Advanced process control includes optimization-based tools that are recently widely implemented in industry to maximize economical effectiveness and to minimize environmental impact. Robust model predictive control (MPC) is one of these strategies and it combines benefits of model predictive control and robust control approaches. This study investigates improvement of control performance and increase of energy savings using the soft-constrained robust MPC with integral action for a laboratory plate heat exchanger. Soft constraints on control inputs keep the heat exchanger in required operation conditions and enable to use the feasible range of manipulated variable effectively with decreasing of energy cost. Integral action of the predictive controller ensures offset-free reference tracking. Simulation results obtained using the newly designed robust predictive controller with soft constraints and integral action confirm improved control response and increased energy savings in comparison with the results reached using the predictive controller with hard constraints and without active soft constraints.