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In this paper, we examine the potential of optimization-based computer-assisted proof methods to be applied much more widely than commonly recognized by engineers and computer scientists. More specifically, we contend that there are vast opportunities to derive valuable mathematical results and properties that may be narrow in scope, such as in highly specialized engineering control applications, that are presently overlooked, because they have characteristics atypical of those that are conventionally studied in the areas of pure and applied mathematics. As a concrete example, we demonstrate use of sum-of-squares (SOS) optimization for certifying polynomial nonnegativity as a part of a proposed dimension-pinning strategy to prove that the inverse of the relative gain array (RGA) of a d -dimensional positive-definite matrix is doubly stochastic for d ≤ 4 . However, it is not specifically this result and solution method that are of principal interest in this paper but rather how they illustrate the relevance of optimization-based proof techniques to engineering system design more broadly. We believe that our paper is the first to explicitly emphasize the fundamental distinction between methods that can be applied to prove results/properties over a fixed number of dimensions versus those that hold generally. The latter class of problems is the conventional domain of mathematicians, but the former is what we propose to be a fertile and largely unrecognized class of problems that are amenable to automated-proof technologies, e.g., as we demonstrate using our novel dimension-pinning approach.

This paper considers a distillation column used in heavy crude oil separation where pairings exhibit negative Niederlinski Index values, potentially leading to system instability. In this study, we address this issue by constructing a Relative Gain Array matrix from a transfer matrix of order 3. We employ mathematical techniques to steer the system towards stability. Through subtle modifications to matrix entries, we achieve stable configurations.

Dynamometers are used to evaluate the real-world performances of drivetrains in various loading conditions. Due to its superior power density, high bandwidth, and design flexibility, a hydrostatic power-regenerative dynamometer is an ideal candidate for hydrostatic wind turbine transmission testing. A dynamometer can emulate the wind turbine rotor dynamics and allow the investigation of the performance of a unique hydrostatic drivetrain without actually building the physical system. The proposed dynamometer is an energy-efficient system with counter-intuitive control challenges. This paper presents the dynamics, control synthesis, and experimental validation of a power-regenerative hydrostatic dynamometer. A fourth-order non-linear model with three inputs was formulated for the dynamometer. The strength of input–output couplings was identified, and two different decoupling controllers were designed and implemented. During wind turbine testing, the synchronous generator turns at a constant speed and the system model is linear. A steady-state decoupling controller was developed for independent control of the drive and transmission. The implemented decoupling controller demonstrated a negligible change in rotor speed for a 40 bar step increase in pressure, but a 20 bar pressure spike for a 4 rpm step change in rotor speed. However, during starting and stopping, the synchronous generator speed is not constant, and the system model is nonlinear. Therefore, a steady-state decoupling controller will not work. Thus, a decentralized controller with feed-forward control and gain scheduling was designed and implemented. A reference command was designed to avoid cavitation, pressure spikes, and power flow reversal during start-up. The experimental results show precise tracking in steady-state and transient operations. The decentralized controller demonstrated a negligible change in rotor speed for a 40 bar step increase in pressure but a 100 bar pressure spike for a 4 rpm step increase in rotor speed. The pressure spike was reduced by 80 bar with the implementation of feed-forward gain. The proposed electro-hydro-mechanical system requires less power and has the potential to reduce energy expenditure by 50%.

Many industrial processes are Multi-Input Multi-Output (MIMO) that has more than one controlled variable. Therefore, without considering the impact of these factors it is not possible to achieve the desired performance. In this paper, two methods, adaptive controller and self-tuning fuzzy PID controller is used to control the quadruple-tank process. Although the both presented methods are able to eliminate disturbance effect and reach steady-state with acceptable performance, the fuzzy controller is preferred to the adaptive controller due to the lower computational effort. Moreover, the fuzzy controller does not need the transfer function of the system, while it has a simple design procedure and simple arithmetic. Superiority of the proposed method is automatic adjustment of multivariable fuzzy controller parameters to achieve desirable performance.

Decentralized control offers a more effective way to avoid the complexities and coordination challenges encountered in centralized control. In the decentralized design of additional controllers for multi-infeed DC transmission systems, it is crucial to focus on the interactions among the controllers. To solve this problem, this paper primarily discusses an enhanced damping characteristic method for hybrid AC-DC systems based on an improved Effective Relative Gain Array (ERGA) index. Initially, feedback signals with better control effects on existing oscillation modes are pre-screened. Subsequently, the ERGA-based interaction index is utilized to pair these feedback signals with control locations, aiming to identify the optimal pairing scheme with the minimum index value, indicating the least interaction effect. This approach minimizes the mutual influence between loops and reduces adverse interactions among controllers. Simulations of multi-DC additional damping controllers designed using the multi-stage Linear Quadratic Regulator (LQR) method in a multi-DC system demonstrate that the optimal pairing scheme significantly outperforms both uncontrolled and poorly paired schemes in controlling low-frequency oscillations, thereby validating the optimality of the proposed method. Furthermore, various disturbances are introduced to verify the effectiveness and robustness of the proposed control strategy against low-frequency oscillations.

In this paper, a novel partially decentralized adaptive control strategy is presented to deal with a class of Multi Inputs Multi Outputs (MIMO) non-square, Linear Parameter Varying (LPV) systems. The key idea is the design of Proportional Integral Derivative (PID) regulator based on online pairing and tuning of its parameters using the Dynamic Relative Gain Array (DRGA) matrix. The proposed adaptive partially decoupled control scheme operates in a straightforward and systematic way. The convergence of the proposed controller is guaranteed by theoretical analysis, numerical simulations and experimental tests carried out on a non-holonomic two Wheeled Mobile Robot (WMR). Studies of the proposed regulator robustness against additive disturbance and stability over the whole parameter range are given to illustrate the effectiveness of the proposed PID scheme.

In this paper, motion control and robust path tracking were extended to nonsquare MIMO (Multi-Input Multi-Output) systems having more outputs than inputs. A path-tracking design based on fractional prefilter approach has been developed and extended to control nonsquare MIMO systems. The nonsquare relative gain array (NRG) is used to assess the performance of nonsquare control systems based on steady-state information. The CRONE control approach developed for multivariable plants based on third-generation SISO CRONE methodology is combined with MIMO-QFT (Quantitative Feedback Theory) robust design methodology, taking into account the plant uncertainties. After the determination of CRONE controller, the parameter of prefilter has been optimized considering physical constraints of actuators and the tracking performance specifications. The proposed design is applied to an example.

This article presents a procedure that utilizes the local polynomial approximation approach in the estimation of the Dynamic Relative Gain Array (DRGA) matrix and its uncertainty bounds for weakly nonlinear systems. This procedure offers enhanced frequency resolution and noise reduction when random excitation is used. It also allows separation of nonlinear distortions with shorter measuring time when multisine excitation is imposed. The procedure is illustrated using the well-known quadruple tank process as a case study in simulation and in real life. Besides, a comparison with the pairing results of the static RGA, nonlinear RGA and DRGA based on linearized quadruple tank model for different simulation cases is performed.

A novel design method of decoupling internal model control is proposed for non-square processes with multiple time delays that are often encountered in complicated industrial processes. The method can obtain a realizable decoupling controller of non-square processes with more inputs than outputs by inserting some compensated terms, which are derived analytically. Meanwhile, based on the relative normalized gain array, an equivalent transfer function matrix is introduced to approximate the pseudo-inverse of the process transfer function matrix, which makes the design of decoupling internal model control simple and easy to calculate. Filters are added to the control structure to improve the robustness. Simulation results have proved the effectiveness and reliability of the proposed method.