Finite-Time State Estimation for an Inverted Pendulum under Input-Multiplicative Uncertainty

A sliding mode observer is presented, which is rigorously proven to achieve finite-time state estimation of a dual-parallel underactuated (i.e., single-input multi-output) cart inverted pendulum system in the presence of parametric uncertainty. A salient feature of the proposed sliding mode observer design is that a rigorous analysis is provided, which proves finite-time estimation of the complete system state in the presence of input-multiplicative parametric uncertainty. The performance of the proposed observer design is demonstrated through numerical case studies using both sliding mode control (SMC)- and linear quadratic regulator (LQR)-based closed-loop control systems. The main contribution presented here is the rigorous analysis of the finite-time state estimator under input-multiplicative parametric uncertainty in addition to a comparative numerical study that quantifies the performance improvement that is achieved by formally incorporating the proposed compensator for input-multiplicative parametric uncertainty in the observer. In summary, our results show performance improvements when applied to both SMC- and LQR-based control systems, with results that include a reduction in the root-mean square error of up to 39% in translational regulation control and a reduction of up to 29% in pendulum angular control

Finite-Time State Estimation for an Inverted Pendulum under Input-Multiplicative Uncertainty

A sliding mode observer is presented, which is rigorously proven to achieve finite-time state estimation of a dual-parallel underactuated (i.e., single-input multi-output) cart inverted pendulum system in the presence of parametric uncertainty. A salient feature of the proposed sliding mode observer design is that a rigorous analysis is provided, which proves finite-time estimation of the complete system state in the presence of input-multiplicative parametric uncertainty. The performance of the proposed observer design is demonstrated through numerical case studies using both sliding mode control (SMC)- and linear quadratic regulator (LQR)-based closed-loop control systems. The main contribution presented here is the rigorous analysis of the finite-time state estimator under input-multiplicative parametric uncertainty in addition to a comparative numerical study that quantifies the performance improvement that is achieved by formally incorporating the proposed compensator for input-multiplicative parametric uncertainty in the observer. In summary, our results show performance improvements when applied to both SMC- and LQR-based control systems, with results that include a reduction in the root-mean square error of up to 39% in translational regulation control and a reduction of up to 29% in pendulum angular control

Development of a Two-Wheel Inverted Pendulum and a Cable Climbing Robot

The research work in this thesis constitutes two parts: one is the development and control of a Two-wheel inverted pendulum (TWIP) robot and the other is the design and manufacturing of a cable climbing robot (CCR) for suspension bridge inspection. The first part of this research investigates a sliding mode controller for self-balancing and stabilizing a two-wheel inverted pendulum (TWIP) robot. The TWIP robot is constructed by using two DC gear motors with a high-resolution encoder and zero backlashes, but with friction. It is a highly nonlinear and unstable system, which poses challenges for controller design. In this study, a dynamic mathematical model is built using the Lagrangian function method. And a sliding mode controller (SMC) is proposed for auto-balancing and yaw rotation. A gyro and an accelerometer are adopted to measure the pitch angle and pitch rate. The effect on the sensor’s installation location is analyzed and compensated, and the precision of the pose estimation is improved accordingly. A comparison of the proposed SMC controller with a proportional-integral-derivative (PID) controller and state feedback controller (SFC) with linear quadratic regulation (LQR) has been conducted. The simulation and experimental test results demonstrate the SMC controller outperforms the PID controller and SFC in terms of transient performance and disturbance rejection ability. In the second part of the research, a wheel-based cable climbing robotic system which can climb up and down the cylindrical cables for the inspection of the suspension bridges is designed and manufactured. Firstly, a rubber track climbing mechanism is designed to generate enough adhesion force for the robot to stick to the surface of a cable and the driving force for the robot to climb up and down the cable, while not too big to damage the cable. The climbing system includes chains and sprockets driven by the DC motors and adhesion system. The unique design of the adhesion mechanism lies in that it can maintain the adhesion force even when the power is lost while the system works as a suspension mechanism. Finally, a safe-landing mechanism is developed to guarantee the safety of the robot during inspection operations on cables. The robot has been fully tested in the inspection of Xili bridge, Guangzhou, P.R. China

Safe experimentation dynamics algorithm for data-driven PID controller of a class of underactuated systems

