The PI+CI compensator, given by the parallel connection of a proportional integral (PI) compensator and a Clegg integrator (CI), has been shown to be effective in a number of practical applications, overcoming fundamental limitations of PI compensation. Two key design aspects of PI+CI compensation is the use of the resetting law (zero crossing/reset band) and a (constant/variable) reset ratio; these two design factors have been previously used in control practice, but using heuristic design methods. This work develops a systematic design method for the tuning of reset PI compensators, specifically for first‐ and second‐order plants, obtaining in both cases simple tuning rules. In addition, several detailed examples are developed; therefore, a detailed analysis of cost of feedback and robustness again parametric uncertainty is also given. Finally, an experiment of pH In‐Line control is made to show the advantages of the proposed tuning rule.

Reset compensation has been used to overcome limitations of linear and time invariant (LTI) compensation. In this work, a new reset compensator, referred to as proportional and integral (PI) + CI (Clegg integrator), is introduced. It basically consists of adding a Clegg integrator to a PI compensator, with the goal of improving the closed loop response by using the nonlinear characteristic of this element. It turns out that by resetting a percentage of the integral term in a PI compensator, a significant improvement can be obtained over a well-tuned PI compensator in some relevant practical cases, such as systems with dominant lag and integrating systems. The work is devoted to the development of PI + CI tuning rules for basic dynamic systems in a wide range of applications, including first and higher order plus dead time systems.

Impulsive dynamical systems is a well-established area of dynamical systems theory, and it is used in this work to analyse several basic properties of reset control systems: existence and uniqueness of solutions, and continuous dependence on the initial condition (well-posedness). The work scope is about reset control systems with a linear and time-invariant base system, and a zero-crossing resetting law. A necessary and sufficient condition for existence and uniqueness of solutions, based on the well-posedness of reset instants, is developed. As a result, it is shown that reset control systems (with strictly proper plants) do not have Zeno solutions. It is also shown that full reset and partial reset (with a special structure) always produce well-posed reset instants. Moreover, a definition of continuous dependence on the initial condition is developed, and also a sufficient condition for reset control systems to satisfy that property. Finally, this property is used to analyse sensitivity of reset control systems to sensor noise. This work also includes a number of illustrative examples motivating the key concepts and main results.

The paper is mainly devoted to the robust stability problem of non-linear QFT designs. The problem is first formulated for SISO non-linear systems, limited in practice to linear-memoryless sector-bounded non-linear interconnections, and in an I/O stability sense. The work investigates several possible robust adaptations of the Circle Criterion, depending on the type of resulting interconnection of linear and non-linear blocks, appearing in the feedback system. Also, the use of the Popov Criterion is investigated as an alternative less conservative than the Circle Criterion in some cases. The proposed techniques are given in usual QFT language, expressed as frequency conditions or boundaries in the Nichols Chart, allowing an easy integration with other design objectives. In addition, multivariable extensions using a conicity condition and the concept of maximal cone are adopted to give stability boundaries in interconnections of SIMO linear-MISO sector-bounded memoryless blocks. All the robust stability criteria are illustrated using significant examples to emphasize the practical application of the resulting techniques.

As it is known, a wide range of research activities deal with the application of the quantitative feedback theory (QFT) for the design of different control structures. All these approaches generally use rational controllers. On the other hand, the importance of fractional order controllers is becoming remarkable nowadays, studying aspects such as the analysis, design and synthesis of this kind of controllers. The purpose of this paper is to apply QFT for the tuning of a fractional PID controller (PI ^lambda D ^mu ) of the form K _P (1 + K _I s ^-lambda + K _D s ^mu ), where lambda, mu are the orders of the fractional integral and derivative, respectively. The objective is to take advantage of the introduction of the fractional orders in the controller and fulfill different design specifications for a set of plants