Over-design in the process industries

The chemical industry in the United States may be cited for numerous instances of over-design. Over-design usually compensates for model and design uncertainties, allowing for increases in capacity and for margins of safe operation. However, over- design also results in order to avoid operation near or within complex operating regimes. Such operating regimes may be characterised by hysteresis and periodic or chaotic behaviour. Designs that avoid these operating regions are frequently deemed prudent (i.e., if these regions were known or suspected to exist) as safeguard against unreliable operation. However, designs that constrain key design parameters, p, to avoid these regions of operation, may prevent operation near steady-state economic optima. Common process characteristics (Table 2-1) that cause control difficulties for non-linear and linear controllers alike, are more pronounced in more complex operating regions. Despite the possible greater economic benefit of operating at process conditions with complex dynamics, this over-design approach prevails (Seider et al., 1990). Unit operations that exhibit complex dynamic and steady state behaviours include exothermic reactors, aerobic fermentation, heterogeneous

Table 2-1 - Common Process Control Design Complications (Bequette, 1991)

Common Process Characteristics

• Multivariable interactions between manipulated and controlled variables • Unmeasured state variables

• Unmeasured and frequent disturbances • High-order and distributed processes • Uncertain and time-varying parameters

• Constraints on manipulated and state variables • Dead-time on inputs and measurements • Sensor noise and inaccurate measurement

Brengel & Seider (1992) regarded this over-design phenomenon as an important opportunity and challenge facing design engineers. Design, modelling and particularly control techniques that allow closer operation to more complex regimes should reduce the instances of over-design in the process industries sharply. The process design and control system synthesis should be coordinated, thereby maximising a profitability objective function penalised for poor controllability. Maximising the process' flexibility is a key requirement.

Luyben and Floudas (1994a) stated that the goal of coordinated process design and controller development is to determine the best-compromise process configuration among the competing economic and open-loop controllability objectives. This best compromise solution may include minimising the cost of the process equipment and optimising any measure of controllability (e.g., relative gain array) and flexibility. Coordinated process design and controller development thus becomes a multi- objective optimisation (Luyben and Floudas, 1994a).

Luyben and Floudas (1994b) used Bristol's relative gain array (RGA) in assessing controllability. RGA was developed for use in control pairing of linear systems. This controllability objective was incorporated with the steady state economic optimisation in a multi-objective design of a reactor-separator-recycle system. The usefulness of linear analytical tools for multi-loop SISO pairing may be limited for non-linear systems, since the process gain matrix is calculated at the steady state economic operating point. For non-linear systems, small deviations from the desired steady state operating point could change the magnitude and sign of process gains significantly. For the reactor-separator-recycle system the optimal design cost was $511 600 per annum and had an RGA of 3.5 (i.e., RGA analysis of 1.0 considered optimal). Though highly process dependent, Luyben and Floudas (1994b) demonstrated that the RGA could be reduced from 3.5 to 1.8 by augmenting the process design without increasing costs significantly. However, further improving the controllability to an RGA of 1.1, increased the cost to $1 046 300 per annum. For this specific case study, an

improvement in controllability to an RGA of 1.8 lightens the complexity of the control task, though controller design techniques that would allow comfortable operation at a RGA of 3.5 are desirable.

Naturally, the most desired coordinated design approach is one in which the problem statement requires less trade-off between controllability and economic return. Only economic considerations should ideally play a role in the design task. Although controllability is defined by the open-loop response of the process, controller development techniques (i.e., design tools) determine whether the process can be maintained reliably at the economic optimum. Clearly, there are two ways of enhancing the operability at the steady state economic conditions, viz. enhance the process design and improve controller development techniques.

Consider a continuous fermentation process as illustrated in Figure 2-4. The economic objective is to minimise the capital and operating costs. The most economic design must optimise bioreactor volume (i.e., height and diameter), filter duty, valve sizes and piping from both an equipment cost and an operating cost perspective. The raw material cost of the nominal, SF, and concentrated, SC, substrate feed and the filtration costs must be included for evaluation. The operating constraints may include cell mass concentration (i.e., oxygen transfer limitations), substrate limiting cell growth, vessel hold-up limits and maximum flow rates of nominal and concentrated substrate feeds. Discrete design decisions may include deciding to use a recycle stream or not. Continuous design decisions relate to bioreactor vessel height and diameter. Random disturbances are expected to exist in the feed rate, feed composition and cell growth kinetics and need to be considered in the process design. Also, a number of parameters in the process model may drift with time, such as the growth kinetics and cost of substrate feeds (i.e., varying economic climate). The coordinated process design and control development is complicated by the open-loop response of the bioreactor at various residence times, dictated by the inherent dynamics of the micro- organisms. As the residence time is decreased the open-loop response changes from open-loop stable, to open-loop unstable eventually exhibiting both hysteresis and chaotic dynamics. A bifurcation analysis revealed that the economic optimal operating point has the most complex dynamics. Multiplicity, i.e. the existence of more than one steady state at the same residence time, destroys the global stability of the set point; thereby much of the power of linear theories. In fact, controllers with integral action may create additional steady state attractors that introduce elements of instability, not originating from the open-loop dynamics of the system (Chang & Chen, 1984). Conceivably, genetic engineering could be used to develop a different micro-organism that did not have such complex dynamic behaviour, but this is clearly outside the scope of conventional chemical engineering process design. For the bioreactor,

may be effective in open-loop stable operating regions, the economic return is 30 [%] less than at the steady state economic optimum.

F F_o X, S V Air Exhaust air R Centrifugal filter S_F αFo S h F_c S_F (1-α)·Fo S α f_v XF_o

Figure 2-4 - Bioreactor flow sheet (Brengel & Seider, 1992).

Clearly, different process designs result in different control structure designs, related to both the pairing of controlled and manipulated variables and the tuning of controller parameters. Any methodology that solves this integrated process design and controller development task must, (1) be capable of optimising non-linear dynamic systems, (2) ensure robust operation despite unmeasured disturbances and time invariant process uncertainties, (3) select the optimal process design from an economic standpoint and (4) select the optimal control strategy. Both structural (i.e., discrete) and continuous decisions are involved in this optimisation.

A comprehensive algorithmic approach to such an optimisation problem has been demonstrated by Bansal et al. (2002), using Mohideen et al.'s (1996) mixed-integer dynamic optimisation (MIDO) approach. The dynamic distillation model has realistic complexity, comprised of hundreds of differential-algebraic equations. However, the 5x5 control structure design is limited to seven possible alternatives using linear PID controllers in the MIDO analysis. Though PID controllers are the industry standard, linear controllers are likely to have sub-optimal performance when controlling such a non-linear process. The controllability of the process is a function of the plant design, but the type of controller determines feasible operation over a range of disturbances (Bahri et al., 1997). Also, limiting the MIDO optimisation to only seven discrete possibilities for control structure does not assure a global optimal solution. Numerous

pairing possibilities exist for a 5x5 dynamic system. Although engineering judgement may reduce the number of feasible control structures, the interface to and from a chemical plant may be via hundreds of sensor measurements and numerous final control elements (i.e. valves, heat duty etc.). The control structure is not a discrete (or integer) optimisation variable and is an important component in a plant-wide control methodology.