In recent decades, various control strategies for underactuated mechanical systems (UMS) have been widely reported which are derived from the systems’ model. Due to the problem of the unmodeled dynamics, there is a significant disparity between the theory of control and its actual applications, which makes the model-based controller difficult to apply. In recent years, control researchers have been switching to the method of data-driven control in order to eliminate this disparity. The control performance of this method is independent of the plant’s model accuracy to attain the control objective. This is because its controller’s design is founded only on the input-output (I/O) data measurement of the actual plants. In the industry, the proportional-integral-derivative (PID) controller is the control method that has been widely implemented because of its simplicity, the fact that it is more understandable and more reliable to be used for industrial purposes. So far, the tuning methods used for data-driven PID for the underactuated systems are mostly based on the multi-agent-based optimization, which means that the design requires substantial computation time and make it not practical for on-line tuning applications. Therefore, it is necessary to develop a tuning strategy that requires less computation time. Previously, a stochastic approximation based method such as the norm-limited simultaneous perturbation stochastic approximation (NL-SPSA) and global NL-SPSA (G-NL-SPSA) have shown successful results as tools for the data-driven PID tuning. Notably, the SPSA and GSPSA based methods only produced the optimal design parameter at the final iteration while it may keep a better design parameter during the tuning process if it has a memory feature. Hence, a memory-based optimization tool has good potential to retain the optimal design parameter during the PID tuning process. This can overcome the existing memory-based algorithms such as random search (RS) and simulated annealing (SA) which currently produce less control accuracy due to the local minimum problem. Motivated by the limitations of the current methods, there is an advantage to using safe experimentation dynamics (SED) as a tool for optimization. SED offers memory-based features and effectiveness to perform with lesser computation time to overcome a range of optimization problems, even for high-dimensional parameter tuning. Moreover, other than the memory-based feature, SED algorithm has fewer design parameters to be addressed and the independence of the gain sequence in the tuning process. Previously, SED algorithm has been applied in to control scheme of wind farm to optimize the total power production but has yet to be applied in PID tuning. Therefore, it is good to study the effectiveness of SED in PID tuning. In this study, the efficiency of the proposed approach is tested by applying the PID controller tuning to the slosh control system, double-pendulum-type overhead crane (DPTOC) control system and multi-input-multi-output (MIMO) crane control system. The performance was evaluated using numerical examples in terms of tracking performance and control input energy. Thirty trials have been performed to evaluate the SED, norm limited SPSA (NL-SPSA), global norm limited SPSA (G-NL-SPSA), and RS algorithms in each example. Next, when the pre-stated termination condition is fitted, each method is evaluated based on the statistical analysis involving the objective function, the total norm of the error and total norm of the input. Then, the rise time, settling time, and percentage of overshoot of the one best trial out of the 30 trials were observed for each method. In the DPTOC control system, we also present the examples with disturbance. The performance comparison was made only between the SED based method and G-NL-SPSA based method. In addition, the average percentage of the control objective improvement retrieved from the 30 trials for each method was also observed

Development of Self-Learning Type-2 Fuzzy Systems for System Identification and Control of Autonomous Systems

