This paper presents an easy-to-use and reliable tuning strategy for unconstrained SISO dynamic matrix control (DMC) and lays a foundation for extension to multivariable systems. The tuning strategy achieves set point tracking with minimal overshoot and modest manipulated input move sizes and is applicable to a broad class of open loop stable processes. The derivation of an analytical expression for the move suppression coefficient, λ, and its demonstration in a DMC tuning strategy is one of the significant contributions of this work. The compact form for the analytical expression for λ is achieved by employing a first order plus dead time (FOPDT) model approximation of the process dynamics. With tuning parameters computed, DMC is then implemented in the classical fashion using a dynamic matrix formulated from step response coefficients of the actual process. Just as the FOPDT model approximation has proved a valuable tool in tuning rules such as Cohen−Coon, ITAE, and IAE for PID implementations, the tuning strategy presented here is significant because it offers an analogous approach for DMC.

Move suppression coefficients serve a dual purpose in the model predictive controller (MPC) architecture. These include suppressing aggressive control action and conditioning the system matrix prior to inversion. The work presented here exploits this dual effect in deriving an analytical expression that computes appropriate move suppression coefficients as a function of process model parameters, other MPC design parameters, and partitioned block condition numbers of the system matrix. The development is based upon an approximate mosaic Hankel matrix structure of the multivariable system matrix. The primary contribution of this work is the derivation of the analytical expression for computing move suppression coefficients and its demonstration in an overall MPC tuning strategy (Table ). The examples presented show that the move suppression coefficient remains properly scaled as the other MPC design parameters and process characteristics change to produce a consistent closed loop performance. This tuning method is applicable to unconstrained multivariable processes, including non-square systems.

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The purpose of this study was to engage expert coaches' in an exploration, conceptualisation, and modelling of their coaching process. Six coaches, each developed a model, with accompanying explanation, of 'their' coaching process. These models and explanations were content analysed to identify features of the coaching process and included examination of how to represent the process pictorially. The coaches were then interviewed where they discussed the identified features and how to represent their coaching process as a 'realistic picture'. As a result of this process of data collection, analysis, and member checking, the coaches' conceptualisation of the coaching process and how best to model it was agreed amongst participants. There were seven core principles that underpinned the model: learning partnership; individualised; clear structure with evolving process; orchestrating approach; influenced by coaching environment; holistic and flexible process; and adaptable and dynamic; and six components parts that described the operationalisation of the coaching process: values, knowledge, and skills; contextual constraint; learning environment; preparation phase; performance phase; review phase. The agreed upon pictorial representation of their coaching process brought the process 'to life' and provides researchers, coaches, and coach developers with a conceptualisation of the process by coaches for coaches. Keywords: coaching process model, coaching practice, expertise, coaching education athlete's performance. Furthermore, it involves a range of activities and skills employed to bring about the desired changes. How, and even if, the process can and should be modelled continues to spark controversy (Barnson, 2014; Cushion, 2007). Researchers have not, yet, captured the subtlety and scope of the coaching process in specific contexts (Cushion, 2014), leaving coaches without a clear set of concepts and principles that reflect actual coaching practice (Cushion et al., 2006). Therefore, the purpose of this study was to engage expert coaches' in an exploration and conceptualisation of the coaching process and the development of a model of their coaching process. A clear conceptualisation of the coaching process can inform coaches' education and development, support coaches' desire to improve (Abraham, Collins & Martindale, 2006; Lyle, 2002), assist coaches to provide quality experiences for participants, and progress the profession (Côté, et al., 1995). Barnson (2014) suggested that it is foolish for coaches to attempt to coach without some form of principled template and that it is coaching science's role to support the development of such a 'unifying platform' (p.73). A recent advancement has been the International Sport Coaching Framework (International Council for Coaching Excellence, 2012), which proposed conceptual clarity regarding the coaching contexts, roles, and competencies, and how they interrelate. This framework was designed to support coach development and professionalism within all coaching domains, and a...