Robust control of ill-conditioned plants: high-purity distillation

Using a high-purity distillation column as an example, the physical reason for the poor conditioning and its implications on control system design and performance are explained. It is shown that an acceptable performance/robustness tradeoff cannot be obtained by simple loop-shaping techniques (using singular values) and that a good understanding of the model uncertainty is essential for robust control system design. Physically motivated uncertainty descriptions (actuator uncertainties) are translated into the H∞/structured singular value framework, which is demonstrated to be a powerful tool to analyze and understand the complex phenomena

Feedback: Still the Simplest and Best Solution

Most engineers are (indirectly) trained to be "feedforward thinkers" and they immediately think of "model inversion" when it comes to doing control. Thus, they prefer to rely on models instead of data, although feedback solutions in most cases are much simpler and more robust

Beyond the Waterbed Effect: Development of Fractional Order CRONE Control with Non-Linear Reset

In this paper a novel reset control synthesis method is proposed: CRONE reset control, combining a robust fractional CRONE controller with non-linear reset control to overcome waterbed effect. In CRONE control, robustness is achieved by creation of constant phase behaviour around bandwidth with the use of fractional operators, also allowing more freedom in shaping the open-loop frequency response. However, being a linear controller it suffers from the inevitable trade-off between robustness and performance as a result of the waterbed effect. Here reset control is introduced in the CRONE design to overcome the fundamental limitations. In the new controller design, reset phase advantage is approximated using describing function analysis and used to achieve better open-loop shape. Sufficient quadratic stability conditions are shown for the designed CRONE reset controllers and the control design is validated on a Lorentz-actuated nanometre precision stage. It is shown that for similar phase margin, better performance in terms of reference-tracking and noise attenuation can be achieved.Comment: American Control Conference 201

No More Differentiator in PID:Development of Nonlinear Lead for Precision Mechatronics

Industrial PID consists of three elements: Lag (integrator), Lead (Differentiator) and Low Pass Filters (LPF). PID being a linear control method is inherently bounded by the waterbed effect due to which there exists a trade-off between precision \& tracking, provided by Lag and LPF on one side and stability \& robustness, provided by Lead on the other side. Nonlinear reset strategies applied in Lag and LPF elements have been very effective in reducing this trade-off. However, there is lack of study in developing a reset Lead element. In this paper, we develop a novel lead element which provides higher precision and stability compared to the linear lead filter and can be used as a replacement for the same. The concept is presented and validated on a Lorentz-actuated nanometer precision stage. Improvements in precision, tracking and bandwidth are shown through two separate designs. Performance is validated in both time and frequency domain to ensure that phase margin achieved on the practical setup matches design theories.Comment: European Control Conference 201

Feedback control of unstable steady states of flow past a flat plate using reduced-order estimators

We present an estimator-based control design procedure for flow control, using reduced-order models of the governing equations, linearized about a possibly unstable steady state. The reduced models are obtained using an approximate balanced truncation method that retains the most controllable and observable modes of the system. The original method is valid only for stable linear systems, and we present an extension to unstable linear systems. The dynamics on the unstable subspace are represented by projecting the original equations onto the global unstable eigenmodes, assumed to be small in number. A snapshot-based algorithm is developed, using approximate balanced truncation, for obtaining a reduced-order model of the dynamics on the stable subspace. The proposed algorithm is used to study feedback control of 2-D flow over a flat plate at a low Reynolds number and at large angles of attack, where the natural flow is vortex shedding, though there also exists an unstable steady state. For control design, we derive reduced-order models valid in the neighborhood of this unstable steady state. The actuation is modeled as a localized body force near the leading edge of the flat plate, and the sensors are two velocity measurements in the near-wake of the plate. A reduced-order Kalman filter is developed based on these models and is shown to accurately reconstruct the flow field from the sensor measurements, and the resulting estimator-based control is shown to stabilize the unstable steady state. For small perturbations of the steady state, the model accurately predicts the response of the full simulation. Furthermore, the resulting controller is even able to suppress the stable periodic vortex shedding, where the nonlinear effects are strong, thus implying a large domain of attraction of the stabilized steady state.Comment: 36 pages, 17 figure

