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A themed project based on the control of a quadruple tank rig using PLCs has been successfully carried out as part of the MSc in Advanced Control and Systems Engineering at the University of Manchester. The themed project involves ten students who address a single multivariable control challenge under the supervision of two academics and four PhD students. As every student is required to write their own MSc dissertation, the key point is the possibility of using different control techniques to be implemented on different hardware platforms.

Abstract-Actuator saturation is a common phenomenon in the control of multivariable systems which causes two major problems for control engineers, namely windup and directionality. This paper focuses on a Two-stage Multivariable IMC Antiwindup (TMIA) structure for open-loop stable plants. This IMC-based control structure is of interest because it tackles the aforementioned problems in an intuitive and easy to tune way. The highlight of this structure is the solution of two low-order quadratic programs to control both steady-state and transient behaviours of the plant. The controller is tested by application to a multivariable Quadruple Tank process controlled by a PLC. The TMIA structure is found to outperform its IMC counterparts in handling windup and directionality. Results obtained demonstrate the realizability of the advanced control technique on an off-the-shelf industrial PLC. Thus the TMIA structure is presented as a competitive alternative in terms of tuning transparency and reduced computations to other advanced control techniques such as MPC which are limited by the low computational power offered by standard PLCs.

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A simple secant-based fast gradient method is developed for problems whose objective function is convex and well-defined. The proposed algorithm extends the classical Nesterov gradient method by updating the estimate-sequence parameter with secant information whenever possible. This is achieved by imposing a secant condition on the choice of search point. Furthermore, the proposed algorithm embodies an "update rule with reset" that parallels the restart rule recently suggested in O' Donoghue and Candes (2013). The proposed algorithm applies to a large class of problems including logistic and least-square losses commonly found in the machine learning literature. Numerical results demonstrating the efficiency of the proposed algorithm are analyzed with the aid of performance profiles.Keywords Convex optimization • Secant Methods • Fast gradient methods • Nesterov gradient method. IntroductionThis paper considers the unconstrained optimization of convex function f :where f : R n → R is a continuously differentiable convex function. The domain of f , dom f , is the convex set R n and x is a real vector. A necessary and sufficient condition for a point x * to be a minimizer of f is ∇f (x * ) = 0 [7]. Furthermore, it is assumed that f is bounded below and there exists a unique minimizer x * : f (x * ) = f * with f * ≤ f (x) ∀ x ∈ R n [27].