Robust constrained MPC stabilization of a CSTR

Abstract

The paper addresses a case study of robust stabilization of a continuous stirred tank reactor using robust model-based predictive control with constrained input variables. One exothermic reaction runs in the reaction mixture and the reactor is modelled in the form of an uncertain polytopic system. The control approach is based on solution of a set of linear matrix inequalities. This formulation enables to use convex optimization methods to design a gain matrix of a state feedback controller in each control step. The task of stabilization is solved in assumed control conditions with respect to symmetric constraints on control inputs. The control performance achieved by robust constrained model-based predictive control is studied via simulations. Obtained results confirm that the robust constrained model-based predictive control ensures the stability demands and the quality requirements represented by chosen quadratic cost function.

Robust MPC of an unstable chemical reactor using the nominal system optimization

“…(12)- (15) ( ) Hence, the CSTR is the fourth-order nonlinear system with two control inputs q r , q c and four states c PO , c PG , T r , T c . The steady-state analysis of the reactor is described in Oravec and Bakošová, 2012. The CSTR has three steady states.…”

“…Ghaffari et al (2013) extended the robust MPC design for additive discrete time uncertain nonlinear systems, designed the controller using the worst-case optimisation and presented the simulation results obtained for the theoretical CSTR with the first order chemical reaction working in the stable operating point. Based on previous works Oravec and Bakošová, 2012), this paper studies the problem of stabilization of an open-loop unstable CSTR using the robust constrained MPC based on the nominal system optimization and the parameter-dependent Lyapunov functions (PDLFs). This approach was compared with the robust MPC designed using the worst-case system optimization.…”

Agile manoeuvres using model predictive control

“…Therefore, MPC has become the most preferred and popular control approach in the process industry, as proven by the survey of Qin and Badgwell (2003). Many successful applications of the MPC strategy control chemical reactors (Oravec and Bakošová, 2012;Bakošová and Oravec, 2014;Oravec and Bakošová, 2015;Bakošová et al, 2013), heat exchangers (Oravec et al, 2016a(Oravec et al, , 2018, and distillation columns (Martin et al, 2013). Alternatively, MPC can also be used as a supervisory control layer that can be coupled with conventional PID controllers (Klaučo et al, 2017).…”

Fast nonlinear model predictive control of a chemical reactor: a random shooting approach

“…In fact, the survey of (Qinand Badgwell, 2003) shows that MPC is indeed the most popular and preferred control approach adopted by the process industry. A plethora of MPC success stories is reported in the literature especially for controlling chemical reactors (Oravec and Bakošová, 2012;Bakošová and Oravec, 2014;Oravec and Bakošová, 2015;Bakošová et al, 2013), distillation columns (Martin et al, 2013), and heat exchangers (Oravec et al, 2016(Oravec et al, , 2018, to name just a few. MPC optimizes the control inputs by employing a mathematical model of the controlled process to predict its future behavior.…”