Real-time Hybrid Simulation Test Research Articles

Comprehensive Assessment of the Seismic Performance of an Innovative Hybrid Semiactive and Passive State Control System for a Low-Degree-of-Freedom Structure Using Real-Time Hybrid Simulation

The dynamic performance of base isolation systems provides an effective means to reduce the seismic vulnerability of buildings. However, large displacements in the base isolation during seismic events pose a major challenge for this control system. Recently, novel control systems have been implemented to control and reduce the excessive displacements. This study presents an evaluation of the seismic performance of unconnected-fiber-reinforced elastomeric isolators (U-FREI) and variable orifice damper (VOD) devices used together as a hybrid control system for a low-degree-of-freedom reference structure by employing real-time hybrid simulation (RTHS) testing technique. This physical cybernetic testing methodology allows a dynamic system of interest to be substructured into two components: numerical and experimental. In this study, the numerical substructure corresponds to a 2-degree of freedom model, representing a reference structure, and an experimental substructure was formed using the hybrid control system described. To develop an interface between the two substructures, a horizontal transfer system (HTS) was implemented and coupled with a vertical transfer system (VTS). Using RTHS, the performance of the reference structure and the hybrid control system was evaluated under six seismic events: CAM, CAT, El Centro, Loma Prieta, Pizarro, and Chihuahua, at a maximum acceleration of 0.10 g (0.981 m·s−2). The experimental behavior of the hybrid control system allows the reference structure to reduce its maximum drift by more than 24% compared to the fixed structure. Finally, the performance and accuracy of the RTHS tests were calculated.

Using real-time hybrid simulation for active mass damper experimentation and validation

This paper proposes a novel real-time hybrid simulation (RTHS) method for advancing active mass driver (AMD) control techniques. A comprehensive derivation of the equations of motion are developed, where the tracking problem of absolute acceleration is addressed by transforming it into a displacement tracking problem, within the RTHS control loop. The simulated and experimental results demonstrate acceptable acceleration tracking using this methodology, enabling a seamless and effective option for controlling the shake table transfer system, within the RTHS framework. To demonstrate and validate the effectiveness of the proposed techniques, complete AMD shake table, and AMD-RTHS experiments are conducted. To address the effects of uncertainty, a series of tests are conducted to form an uncertainty response envelope. Comparisons between RTHS and shake table tests show that the responses lie within RTHS uncertainty regions, demonstrating that acceleration can be successfully tracked. This study shows that an AMD control experiment can be realized using RTHS techniques, thus offering an option to advance the development of AMD control techniques. Finally, an RTHS framework is proposed for performance evaluation of structural control methods using AMDs.

TOPSIS based multi-fidelity Co-Kriging for multiple response prediction of structures with uncertainties through real-time hybrid simulation

Energy dissipation devices in vibration control often present challenges for accurate modeling and uncertainty quantification through computational simulation. Simplified numerical models of these devices might not realistically represent their behavior under earthquakes thus lead to errors in response prediction and uncertainty quantification. This study further explores the integration of Co-Kriging meta-modeling and real-time hybrid simulation (RTHS) for global response prediction of multi-degree-of-freedom systems under the presence of structural uncertainties. RTHS in laboratory is taken as high-fidelity (HF) model while computational simulation with approximate modeling is used as low-fidelity (LF) model. Multi-fidelity modeling is integrated through Co-Kriging to render accurate response prediction over the entire sample space of uncertainty. An entropy-based sequential sampling is integrated with theTechnique for Order of Preference by Similarity to Ideal Solution(TOPSIS) to sequentially determine new sampling points for HF and LF simulation. The proposed TOPSIS based multi-fidelity Co-Kriging approach is experimentally evaluated through RTHS of a two-degree-of-freedom structure with self-centering viscous dampers. Accuracy of Co-Kriging prediction are further evaluated through validation tests. It is demonstrated that TOPSIS can effectively reduce the number of RTHS tests in laboratory required by multi-fidelity Co-Kriging to achieve better prediction accuracy. The study presents an innovative and effective way to apply RTHS for efficient uncertainty quantification of multiple response quantities.

