The four-tank benchmark: a simple solution by embedded model control

The four-tank benchmark is a multivariate and nonlinear control problem which has been widely studied in the literature. Two pairs of tanks in series are supplied by two pumps. Under certain configurations, the Embedded Model Control approach provides a simple decoupled solution by separately controlling the two output tank levels and treating the input flow as a partly unknown disturbance. Neglected dynamics in a form of unknown delays both in sensors and actuator dynamics is considered. The core of the control unit is a discrete-time embedded model consisting of unknown disturbance dynamics and partly known nonlinear interactions. The embedded model is driven by the plant command and by a feedback vector which is retrieved from the model error. The feedback is capable of keeping updated the unknown disturbance prediction, ready to be cancelled by the control law. The control gains are tuned using two sets of closed-loop eigenvalues in order to trade-off between disturbance rejection and robust stability. Simulated runs under different tank interactions prove design effectiveness

The four-tank control problem: Comparison of two disturbance rejection control solutions

The paper aims to compare and prove a pair of disturbance/uncertainty rejection control laws for the well-known four tank control problems. Control requirements are expressed in terms of a set point sequence as it usual in the literature. Uncertainty class is defined as the union of four sub-classes: unknown disturbance, parametric uncertainty, measurement errors and neglected dynamics. Modelling and design allow insight of the dynamic properties of the problem. They are formulated by a pair of theorems which fix the range of application. Theorem are confirmed by the results simulated runs, and indicate the correct way to further broaden control design applicability. Disturbance rejection (better uncertainty) design is deployed using the Embedded Model Control methodology: only unknown disturbance and parametric uncertainty can be rejected, whereas neglected dynamics effects must be filtered. As a result, simple performance and stability inequality can be formulated in the frequency domain and lead to closed-loop pole placement. Inequalities are such to reveal whether pole placement is feasible and how feasibility can be recovered, an issue which at authors knowledge is rarely encountered in the literature. Simulated runs prove the design procedure

Rate analysis of inexact dual first order methods: Application to distributed MPC for network systems

In this paper we propose and analyze two dual methods based on inexact gradient information and averaging that generate approximate primal solutions for smooth convex optimization problems. The complicating constraints are moved into the cost using the Lagrange multipliers. The dual problem is solved by inexact first order methods based on approximate gradients and we prove sublinear rate of convergence for these methods. In particular, we provide, for the first time, estimates on the primal feasibility violation and primal and dual suboptimality of the generated approximate primal and dual solutions. Moreover, we solve approximately the inner problems with a parallel coordinate descent algorithm and we show that it has linear convergence rate. In our analysis we rely on the Lipschitz property of the dual function and inexact dual gradients. Further, we apply these methods to distributed model predictive control for network systems. By tightening the complicating constraints we are also able to ensure the primal feasibility of the approximate solutions generated by the proposed algorithms. We obtain a distributed control strategy that has the following features: state and input constraints are satisfied, stability of the plant is guaranteed, whilst the number of iterations for the suboptimal solution can be precisely determined.Comment: 26 pages, 2 figure

Hierarchical distributed model predictive control based on fuzzy negotiation

This work presents a hierarchical distributed model predictive control approach for multiple agents with cooperative negotiations based on fuzzy inference. Specifically, a fuzzy-based two-layer control architecture is proposed. In the lower control layer, there are pairwise negotiations between agents according to the couplings and the communication network. The resulting pairwise control sequences are sent to a coordinator in the upper control layer, which merges them to compute the final ones. Furthermore, conditions to guarantee feasibility and stability in the closed-loop system are provided. The proposed control algorithm has been tested on an eightcoupled tank plant via simulation

A multiobjective-based switching topology for hierarchical model predictive control applied to a hydro-power valley

In a Hierarchical Model Predictive Control (H-MPC) framework, this paper explores suitable time-variant structures for the hierarchies of different local MPC controllers. The idea is to adapt to different operational conditions by changing the importance of the local controllers. This is done by defining the level of the hierarchy they belong to, and solving within each level the local MPC problem using the information provided by the higher levels at the current time step and the predicted information from the lower levels obtained in the previous time step. As selecting a hierarchy results in a combinatorial optimization problem, it is explicitly solved for a limited number of relevant topologies only and then the switching between topologies is defined with a multiobjective optimizer, so as to decide the best H-MPC scheme according to the expected performance. A comparison with fixed-topology H-MPC controllers is done, showing the effectiveness of the proposed approach for the power control of a hydro-power valley.Peer ReviewedPostprint (author’s final draft

A communication-based distributed model predictive control approach for large-scale systems

This work presents a distributed model predictive control strategy as an alternative to conventional centralized approaches, which often suffer from implementation issues when applied to large-scale systems. The overall system is partitioned into minimally coupled subsystems based on its structural properties. Then, the coordination among the subproblems is achieved by means of a communication protocol, which allows each local controller to broadcast its solution to the rest of controllers with a coupled variable. The proposed approach is tested on the quadruple-tank process, and its effectiveness is proved by comparing the obtained results to those documented in an existing benchmark.Peer ReviewedPostprint (author's final draft

Accelerated Multi-Agent Optimization Method over Stochastic Networks

We propose a distributed method to solve a multi-agent optimization problem with strongly convex cost function and equality coupling constraints. The method is based on Nesterov's accelerated gradient approach and works over stochastically time-varying communication networks. We consider the standard assumptions of Nesterov's method and show that the sequence of the expected dual values converge toward the optimal value with the rate of $\mathcal{O}(1/k^2)$. Furthermore, we provide a simulation study of solving an optimal power flow problem with a well-known benchmark case.Comment: to appear at the 59th Conference on Decision and Contro

A distributed model predictive control strategy for back-to-back converters

In recent years Model Predictive Control (MPC) has been successfully used for the control of power electronics converters with different topologies and for different applications. MPC offers many advantages over more traditional control techniques such as the ability to avoid cascaded control loops, easy inclusion of constraint and fast transient response. On the other hand, the controller computational burden increases exponentially with the system complexity and may result in an unfeasible realization on modern digital control boards. This paper proposes a novel Distributed Model Predictive Control, which is able to achieve the same performance of the classical Model Predictive Control whilst reducing the computational requirements of its implementation. The proposed control approach is tested on a AC/AC converter in a back-to-back configuration used for power flow management. Simulation results are provided and validated through experimental testing in several operating conditions