Andrea Wellenreuther

Optimal control of a reverse osmosis desalination plant using multi-objective optimization

In this contribution, the control of a reverse osmosis desalination plant by using an optimal multi-loop approach is presented. Controllers are assumed to be players of a cooperative game, whose solution is obtained by multi-objective optimization (MOO). The MOO problem is solved by applying a genetic algorithm and the final solution is found from this Pareto set. For the reverse osmosis plant a control scheme consisting of two PI control loops are proposed. Simulation results show that in some cases, as for example this desalination plant, multi-loop control with several controllers, which have been obtained by join multi-objective optimization, perform as good as more complex controllers but with less implementation effort.

A New Approach to Design Multi-loop Control Systems with Multiple Controllers

In this contribution, a new method to design multi-loop control systems with several controllers is proposed. Controllers are assumed to be players of a cooperative dynamic game, whose solution is obtained by multi-objective optimization (MOO). The MOO problem is solved by applying a genetic algorithm and the final solution is found from an optimal Pareto set. As illustrative example, the control system design of a reverse osmosis desalination plant is used. Simulation results are satisfactory and show that in many cases, as for example this desalination plant, multi-loop control with several controllers, which have been obtained by join multi-objective optimization, perform as good as more complex controllers but with less implementation effort

Multi-loop controller design for a heat exchanger

A new method to tune the parameters of two discrete controllers in a cascaded control structure is proposed and applied to the linear controller design of a heat exchanger system. Normally, this problem is solved either by decoupling the multiple loops and tuning the controllers independently or by keeping the structure but tuning the controllers consecutively from inwards to outwards. However, these methods are not always an appropriate solution. Therefore, this approach that is derivated from the game theory is applied in this paper for a heat exchanger system where discrete controllers of two cascaded loops act as players in a cooperative game. The players operate simultaneously and influence themselves. Each player has its own objective function, which also depends on parameters of the other players. Target of the game is to get values for the parameters, satisfying the objective functions of the players, which is done via multi-objective optimization.

Comparing different holonomic mobile robots

This paper presents a comparison between three different holonomic mobile robots. The first has three caster wheels with wheel angular velocities actuation and carries the name C3P. The second is omni-directional wheeled mobile robot and the third is a special holonomic robot configuration developed by ETH named Ramsis II. Inverse kinematic and forward dynamic models are presented for each robot for the simulation process. The simulation results illustrate the performance of each robot in comparison to the others. The comparison is done with respect to three main aspects; 1) the mobility, 2)the total energy consumed by each robot in a finite interval of time, and 3) the hardware complexity. A cost functional is obtained to demonstrate the comparison, and a criteria is developed to measure the hardware complexity of each robot. The weight sum method enables the cost functional to show the importance of each aspect and to distinguish between the lowest cost platform with respect to each aspect importance.

Multi-loop control system design: A game theoretical approach for computer-controlled systems

In this contribution, previous work for the design of multi-loop control systems with several controllers is extended in several directions. The main idea is to model the whole control system as a cooperative dynamic game, where controllers are the players. The solution of this game is obtained by using multi- objective optimization (MOO). The extensions considered in this paper are the following: First, the problem is formulated in a discrete-time framework so that digital control systems will be able to be designed in a natural way. Moreover, the choice of objective functions and control laws are discussed in details. Finally, a more complex (compared with the previous work) simulation example illustrates the advantage of using the method.

Practical evaluation for two different holonomic wheeled mobile robots

This work is a practical evaluation between two different holonomic wheeled mobile robot platforms. The evaluation criteria had been theoretically explained and used on the simulation level in previous publication. The main objective of this paper is evaluating each wheeled mobile robot practically using the proposed criteria. The first robot is the C3P, which has three caster wheels with wheel angular velocities actuation. The second robot is omni-directional wheeled platform with three omni-directional wheels. The inverse and forward kinematics required in the control structure is presented for the practical experiments, which illustrate the performance of each robot. The comparison is done with respect to three main aspects; 1) the mobility, 2) the total energy consumed by each robot in a finite interval of time, and 3) the hardware complexity. A cost functional is obtained to demonstrate the comparison, and a criteria is developed to measure the hardware complexity of each robot. The weight sum method enables the cost functional to show the importance of each aspect and to distinguish between the lowest cost platform with respect to each aspect importance.

Game-theoretical analysis for choosing the topology in multi-loop control systems

The focus of the paper is the review of the control structure selection for a given system. If a framework, derived from game theory is used for the control system design of multi-loop systems, the question arises, how unequally distributed or incomplete information affects the selection of the players strategies. In the field of game theory, information is an essential component. Different information sets lead to different strategy selections provided by the controllers and the belonging control laws. In the present paper, an asymmetric triangular multi-loop control structure was chosen as basis to study and discuss the effects of different information sets to the solution of each game. The solution of the game provides a Pareto-optimal set of controller parameters for the multi-loop control system.

Controller tuning of stochastic disturbed multi-loop control systems

A controller tuning method in a game-theoretic framework is extended, to keep the requirements of optimal system performance due to stochastic disturbances. First, a minimum variance controller, known in the literature for use in systems with stochastic disturbances, is applied to a single-loop control system. The extended controller tuning method, derived from game theory, is presented and applied to the single-loop control system as well and finally compared with the simulation results obtained using the minimum variance controller. For multi-loop systems, the authors tried to extend both methods and apply them on an example to show their capabilities as well as their limits. The use of the minimum variance controller in multi-loop system fails, while the proposed extended controller tuning method is successful applicable to such kind of systems.

Game-theoretical analysis of a multi-loop control structure with constrained strategy sets

The comparison of different multi-loop control structures for a basic triangular system is the focus of the present paper. The idea is originated from game theory, where information is an essential component. Hence, the game-theoretic view of controller design in multi-loop control systems allows the question, how unequally distributed or incomplete information affects the control structure and the selection of the playerspsila strategies. Additionally, if constraints on the control signals are considered, the strategy set of each player is bounded. Thus, the solution of each game provides different Pareto-optimal sets depending on different bounded strategy sets. In the present paper, an asymmetric triangular multi-loop control structure of a reverse osmosis desalination plant was chosen as basis to study and discuss the effects of different information sets, due to the control structure, to the solution of each game.

Application of a Game-Theoretic Multi-Loop Control System Design with Robust Performance

Abstract The game-theoretic view of control system design for multi-loop systems is extended in this work to ensure a closed-loop system with robust stability. The control system design is modeled as a differential cooperative game to incorporate interactions between the multiple loops of the control system. A robust stability indicator is formulated as an additional cost function. The developed approach is applied to a reverse osmosis desalination plant with different constraint settings on the control signals. The solution of the game provides Pareto-optimal sets, depending on the control signal constraints. Single points are chosen from the Pareto-optimal sets resulting in controller parameters leading to a reverse osmosis system with optimal performance concerning the error convergence, control effort and robust stability.