Question 1 Two continuously-stirred tank reactors consume a species A. As shown in Figure Q1 (on the next page), the units are connected in series, and operate at constant temperature conditions. In the first reactor, the species is consumed at a rate k1CA1. In the second reactor, the species is consumed at a rate k2CA22. All material properties can be regarded as constant. Overbars denote steady state values. The volumes of liquid in each tank, V1 and V2, must remain constant. a) (i) (ii) (iii) b) (i) Derive equations for the molar balance of component A in each tank. (ii) Determine the number of non-linear terms in the equations, and linearise about the steady state conditions. Express your result in deviation variables. (iii) Show that the linearised system of equations of part 1b)(ii) can be expressed in the Laplace domain as a single equation CA2(s)=(1s+1)(2s+1)KCA0CA0(s)+(2s+1)Kqq(s) (iv) Provide expressions for the steady-state gains KCA0 and Kq, and the time constants 1 and 2. c) (i) A step change in the inlet concentration, CA0>0, occurs for t0. Explain a potential control action involving q to maintain CA2 at its setpoint at all times (1-2 sentences). Find the corresponding mathematical expression for q(t). Explain the effect of the control strategy on the outlet flow rate, q2. (ii) Determine whether the control strategy of part 1c)(i) can be implemented and why (1-2 sentences). (iii) Consider a mechanism based on proportional feedback control to maintain the concentration of the outlet, CA2, at, or close to, a set point. Derive the corresponding closed-loop transfer function and compute the offset observed due to a step change in the inlet concentration. Figure Q1