MPC in systems with continuous and discrete control inputs

Abstract

In this paper we point out potential problems in systems where both logic and continuous control influence a continuous plant. We also propose model predictive control (MPC) based approaches for handling the problems. Simulations on a simple but nontrivial plant support the discussion

Explicit Model Predictive Control of a Hybrid System Using Support Vector Machines

“…The control objective is to keep the temperature in the second tank at its setpoint while keeping the levels of the tanks within preset limits. The system, which was first studied by Slupphaug et al (1998), is controlled by two on/off valves, a heater and a pump. The pump has three operational levels (off, medium, high).…”

“…From inspection of the training data for the inlet valve u d 3 , it was seen that the underlying control law could be described exactly as a simple on/off controller with feedback from the level h 1 of the buffer tank. A similar approach was used by Slupphaug et al (1998). However, in our case a small dead-band of 32 cm was introduced in order to avoid excessive valve movement.…”

“…The temperature in the first tank is not controlled. The system is described by the mass and energy balances (Slupphaug et al, 1998) …”

Hybrid Predictive Control based on Fuzzy Model

“…On the other hand and regarding to hybrid predictive-control design, Slupphaug [5] and Slupphaug & Foss [6] integer-input variables that is tuned using nonlinear mixed-integer programming. It was shown that it performs better than a predictive control strategy with separation of continuous and integer variables.…”

Knowledge discovery — A control theory perspective

“…Second, the combination of continuous and discrete control inputs is considered utilizing a two-tank example as case. Different approaches to handle this heterogeneous case are considered (Slupphaug, Vada & Foss 1997). …”