Integrating adaptive Kriging with expansion optimal linear estimation into real-time hybrid simulation for time-variant experimental analysis of structures with deterioration

Seismic response evaluation often poses challenges for computational simulation when parts of structures are difficult for accurate modeling due to their complexity or nonlinearity. Failure to accurately replicate their behavior might lead to errors in response estimation for traditional computational simulation and reliability analysis when uncertainties need to be considered for the structure under investigation. Real-time hybrid simulation (RTHS) provides an efficient experimental technique for performance evaluation of large- or full-scale structures in size limited laboratories. Components that are difficult for accurate modeling are physically tested in the laboratory to enable system responses to be evaluated while the remaining parts of the structure are represented by numerical modeling. Traditional applications of RTHS often considers deterministic structural properties which however often vary with time. In this study, an innovative AK-TL-RTHS approach is proposed to integrate adaptive Kriging (AK) with transfer learning (TL) for RTHS to account for both time-dependent and independent uncertainties in response evaluation. The expansion optimal linear estimation (EOLE) is applied to discretize the stochastic process for time dependent structural deterioration. Kriging meta-model is utilized to surrogate measured structural responses from RTHS tests and a modified U-function from active learning is applied to sequentially select sample points for further RTHS tests. Selected samples and associated experimental results are transferred between random variables of discretized stochastic process to further reduce the number of tests in laboratory. RTHS of a single-degree-of-freedom (SDOF) structure with a self-centering viscous damper (SC-VD) is conducted as proof of concept to experimentally demonstrate the effectiveness of proposed AK-TL-RTHS method. It is shown that the proposed method provides an efficient and effective approach for time variant performance evaluation of structures in laboratory especially when pure numerical analysis is not feasible. The proposed approach also significantly enhances the capacity of RTHS to account for structural uncertainties and deterioration in seismic reliability analysis.

Relative stability analysis for robustness design of real-time hybrid simulation

Stability is a prerequisite of a successful real-time hybrid simulation (RTHS), which depends on the time-integration algorithm, the delay-compensation method, the loading system dynamics (mostly characterized as a time delay), and the nonlinearity of the structures being tested. The existing stability analysis methods generally provide a qualitative judgement based on one or some of the factors above, without considering all these factors to estimate quantitative stability margin. However, it is critical to design a robust RTHS system with enough stability margin (i.e., robust RTHS system) to ensure the success of the actual test with inescapable uncertainties. To this end, a relative stability analysis method for robustness design of RTHS systems is proposed. In this method, the critical gain of the stiffness of an experimental substructure is used to quantify the stability limit, and the critical delay is used to quantitatively represent the sensitivity of an RTHS system to the phase discrepancy at the interface. The RTHS system with a nonlinear experimental substructure is modeled by a discrete transfer function in an incremental form, wherein the time-integration algorithm, the delay-compensation method, the loading system dynamics, and the nonlinearities of the experimental substructure are considered. The critical delay and gain are obtained from the discrete transfer function. Two relative stability criteria are proposed based on the critical delay and the critical gain of an RTHS system to facilitate the evaluation of the system's stability performance and the design of a robust RTHS system. To verify the critical delay and gain estimated using the proposed method, numerical simulation of RTHS systems was carried out first. Then RTHS experiments of single-degree-of-freedom models with experimental substructures consisting of a linear spring and a nonlinear stiffness hardening specimen were conducted. The consistent results of the numerical simulation and the physical RTHS tests with those derived from the proposed relative stability analysis method demonstrate its effectiveness and accuracy in determining the stability properties of RTHS systems, which can be further utilized in designing more robust RTHS testing systems.

Characterization and real‐time hybrid simulation testing of rolling pendulum isolation bearings with different surface treatments

AbstractDamage caused by earthquakes to buildings and their contents (e.g., sensitive equipment) can impact life safety and disrupt business operations following an event. Floor isolation systems (FISs) are a promising retrofit strategy for protecting vital building contents. In this study, real‐time hybrid simulation (RTHS) is utilized to experimentally incorporate multi‐scale (building–FIS–equipment) interactions. For this, an experimental setup representing one bearing of a rolling pendulum (RP) based FIS is studied—first through characterization tests and then through RTHS. A series of tests was conducted at the Natural Hazards Engineering Research Infrastructure (NHERI) Experimental Facility at Lehigh University. Multiple excitations were used to study the experimental setup under uni‐axial loading. Details of the experimental testbed and test protocols for the characterization and RTHS tests are presented, along with results from these tests, which focused on the effect of different rolling surface treatments for supplemental damping, the FIS–equipment and building–FIS interactions, and rigorous evaluation of different RP isolation bearing designs through RTHS.

