A numerically robust state-space approach to stable-predictive control strategies

Pole-placement Predictive Functional Control for over-damped systems with real poles

“…For example, conventional PFC requires changes in the underlying loop structure and prediction models to cater for unstable open-loop plants. Within the broader MPC literature ideas such as prestabilisation [14,17] are commonplace. There us also minor interest in what happens when targets take the form of ramps rather than steps; again this requires a significant change in the underlying approach as the use of two integrators within the loop is now implicit in order to achieve no offset and this radically changes the performance that is achievable, as is well known from the mainstream literature.…”

Input shaping for PFC: how and why?

“…Remark 4 Subsequent work in MPC (Rossiter et al (1998)) has proposed a cascade structure for MPC where an inner loop gives stable behaviour and the outer loop is used to tailor performance. Such an approach is not explored here as it is likely to lead to more challenging constraint handling which is not consistent with the PFC philosophy of requiring very simple and brief code.…”

“…The approach is presented next before the paper moves on to show how this can be deployed within a PFC framework. This section outlines the algebra needed to parameterise the future input predictions which ensure convergent output predictions (Rossiter, 2003). The model equation in terms of input increments is given as:…”

“…Of course, such a concept is also implicit in dual-mode approaches to MPC (Rossiter et al (1998)). Consequently, a key future work is to explore the extent to which such an approach is effective compared to the use of input shaping, for example: (i) how is the pre-stabilising loop controller selected?…”

“…While numerous alternatives have been proposed in the literature, the most popular is model predictive control (MPC) e.g. (Maciejowski, 2001;Richalet and Donovan, 2009;Rossiter, 2003). Within typical industrial applications of MPC, there is a clear divide between: (i) conventional large scale, and expensive, implementations which tend to use dynamic matrix control (Cutler and Ramaker , 1980) or dual-mode approaches (Sockaert and Rawlings, 1998) and (ii) smaller scale, mostly single input single output, less expensive implementations based on the predictive functional control (PFC) algorithm (Richalet et al, 1978(Richalet et al, , 2004.…”