Modelling and control of dynamic systems are faced by multiple technical challenges, mainly due to the nature of uncertain complex, nonlinear, and time-varying systems. Traditional modelling techniques require a complete understanding of system dynamics and obtaining comprehensive mathematical models is not always achievable due to limited knowledge of the systems as well as the presence of multiple uncertainties in the environment. As universal approximators, fuzzy logic systems (FLSs), neural networks (NNs) and neuro-fuzzy systems have proved to be successful computational tools for representing the behaviour of complex dynamical systems. Moreover, FLSs, NNs and learning-based techniques have been gaining popularity for controlling complex, ill-defined, nonlinear, and time-varying systems in the face of uncertainties. However, fuzzy rules derived by experts can be too ad-hoc, and the performance is less than optimum. In other words, generating fuzzy rules and membership functions in fuzzy systems is a potential challenge especially for systems with many variables. Moreover, under the umbrella of FLSs, although type-1 fuzzy logic control systems (T1-FLCs) have been applied to control various complex nonlinear systems, they have limited capability to handle uncertainties. Aiming to accommodate uncertainties, type-2 fuzzy logic control systems (T2-FLCs) were established. This thesis aims to address the shortcomings of existing fuzzy techniques by utilisation of type-2 FLCs with novel adaptive capabilities. The first contribution of this thesis is a novel online system identification technique by means of a recursive interval type-2 Takagi-Sugeno fuzzy C-means clustering technique (IT2-TS-FC) to accommodate the footprint-of-uncertainties (FoUs). This development is meant to specifically address the shortcomings of type-1 fuzzy systems in capturing the footprint-of-uncertainties such as mechanical wear, rotor damage, battery drain and sensor and actuator faults. Unlike previous type-2 TS fuzzy models, the proposed method constructs two fuzzifiers (upper and lower) and two regression coefficients in the consequent part to handle uncertainties. The weighted least square method is employed to compute the regression coefficients. The proposed method is validated using two benchmarks, namely, real flight test data of a quadcopter drone and Mackey-Glass time series data. The algorithm has the capability to model uncertainties (e.g., noisy dataset). The second contribution of this thesis is the development of a novel self-adaptive interval type-2 fuzzy controller named the SAF2C for controlling multi-input multi-output (MIMO) nonlinear systems. The adaptation law is derived using sliding mode control (SMC) theory to reduce the computation time so that the learning process can be expedited by 80% compared to separate single-input single-output (SISO) controllers. The system employs the `Enhanced Iterative Algorithm with Stop Condition' (EIASC) type-reduction method, which is more computationally efficient than the `Karnik-Mendel' type-reduction algorithm. The stability of the SAF2C is proven using the Lyapunov technique. To ensure the applicability of the proposed control scheme, SAF2C is implemented to control several dynamical systems, including a simulated MIMO hexacopter unmanned aerial vehicle (UAV) in the face of external disturbance and parameter variations. The ability of SAF2C to filter the measurement noise is demonstrated, where significant improvement is obtained using the proposed controller in the face of measurement noise. Also, the proposed closed-loop control system is applied to control other benchmark dynamic systems (e.g., a simulated autonomous underwater vehicle and inverted pendulum on a cart system) demonstrating high accuracy and robustness to variations in system parameters and external disturbance. Another contribution of this thesis is a novel stand-alone enhanced self-adaptive interval type-2 fuzzy controller named the ESAF2C algorithm, whose type-2 fuzzy parameters are tuned online using the SMC theory. This way, we expect to design a computationally efficient adaptive Type-2 fuzzy system, suitable for real-time applications by introducing the EIASC type-reducer. The proposed technique is applied on a quadcopter UAV (QUAV), where extensive simulations and real-time flight tests for a hovering QUAV under wind disturbances are also conducted to validate the efficacy of the ESAF2C. Specifically, the control performance is investigated in the face of external wind gust disturbances, generated using an industrial fan. Stability analysis of the ESAF2C control system is investigated using the Lyapunov theory. Yet another contribution of this thesis is the development of a type-2 evolving fuzzy control system (T2-EFCS) to facilitate self-learning (either from scratch or from a certain predefined rule). T2-EFCS has two phases, namely, the structure learning and the parameters learning. The structure of T2-EFCS does not require previous information about the fuzzy structure, and it can start the construction of its rules from scratch with only one rule. The rules are then added and pruned in an online fashion to achieve the desired set-point. The proposed technique is applied to control an unmanned ground vehicle (UGV) in the presence of multiple external disturbances demonstrating the robustness of the proposed control systems. The proposed approach turns out to be computationally efficient as the system employs fewer fuzzy parameters while maintaining superior control performance

Nonlinear control with two complementary Lyapunov function

If a Lyapunov function is known, a dynamic system can be stabilized. However, computing or selecting a Lyapunov function is often challenging. This dissertation presents a new approach which eliminates this challenge: a simple control Lyapunov function [CLF] is assumed then the algorithm seeks to reduce the value of the Lyapunov function. If the control effort would have no effect at any iteration, the CLF is switched in an attempt to regain control. There is some flexibility in choosing these two complementary CLF’s but they must satisfy a few characteristics. The method is proven to asymptotically stabilize a wide range of nonlinear systems and was tested on an even broader variety in simulation. It was also tested on an industrial robot to provide compliant behavior. The simulated and hardware demonstrations provide a broad perspective on the algorithm’s usefulness and limitations. In comparison to the ubiquitous PID controller, the algorithm’s advantages include enhanced performance, ease of tuning, and extensions to higher-order and/or coupled systems. Those claimed advantages are validated by a test with four engineering students, which validates the controller as a viable option for nonlinear control (even at the undergraduate level). The algorithm’s drawbacks include the necessity of a dynamic model and, when linearization is required, the reliance on a small simulation time step; however, for the motivating application –interactive industrial robotic systems – both requirements were already met. Finally, the developed software was released to the public as part of the Robot Operating System (ROS) and the details of that release are included in this report.Mechanical Engineerin

Feedback Synthesis for Controllable Underactuated Systems using Sequential Second Order Actions

This paper derives nonlinear feedback control synthesis for general control affine systems using second-order actions---the needle variations of optimal control---as the basis for choosing each control response to the current state. A second result of the paper is that the method provably exploits the nonlinear controllability of a system by virtue of an explicit dependence of the second-order needle variation on the Lie bracket between vector fields. As a result, each control decision necessarily decreases the objective when the system is nonlinearly controllable using first-order Lie brackets. Simulation results using a differential drive cart, an underactuated kinematic vehicle in three dimensions, and an underactuated dynamic model of an underwater vehicle demonstrate that the method finds control solutions when the first-order analysis is singular. Moreover, the simulated examples demonstrate superior convergence when compared to synthesis based on first-order needle variations. Lastly, the underactuated dynamic underwater vehicle model demonstrates the convergence even in the presence of a velocity field.Comment: 9 page