Implementation of real‐time hybrid simulation based on GPU computing

AbstractWith combination of physical experiment and numerical simulation, real‐time hybrid simulation (RTHS) can enlarge the dimensions of testing specimens and improve the testing accuracy. However, due to the limitation of computing capacity, the maximum degrees of freedom for numerical substructure are less than 7000 from the reported RTHS testing. It cannot meet the testing requirements for evaluating the dynamic performance of large and complex engineering structures. Taking advantages of parallel computing toolbox (PCT) in Matlab and high‐performance computing of graphics processing unit (GPU). A RTHS framework based on MATLAB and GPU was established in this work. Using this framework, a soil‐structure interaction system (SSI) was tested by a shaking table based RTHS. Meanwhile, the dynamic response of this SSI system was simulated by finite element analysis. The comparison of simulation and testing results demonstrated that the proposed testing framework can implement RTHS testing successfully. Using this method, the maximum degrees of freedom for numerical substructure can reach to 27,000, which significantly enhance the testing capacity of RTHS testing for large and complex engineering structures.

Moving Safety Evaluation of High-speed Train on Post-earthquake Bridge Utilizing Real-time Hybrid Simulation

ABSTRACT This study aimed to provide an experimental evaluation method for train’s moving safety on a post-earthquake bridge. First, an improved real-time hybrid simulation (RTHS) framework was constructed, based on utilizing the moving load superposition algorithm to solve the train-track-bridge interaction (TTBI) problem. An RTHS test was then conducted for the TTBI problem. The train model was tested using a shake table and was dynamically linked to the numerical substructure. A post-earthquake seven-span high-speed railway simply supported bridge was studied, in which earthquake-induced damage, such as stiffness reductions, residual displacements of piers, girder gap expansions, and pier settlements were all tested.

Validation of Model-Based Real-Time Hybrid Simulation for a Lightly-Damped and Highly-Nonlinear Structural System

Hybrid simulation (HS) is a cost-effective alternative to shake table testing for evaluating the seismic performance of structures. HS structures are partitioned into linked physical and numerical substructures, with actuators and sensors providing the means for the interaction. Load application in conventional HS is conducted at slow rates and is sufficient when material rate-effects are negligible. Real-time hybrid simulation (RTHS) is a variation of the HS method, where no time-scaling is applied. Despite the recent strides made in RTHS research, the body of literature validating the performance of RTHS, compared to shake table testing, remains limited. In the few available studies, the tested structures and assemblies are linear or modestly nonlinear, and artificial damping is added to the numerical substructure to ensure convergence and stable execution of the simulation. The objective of this study is the validation of a recently proposed model-based RTHS framework, focusing on lightly-damped and highly-nonlinear structural systems; such structures are particularly challenging to consider using RTHS. The boundary condition in the RTHS tests are enforced via displacement and acceleration tracking. The modified Model-Based Control (mMBC) compensator is employed for the tracking action. A two-story steel frame structure with a roof-level track nonlinear energy sink (NES) device is selected due to its light damping, high nonlinearity, and repeatability. The complete structure is first tested on a shaking table, and then substructured and tested via the RTHS method. The model-based RTHS approach is shown to perform similar to the shake table method, even for lightly-damped and highly-nonlinear structures.

Real-Time Hybrid Test Using Two-Individual Actuators to Evaluate Seismic Performance of RC Frame Model Controlled by AMD

Seismic responses of a single-story RC frame building model under control using an active mass damper (AMD) are demonstrated through a real-time hybrid simulation (RTHS) method. In this study, the RTHS test is carried out by using a hydraulic actuator and a shaking table under a synchronization. Most parts of the target RC frame model are provided as an analytical model for an online computer simulation, and the only single column of the first story is prepared as an experimental substructure. A hydraulic actuator deforms the actual RC column, and uncertainty or nonlinearity of the RC column’s behavior is focused on this RTHS test. At the same time, a control device of AMD is actually tested under a situation of installing it on the target building's floor. The floor response of the target building model is generated using a shaking table. A control motion of the AMD is manipulated based on an online simulation of the entire RC building model. Firstly, a time delay compensation of the hydraulic actuator is considered. Time delay parameters are identified using a combination model of a time lag and a first-order delay. A PID controller and a time series compensator (TSC) are applied to improve actuator performances. Next, the reproducibility of the RTHS test using two-individual actuators is evaluated. The tracking of a restoring force and deformation of the actual RC column specimen generated by the hydraulic actuator and floor motion responses reproduced on the shaking table are investigated. To improve the online numerical simulation based on the measured force responses of the RC column specimen, a high-pass filter (HPF) is applied for a force correction to utilize its phase-lead property. The effect of this HPF force correction is evaluated in both a linear region and a strong nonlinear region of the actual RC column specimen. Finally, the RTHS test results are compared to fully-numerical simulations, and the control effect of the AMD to increase the damping effect for the target RC building model is also investigated.

