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    Adaptive Control of a 3 DoF Helicopter with Linear and Nonlinear Reference Models
    (IEEE, 2018) Kocagil, Bedrettin Mahmut; Ozcan, Sinan; Arican, Ahmet Cagri; Guzey, Umit Mufit; Copur, Engin Hasan; Salamci, Metin U.
    Adaptive control methods are widely used for the control of both linear and nonlinear dynamical systems. Among the adaptive control approaches, Model Reference Adaptive Control (MRAC) method has a systematic design feature in which response of a stable reference model is targeted to be followed by the dynamical system. In general, Linear Time Invariant (LTI) Reference Models are considered in the MRAC design and the adaptation rule is formulated accordingly. In this paper, the linear reference model is altered with a stable nonlinear one and the adaptation rule is re-formulated to cope with the nonlinearity. The stable nonlinear reference model is generated by using the State Dependent Riccati Equation (SDRE) approach and the adaptation rule is also updated by using the same SDRE idea. The effects of altering the linear reference model to the nonlinear counterpart are shown in the MRAC formulations. In addition to the new MRAC formulations, the proposed MRAC algorithm is applied to a 3 DoF helicopter test bed to reveal the advantages of the nonlinear reference model.
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    Experiment of Sliding Mode Control with Nonlinear Sliding Surface Design for a 3-DOF Helicopter Model
    (IEEE, 2019) Guzey, Umit M.; Copur, Engin H.; Ozcan, Sinan; Arican, A. Cagri; Kocagil, B. Mahmut; Salamci, Metin U.
    Sliding Mode Control (SMC) is one of the effective robust control techniques against external disturbances, parameter uncertainties and unmodelled dynamics. However, there is no certain way to design the sliding surface (SS) for nonlinear systems, which has a key role in satisfying the stability and performance criteria. Thus, an optimal method can be useful in the design process of SS to deal with these weaknesses. In this study, State Dependent Riccati Equation (SDRE) based SMC is used to control the motion of a laboratory helicopter in two axes, namely travel and elevation axes. Experimental evaluation is performed using this 3-DOF helicopter platform and results are compared against a SMC with linear time-invariant SS to establish the efficacy of the approach. Therefore, this study presents experimental investigation for establishing the feasibility of the proposed optimal robust control architecture.
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    Linear and Nonlinear Optimal Controller Design for a 3 DOF Helicopter
    (IEEE, 2018) Arican, Ahmet Cagri; Ozcan, Sinan; Kocagil, Bedrettin Mahmut; Guzey, Umit Mufit; Copur, Engin Hasan; Salamci, Metin Uymaz
    The paper presents the application of State-Dependent Riccati Equation (SDRE) based optimal control for a nonlinear system. The performance of linear control methods in controlling nonlinear systems is inconsistent due to their inability to adapt themselves to the varying operating conditions of nonlinear systems. This stubborn feature of linear control methods limits their control performance. However, SDRE technique offers a flexible design to obtain an optimal control strategy, thereby accounting for the varying operating conditions. With the existence of this flexibility, SDRE control method has attracted a lot of interest in controlling nonlinear systems. A 3-DOF laboratory helicopter is thus used to investigate experimentally the performance of the proposed SDRE control method in tracking the reference motions in both travel and elevation axes. To establish the feasibility of the SDRE control method, it is compared with the well-known Linear Quadratic Regulator (LQR) control method in terms of the cost function value. Results show that SDRE control method is more effective than LQR one.
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    A Modified SDRE-based Sub-optimal Hypersurface Design in SMC
    (Elsevier, 2020) Ozcan, Sinan; Copur, Engin H.; Arican, Ahmet C.; Salamci, Metin U.
    Sliding Mode Control (SMC) plays a prominent role in dealing with matched uncertainties. In classical SMC design, the sliding surface (SS) is crucial to the guarantee for the stability and desired performance, especially if the system is nonlinear. A possible way to fulfill these desired performances for nonlinear systems is to use State Dependent Riccati Equation (SDRE) method, enabling SS to be designed even optimally. However, SDRE may suffer an inherent stability problem as well as a computational burden. To overcome these issues, in a recent study, a new SDRE method has been proposed. Therefore, this study takes advantages of the advanced SDRE method in designing a sub-optimal SS and also provides some comparative results with the conventional one to establish the feasibility of the proposed SDRE-based SMC control architecture experimentally. Experiments are conducted by using a 3-DOF helicopter platform and the results reveal that the proposed SDRE-based SMC is able to produce smoother SS than the conventional counterpart. Copyright (C) 2020 The Authors.
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    MRAC of a 3-DoF Helicopter with Nonlinear Reference Model
    (IEEE, 2018) Kocagil, B. Mahmut; Ozcan, Sinan; Arican, A. Cagri; Guzey, Umit M.; Copur, Engin H.; Salamci, Metin U.
    Model Reference Adaptive Control (MRAC) technique, which is considered to be an effective tool for the control of unknown dynamical systems behavior, is widely used in practical applications. In principal, a known stable linear model dynamics is taken as a reference model such that its response is tracked by the unknown dynamical system by means of an adaptive control scheme. In this paper, rather than using a linear reference model, we propose a nonlinear reference model to be used in the MRAC of nonlinear plant dynamics. First, a stable nonlinear reference model is formed by using State Dependent Riccati Equation (SDRE) approach. Then an adaptation rule is derived to ensure the convergence of the response of nonlinear plant dynamics to that of the nonlinear reference model. The proposed method is tested experimentally using a 3-DoF helicopter test bed with different parameters and working conditions.
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    An update algorithm design using moving Region of Attraction for SDRE based control law
    (Pergamon-Elsevier Science Ltd, 2019) Copur, Engin H.; Arican, Ahmet C.; Ozcan, Sinan; Salamci, Metin U.
    State Dependent Riccati Equation (SDRE) methods have the considerable advantages over other nonlinear control methods. However, stability issues can be arisen in SDRE based control system due to the lack of the global asymptotic stability property. Therefore, the previous studies have usually shown that local asymptotic stability can be ensured by estimating a Region of Attraction (ROA) around the equilibrium point. These estimated regions for stability may become narrow or the condition to keep the states in this region may be very conservative. To resolve these issues, this paper proposes a novel SDRE method employing an update algorithm to re-estimate the ROA when the states tend to move out of the stable region. The tendency is checked using a condition which is developed based on a new theorem. The theorem proves that it is possible to redesign the previous ROA with respect to the current states lying close to its boundary for ensuring the non-local stability along the trajectory without the need of solving SDRE at each time instant, unlike the standard SDRE approach. Therefore, the new theorem is now able to enhance the stability of the SDRE based closed-loop control system. The feasibility of the proposed SDRE control method is tested in both simulations and experiments. A validated 3-DOF laboratory helicopter is used for experiments and the control objective for the helicopter is to realise a preplanned movement in both elevation and travel axes. The results reveal that the proposed SDRE approach enables the controlled plant to track the desired trajectory as satisfactorily as the standard SDRE approach, while only solving SDRE when needed. The proposed SDRE method reduces the computational load for practical implementation of the control algorithm whilst ensuring the stability over the operational region. (C) 2019 The Franklin Institute. Published by Elsevier Ltd. All rights reserved.