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This paper presents a robust feedback control solution for systems with multiple manipulated inputs and a single measurable output. A structure of parallel controllers achieves robust stability and robust disturbance rejection. Each controller uses the least possible amount of feedback at each frequency. The controller design is carried out in the Quantitative Feedback Theory framework. The method pursues a smart load sharing along the frequency spectrum, where each branch must either collaborate in the control task or be inhibited at each frequency. This reduces useless fatigue and saturation risk of actuators. Different examples illustrate the ability to deal with complex control problems that current MISO methodologies cannot solve. Main control challenges arise due to the uncertainty of plant and disturbance models and when a fast-slow hierarchy of plants cannot be uniquely established.

SUMMARYThis paper introduces a novel solution for the multi‐input multi‐output (MIMO) quantitative feedback theory control design problem with tracking error specifications. Looking for a minimum controller overdesign, the technique finds new controller quantitative feedback theory bounds based on necessary and sufficient conditions for the existence of suitable associated prefilter matrix elements. It improves previous approaches to the subject and includes (i) the possibility of a free selection of the nominal plant, (ii) a less conservative application of the Schwartz inequality to decisively reduce the potential controller overdesign, (iii) a methodology to design independently the elements of the prefilter matrix, and (iv) a scope of application to both sequential and nonsequential MIMO controller design methods. The benefits of the new control design technique are illustrated by means of two examples. The first one, a standard 2 × 2 MIMO problem, is provided for comparison purposes with previous approaches. The second example, included as a major control challenge, deals with a well‐known demanding distillation column benchmark problem. Copyright © 2013 John Wiley & Sons, Ltd.

SUMMARYThis article extends two recent contributions in the field of quantitative feedback theory to the multivariable case. They concern the model matching and the measured disturbance rejection problems. The model matching problem is a tracking control problem with specifications given as acceptable deviations from an ideal response. The measured disturbance rejection problem balances feedback and feedforward actions to reject disturbances. Both perspectives present advantages over classical quantitative feedback theory techniques in certain situations. This paper develops the necessary tools to solve both control problems in the case of multi-input multi-output plants. In particular, it shows how to derive nonconservative controller bounds for each of the single-input single-output control problems in which the overall multivariable problem is divided. The result is a systematic controller design methodology for multi-input multi-output plants with structured uncertainty. The application of the technique to the well-known quadruple-tank process illustrates the benefits of the method.

The regulation of a disturbed output can be improved when several manipulated inputs are available. A popular choice in these cases is the series control scheme, characterized by (1) a sequential intervention of loops and (2) faster loops being reset by slower loops, to keep their control action around convenient values. This paper tackles the problem from the frequency-domain perspective. First, the working frequencies for each loop are determined and closed-loop specifications are defined. Then, Quantitative Feedback Theory (QFT) bounds are computed for each loop, and a sequential loop-shaping of controllers takes place. The obtained controllers are placed in a new series architecture, which unlike the classical series architecture only requires one controller with integral action. The benefits of the method are greater as the number of control inputs grow. A continuous stirred tank reactor (CSTR) is presented as an application example.

SUMMARY An alternative to the traditional QFT tracking problem, in which upper and lower tolerances are imposed on the magnitude of the tracking transfer function, is to define the robust specification as a boundary on the deviation of such function from a predefined model. However, previous research exploring this approach reveals a certain overdesign and dependence on the choice of the nominal plant. This paper establishes a necessary condition on the controller from tracking error specifications. With this condition, the controller bounds introduce no overdesign, and the resulting two‐degrees‐of‐freedom design is independent of the choice of the nominal plant, similar to the traditional approach. Copyright © 2011 John Wiley & Sons, Ltd.

Autothermal Thermophilic Aerobic Digestion (ATAD technology) is a promising alternative to conventional digestion systems. Aeration is a key factor in the performance of these kinds of reactors, in relation to effluent quality and operating costs. At present, the realisation of automatic control in ATADs is in its infancy. Additionally, the lack of robust sensors also makes the control of these processes difficult: only redox potential and temperature sensors are reliable for operation in full-scale plants. Based as it is on the existing simulation protocols for benchmarking of control strategies for wastewater treatment plants (WWTP), this paper presents the definition and implementation of a similar protocol but specifically adapted to the needs of ATAD technology. The implemented simulation protocol has been used to validate two different control strategies for aeration (ST1 and ST2). In comparison to an open-loop operation for the ATAD, simulation results showed that the ST1 strategy was able to save aeration costs of around 2-4%. Unlike ST1, ST2 achieved maximum sludge stabilisation but at the expense of higher aeration costs.

This paper examines methods to incorporate feedforward loops of known external inputs (output reference) into a multi-input feedback control structure to achieve certain robust performance of its output. Undoubtedly, feedforward can reduce the need for feedback and therefore the amplification of sensor noise at actuators, as occurs in single-input control. Beyond that, since there are several available inputs, a convenient distribution of feedforward and feedback can minimise the control action at each input and offer benefits at all frequencies. The procedure is as follows: because there are rough plant models of the behaviour from each input to the output, it is possible to approximate the individual control demand that will satisfy the performance. Based on this, individual feedforward filters allocate the control bandwidth among the inputs in order to build an equivalent plant that has an equal or greater magnitude than any individual plant at each frequency. Next, the uncertainty of this equivalent plant is addressed by feedback that reduces the closed loop deviation of magnitude frequency responses. The reduction is sufficient to enable a master feedforward to place them, at a second step, around the desired tracking performance model without violating any deviation tolerances. Individual feedback controllers distribute the total feedback among the inputs in order to have the least possible feedback at each frequency. A first example illustrates the method and the relevance of a feedforward orientation to reduce the individual control action, instead of the individual feedback action. Another example proves the superiority of adding feedforward loops to feedback-only schemes and highlights the benefits of robust design methods such as Quantitative Feedback Theory (QFT). This paper also provides the algorithms to employ in response to new robust control specifications in the framework of QFT.