Sliding mode control design for the benchmark problem in real-time hybrid simulation

Real-time hybrid simulation (RTHS) is a novel cyber-physical testing technique for investigating especially large or complicated structural systems. Controllers are required to compensate for the dynamics of transfer systems that emulate the interactions between the physical and numerical substructures. Thus, both the stability and accuracy of RTHS testing highly depend on the effectiveness of the control strategy. This paper proposes a robust sliding mode controller (SMC) as a transfer system control strategy in RTHS. A design procedure of the SMC control strategy is presented. The benchmark problem on RTHS control is utilized for demonstration and validation of SMC for this class of problems. Virtual RTHS results show that the SMC strategy significantly improves the performance and robustness of RTHS testing.

Real-Time Hybrid Simulation with Deep Learning Computational Substructures: System Validation Using Linear Specimens

Hybrid simulation (HS) is an advanced simulation method that couples experimental testing and analytical modeling to better understand structural systems and individual components’ behavior under extreme events such as earthquakes. Conducting HS and real-time HS (RTHS) can be challenging with complex analytical substructures due to the nature of direct integration algorithms when the finite element method is employed. Thus, alternative methods such as machine learning (ML) models could help tackle these difficulties. This study aims to investigate the quality of the RTHS tests when a deep learning algorithm is used as a metamodel to represent the dynamic behavior of a nonlinear analytical substructure. The compact HS laboratory at the University of Nevada, Reno was utilized to conduct exclusive RTHS tests. Simulating a braced frame structure, the RTHS tests combined, for the first time, linear brace model specimens (physical substructure) along with nonlinear ML models for the frame (analytical substructure). Deep long short-term memory (Deep-LSTM) networks were employed and trained to develop the metamodels of the analytical substructure using the Python environment. The training dataset was obtained from pure analytical finite element simulations for the complete structure under earthquake excitation. The RTHS evaluations were first conducted for virtual RTHS tests, where substructuring was sought between the LSTM metamodel and virtual experimental substructure. To validate the proposed RTHS testing methodology and full system, several actual RTHS tests were conducted. The results from ML-based RTHS were evaluated for different ML models and compared against results from conventional RTHS with finite element models. The paper demonstrates the potential of conducting successful experimental RTHS using Deep-LSTM models, which could open the door for unparalleled new opportunities in structural systems design and assessment.

Communication Development and Verification for Python-Based Machine Learning Models for Real-Time Hybrid Simulation

Hybrid simulation (HS) combines analytical modeling with experimental testing to provide a better understanding of both structural elements and entire systems while keeping cost-effective solutions. However, extending real-time HS (RTHS) to bigger problems becomes challenging when the analytical models get more complex. On the other hand, using machine learning (ML) techniques in solving engineering problems across the different disciplines keep evolving and likewise, is promising resource for structural engineering. The main goal of this study is to explore the validity of ML models for conducting RTHS and specifically introduce and validate the necessary communication schemes to achieve this goal. A preliminary study with a simplified linear regression ML model, that can be readily implemented in Simulink, is presented first to introduce the idea of using metamodels as analytical substructures. However, for ML, commonly used platforms for RTHS such as Simulink and Matlab have limited capacity when compared to Python for instance. Thus, the main focus of this study was to introduce Python-based advanced ML models for RTHS analytical substructures. Deep long short-term memory (LSTM) networks in Python were considered for the advanced metamodeling for RTHS tests. The performance of Python can be enhanced by running the models using high-performance computers, which was also considered in this study. Several RTHS tests were successfully conducted at the University of Nevada, Reno with Python-based ML algorithms that were run from both local PC and a cluster. The tests were validated through comparisons with the pure analytical solutions obtained from finite element models. The study also explored the idea of eliminating delay compensators when ML models are used for RTHS.

