many applications in the process industry. Popularity of the framework is mainly due to its ability to optimize behavior of the process while respecting physical and economical constraints. The major challenge of implementing MPC in real time on low-cost hardware is the inherent computational complexity. To address this goal, it is proposed to solve a given MPC problem using parametric programming, which encodes the optimal control moves as a lookup table. A great advantage being that such tables can then be processed even with low computational resources and therefore allow MPC to be deployed to low cost control devices. In the paper we present a unique software tool which allows MPC problems to be designed with low human effort, and is capable to automatically generate real-time executable code for various target platforms.

Stabilizing polynomial approximation of explicit MPC

A given explicit piecewise affine representation of an MPC feedback law is approximated by a single polynomial, computed using linear programming. This polynomial state feedback control law guarantees closed-loop stability and constraint satisfaction. The polynomial feedback can be implemented in real time even on very simple devices with severe limitations on memory storage.

ArPi Lab: A Low-cost Remote Laboratory for Control Education

Abstract In this paper, we present a cost effective approach to remote experimentation. We propose ArPi Lab – remote laboratory for education in area of process control. This lab is built on very cheap hardware components, including single-board computers Raspberry Pi and open prototyping platforms Arduino based on 8-bit micro-controllers. This approach combines several different software technologies. These are HTML 5 and JavaScript for client-side application, PHP and MySQL for laboratory server implementation, JSON as structure for data transfer, and C language for experiment server and micro-controller programming. ArPi Lab provides three different types of educational physical systems. Three thermal plants, one magnetic levitation, and one hydraulic tank system are available for remote laboratory experiments. Each part of ArPi Labs hardware architecture can be controlled in the meaning of power supply. For this purpose we propose an efficient power management model, designed to solve occasional hardware and communication failures in such kind of laboratories, where physical absence of supervising person can result in serious malfunctions or security issues.

Complexity reduction of explicit model predictive control via separation

The problem of reducing complexity of explicit MPC feedback laws for linear systems is considered. We propose to simplify controllers defined by continuous Piecewise Affine (PWA) functions by employing separating functions. If a state resides in a region where the optimal control action attains a saturated value, the optimal control move is determined from the sign of the separator. Thus, instead of storing all regions, only the unconstrained regions and the separator are needed. We propose several approaches to construct separators with different efficacy and properties.

Low-complexity polynomial approximation of explicit MPC via linear programming

This paper addresses the issue of the practical implementation of Model Predictive Controllers (MPC) to processes with short sampling times. Given an explicit solution to an MPC problem, the main idea is to approximate the optimal control law defined over state space regions by a single polynomial of pre-specified degree which, when applied as a state-feedback, guarantees closed-loop stability, constraint satisfaction, and a bounded performance decay. It is shown how to search for such a polynomial by solving a single linear program.

Polynomial Approximation of Closed-form MPC for Piecewise Affine Systems

Abstract This paper addresses the issue of the practical implementation of closed-form Model Predictive Controllers (MPC) to processes with very short sampling times. Such questions come in consideration when the solution to MPC problems is expressed in a so-called parametric or closed-form fashion. The underlying idea of this paper is to approximate the optimal control law defined over state space regions by a higher degree polynomial which then guarantees closed-loop stability, constraint satisfaction, and a bounded performance decay. The advantage of the proposed scheme lies in faster controller evaluation and lower storage demand compared to currently available techniques.

Performance-lossless complexity reduction in Explicit MPC

The idea of Explicit Model Predictive Control (MPC) is to find the optimal control input as an explicit Piecewise Affine (PWA) function of the initial conditions. The function, however, is often too complex to be processed by a typical control hardware setup in real time. Therefore the paper proposes a novel method of replacing a generic continuous PWA function by a different function of significantly lower complexity in such a way that optimal closed-loop performance, stability and constraint satisfaction are preserved. The idea is based on eliminating a significant portion of the regions of the PWA function over which the function attains a saturated value. An extensive case study is presented which confirms that a significant reduction of complexity is achieved in general.

Mathematical Modeling of Diafiltration

The main objective of this study is to provide a general mathematical model in a compact form for batch diafiltration techniques. The presented mathematical framework gives a rich representation of diafiltration processes due to the employment of concentration-dependent solute rejections. It unifies the existing models for constant-volume dilution mode, variable-volume dilution mode, and concentration mode operations. The use of such a mathematical framework allows the optimization of the overall diafiltration process. The provided methodology is particularly applicable for decision makers to choose an appropriate diafiltration technique for the given separation design problem.