Solution strategies for nonlinear conservation laws

Nonlinear conservation laws form the basis for models for a wide range of physical phenomena. Finding an optimal strategy for solving these problems can be challenging, and a good strategy for one problem may fail spectacularly for others. As different problems have different challenging features, exploiting knowledge about the problem structure is a key factor in achieving an efficient solution strategy. Most strategies found in literature for solving nonlinear problems involve a linearization step, usually using Newton's method, which replaces the original nonlinear problem by an iteration process consisting of a series of linear problems. A large effort is then spent on finding a good strategy for solving these linear problems. This involves choosing suitable preconditioners and linear solvers. This approach is in many cases a good choice and a multitude of different methods have been developed. However, the linearization step to some degree involves a loss of information about the original problem. This is not necessarily critical, but in many cases the structure of the nonlinear problem can be exploited to a larger extent than what is possible when working solely on the linearized problem. This may involve knowledge about dominating physical processes and specifically on whether a process is near equilibrium. By using nonlinear preconditioning techniques developed in recent years, certain attractive features such as automatic localization of computations to parts of the problem domain with the highest degree of nonlinearities arise. In the present work, these methods are further refined to obtain a framework for nonlinear preconditioning that also takes into account equilibrium information. This framework is developed mainly in the context of porous media, but in a general manner, allowing for application to a wide range of problems. A scalability study shows that the method is scalable for challenging two-phase flow problems. It is also demonstrated for nonlinear elasticity problems. Some models arising from nonlinear conservation laws are best solved using completely different strategies than the approach outlined above. One such example can be found in the field of surface gravity waves. For special types of nonlinear waves, such as solitary waves and undular bores, the well-known Korteweg-de Vries (KdV) equation has been shown to be a suitable model. This equation has many interesting properties not typical of nonlinear equations which may be exploited in the solver, and strategies usually reserved to linear problems may be applied. In this work includes a comparative study of two discretization methods with highly different properties for this equation

A simple approach for on-line PI controller tuning using closed-loop setpoint responses

The proposed method is similar to the Ziegler-Nichols (1942) tuning method, but it is faster to use and does not require the system to approach instability with sustained oscillations. The method requires one closed-loop step setpoint response experiment using a proportional only controller with gain Kc0. Based on simulations for a range of first-order with delay processes, simple correlations have been derived to give PI controller settings similar to those of the SIMC tuning rules (Skogestad, 2003). The controller gain (Kc/Kc0) is only a function of the overshoot observed in the setpoint experiment whereas the controller integral time (τI) is mainly a function of the time to reach the peak (tp). Importantly, the method includes a detuning factor F that allows the user to adjust the final closed-loop response time and robustness. The proposed tuning method, originally derived for first-order with delay processes, has been tested on a wide range of other processes typical for process control applications and the results are comparable with the SIMC tunings using the open-loop model

Global self-optimizing control for uncertain constrained process systems

Self-optimizing control is a promising control strategy to achieve real-time optimization (RTO) for uncertain process systems. Recently, a global self-optimizing control (gSOC) approach has been developed to extend the economic performance to be globally acceptable in the entire uncertain space spanned by disturbances and measurement noise. Nevertheless, the gSOC approach was derived based on the assumption of no change in active constraints, which limits the applicability of the approach. To address this deficiency, this paper proposes a new CV selection approach to handle active constraint changes. It ensures that all constraints are within their feasible regions when the selected CVs are maintained at constant setpoints for all expected uncertainties. In particular, constraints of interest are linearized at multiple operating conditions to get better estimates of their values and then incorporated into the optimization formulation when solving the globally self-optimizing CVs. The new CV selection approach is able to ensure an improved operational economic performance without potential constraint violations, as illustrated in an evaporator case study