Online Stability Analysis for Real-Time Hybrid Simulation Testing

Real-time hybrid simulation (RTHS) is an experimental technique where a critical element of a structural system is tested in the laboratory while the rest is represented through numerical simulations. A challenging aspect of this technique is the correct application of boundary conditions on the experimental substructure using actuators and sensors. The inherent dynamics of an actuator and its interaction with the physical specimen causes a time delay between commanded and measured displacements. It has been shown that delay in RTHS affects the accuracy of an experiment and even can cause instability. Therefore, to avoid stability problems, a proper partitioning choice and an appropriate compensation method for actuator dynamics should be considered. However, there will always be uncertainty in the experimental structure's behavior, so it is essential to check the system's stability during the test execution. In this paper, a stability analysis using energy methods is performed to develop an online stability indicator for the RTHS test. This indicator's goal is to detect stability problems before it can cause excessive displacements in the system, thus damaging the physical specimen or the laboratory equipment. The effectiveness of the proposed online stability indicator is demonstrated through numerical simulations taking into account the virtual RTHS benchmark problem with different compensation strategies. The proposed indicator is an excellent tool to monitor the RTHS test, improving the reliability of the experimental test while maintaining the safety of the laboratory resources.

Decoupled model-based real-time hybrid simulation with multi-axial load and boundary condition boxes

Real-time hybrid simulation (RTHS) is a cost and space efficient alternative to shake table testing for seismic assessment of structural systems. In this method, complete structural systems are partitioned into numerical and physical components and tested at real earthquake velocities. Well-understood components of the structure are modeled in finite-element numerical models. Meanwhile, the physical substructure, which often contains the highly nonlinear and numerically burdensome components is fabricated and tested in a laboratory facility. Testing at real earthquake velocities is useful to obtain nonlinear rate-dependent material behaviors. Realistic reproduction of seismic conditions for structural assessment has required researchers to develop multi-axial RTHS capabilities. In such developments, multiple actuators are arranged at the boundary condition with the physical specimen to impose realistic displacements and rotations. But, varying degrees of dynamic coupling exist between the actuators in multi-axial boundary conditions. Controllers and kinematic transformations are developed for the tracking action of the actuators to compensate for the amplitude and phase discrepancies between target and measured displacement signals, otherwise stability issues are likely to result. In this paper, a multi-axial framework is introduced for RTHS testing, using a Load and Boundary Condition Box (LBCB) at the University of Illinois at Urbana-Champaign. The previously developed multi-axial RTHS framework for the LBCBs compensates for actuator dynamics in Cartesian coordinates; this approach lacked stability robustness when testing stiff specimens. The distinguishing feature of the proposed framework is that tracking compensation is executed in the actuator coordinates. The differences between the previous and proposed multi-axial RTHS frameworks are explored in detail herein. This paper presents the components of the framework and the describes a six-degree-of-freedom moment frame RTHS experiment. Finally, experimental results are discussed and directions for future research efforts are considered.

Generalized hyper-viscoelastic modeling and experimental characterization of unfilled and carbon black filled natural rubber for civil structural applications

Unfilled and carbon black filled natural rubber have attracted considerable attention and have been extensively used as a novel construction material in civil infrastructure applications because of their superior physical and mechanical properties. However, their mechanical behavior is highly nonlinear and further complicated by the significant sensitivity to the loading rate. In this paper, a generalized constitutive model was proposed to improve the description of rate-dependent mechanical behavior of unfilled and carbon black filled natural rubber. The proposed model consisted of a hyperelastic spring to characterize the equilibrium response and a Maxwell element to capture the rate dependency as well as link the overstress to the loading rate. Subsequently, the stress–strain response of both unfilled and filled natural rubber subjected to the cyclic shear loading with different strain rates was experimentally characterized, multi-step relaxation and cyclic shear tests were carried out to calibrate material parameters in the model. Afterwards, a nonlinear viscosity coefficient was derived to completely establish the proposed model and its three-dimensional function versus strain and strain rate was also obtained based on the experimental data. Finally, comparing numerical simulations with cyclic shear tests and real-time hybrid simulation tests, it was found that the simulated results were in good agreement with the test results, indicating the proposed model is capable to accurately describe the hyper-viscoelastic behavior of both unfilled and filled natural rubber under cyclic shear loading, which might become an appropriate choice to be used by researchers and engineers for civil structural applications.

