4. Simulation Results
The control performance evaluation of the proposed SMC is carried out on a nonlinear CSTR system. CSTR is a widely utilized chemical reactor system in industry, mainly used to produce polymers, pharmaceuticals, and other various chemical products [1][48][49]. The schematic diagram of the CSTR system is illustrated in Figure 3[48][50][51].
In CSTR system, isothermal, liquid-phase, successive multicomponent chemical reactions can be performed [48][49]. Let us consider that a chemical reaction given as follows is carried out in CSTR:
where A,B are the inlet reactants mixed in a vessel with constant volume via an agitator and transume to the product C. The reaction in (49) is composed of two sides: first is among A-B, and second one is between B and C. Therefore, in CSTR, the aim is to control the concentration of product C by adjusting the molar feed rate of reactant B. The differential equations describing the dynamical behavior of the system, proposed by Kravaris and Palanki [48], are expressed as follows:
where x1(t), x2(t) and x3(t) are states obtained from the concentrations of reactant A, middle reactant B and product C, respectively, Da1 = 3, Da2 = 0.5 , Da3 = 1 , u(t) is the control signal, x3(t) is the controlled output of the system, d2(t) is the time-varying parameter of the system which represents the activity of the reaction, the nominal value of which is d2nom(t) = 1 as given in [39][49][52][53]. The limitation for control signal is given as u_min = 0 and u_max = 1 ; and duration of control signal is set as tmin = tmax = Ts = 0.1 seconds where Ts is sampling time. The performance of the system has been evaluated for three different cases: 1) Nominal case: when there is no noise and parametric uncertainty in the system 2) Measurement noise case: 30 dB Gaussian measurement noise is added to the output of the system 3) Parametric uncertainty: time-varying parameter is introduced to the system.
I've attached a document with more understandable info.
Can you solve this in matlab ?