Compact Hybrid Simulation System: Validation and Applications for Braced Frames Seismic Testing

ABSTRACT Hybrid Simulation (HS) is a well-established testing method that combines both experimental and analytical components to evaluate the performance of structures under extreme events, commonly earthquakes. While several configurations and systems are available around the world to conduct HS, one goal of this paper is to document the development and verification of a compact HS setup at the University of Nevada, Reno to be used for tackling new research problems and educational purposes. A new substructured HS approach is proposed for seismic testing of concentric-braced frames (CBFs) with focus on capturing brace buckling and low-cycle fatigue induced-rupture. The paper presents the capabilities and verification methods for the developed system for slow and real-time HS testing with two different alternatives for the computational substructures: Simulink and OpenSEES along with OpenFresco. Two new applications were pursued to demonstrate HS testing of CBFs. The first used cyclic loading and HS under earthquake loading to capture brace buckling and failure to compare damage accumulation and brace fatigue life through rupture. The second application used HS testing to investigate the effect of earthquake duration on seismic performance of CBFs. The two applications demonstrate that the proposed HS approach can be potentially used to accurately capture CBFs seismic behavior and provide new datasets for modeling brace buckling and rupture under realistic earthquake loading. The paper also provides a brief discussion on the potential use of the compact HS setup for developing teaching modules.

Real-time hybrid simulation using analogue electronic computer technology

In the field of structural dynamics, real-time hybrid simulation (RTHS) continues to receive increased interest from researchers conducting component testing incorporating system-level behaviour. Increased digital computing power has allowed advances in RTHS. However, limitations in RTHS will persist due to the effects of discrete errors caused by quantisation and corresponding numerical integration time step limitations, which can limit the bandwidth and nonlinearities of the system studied. In this paper, an analogue electronic computer is constructed to conduct RTHS of a modelled base-isolated structure with a physically tested viscous damping device. The analogue computer models a two-degree-of-freedom (2DOF) structure and solves the equations of motion required in RTHS testing. Results of the RTHS tests using the analogue computer are compared to RTHS tests implemented with a digital computer in order to validate the proposed analogue RTHS method. Further applications of RTHS testing with analogue computing including high-frequency dynamic testing are discussed.

Real-time hybrid simulation using analogue electronic computer technology

In the field of structural dynamics, real-time hybrid simulation (RTHS) continues to receive increased interest from researchers conducting component testing incorporating system-level behaviour. Increased digital computing power has allowed advances in RTHS. However, limitations in RTHS will persist due to the effects of discrete errors caused by quantisation and corresponding numerical integration time step limitations, which can limit the bandwidth and nonlinearities of the system studied. In this paper, an analogue electronic computer is constructed to conduct RTHS of a modelled base-isolated structure with a physically tested viscous damping device. The analogue computer models a two-degree-of-freedom (2DOF) structure and solves the equations of motion required in RTHS testing. Results of the RTHS tests using the analogue computer are compared to RTHS tests implemented with a digital computer in order to validate the proposed analogue RTHS method. Further applications of RTHS testing with analogue computing including high-frequency dynamic testing are discussed.

A robust linear-quadratic-gaussian controller for the real-time hybrid simulation on a benchmark problem

Abstract During a real-time hybrid simulation (RTHS), inevitable time delay of actuators when responding to a command will reduce the accuracy of test results and sometimes even cause unstable testing. The inner-loop controller of an actuator is generally capable of eliminating the effects due to small time-delays. However, if a test specimen behaves nonlinearly, accuracy of RTHS results will be impaired. In addition to the uncertainty of test specimens and transfer system, measurement noises of the displacement and force sensors also require a robust external controller for RTHS. In this paper, a robust linear-quadratic-gaussian (LQG) controller with a Loop Transfer Recovery (LTR) procedure and a polynomial-based feedforward prediction (FP) algorithm is proposed to compensate the adverse effects due to time delay and uncertainties within the RTHS testing system. The stability and robustness of the proposed controller are analysed in the frequency domain using the Nyquist curve and the Bode diagrams. Numerical simulations are then carried out on the benchmark problem using both the proposed robust and the conventional LQG controllers and their performance is compared using the nine evaluation criteria. It is demonstrated that the robust LQG (RLQG) controller outperforms the conventional LQG controller in terms of compensating the parameter uncertainties in the testing system and achieving accurate RTHS results.