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

DESIGN OF BLOCK-BACKSTEPPING CONTROLLER TO BALL AND ARC SYSTEM BASED ON ZERO DYNAMIC THEORY

This paper develops a proposed block-backstepping algorithm for balancing and tracking control of ball and arc system. Two block-backstepping designs have been presented; one from the linearized model and other from a nonlinear model of the considered underactuated system. Also, two main control objectives have been achieved; firstly to bring the ball to rest on the top of the arc and secondly to make the cart track a defined reference trajectory. Moreover, integral action is included in the developed block-backstepping control law to improve the steadystate characteristics and to enhance the robustness of the overall system. Additionally, the internal stability of the nonlinear system has been analyzed using zero dynamic criteria to guarantee the global asymptotic stability at the desired equilibrium point. The performance of the designed control algorithm is assessed via simulated results. The results show that the block-backstepping controller designed for nonlinear system gives better transient performance than that designed for the linear system. Also, the nonlinear controller can cope with larger initial angular ball position without loss of stability

Bio-inspired robotic control in underactuation: principles for energy efficacy, dynamic compliance interactions and adaptability.

Biological systems achieve energy efficient and adaptive behaviours through extensive autologous and exogenous compliant interactions. Active dynamic compliances are created and enhanced from musculoskeletal system (joint-space) to external environment (task-space) amongst the underactuated motions. Underactuated systems with viscoelastic property are similar to these biological systems, in that their self-organisation and overall tasks must be achieved by coordinating the subsystems and dynamically interacting with the environment. One important question to raise is: How can we design control systems to achieve efficient locomotion, while adapt to dynamic conditions as the living systems do? In this thesis, a trajectory planning algorithm is developed for underactuated microrobotic systems with bio-inspired self-propulsion and viscoelastic property to achieve synchronized motion in an energy efficient, adaptive and analysable manner. The geometry of the state space of the systems is explicitly utilized, such that a synchronization of the generalized coordinates is achieved in terms of geometric relations along the desired motion trajectory. As a result, the internal dynamics complexity is sufficiently reduced, the dynamic couplings are explicitly characterised, and then the underactuated dynamics are projected onto a hyper-manifold. Following such a reduction and characterization, we arrive at mappings of system compliance and integrable second-order dynamics with the passive degrees of freedom. As such, the issue of trajectory planning is converted into convenient nonlinear geometric analysis and optimal trajectory parameterization. Solutions of the reduced dynamics and the geometric relations can be obtained through an optimal motion trajectory generator. Theoretical background of the proposed approach is presented with rigorous analysis and developed in detail for a particular example. Experimental studies are conducted to verify the effectiveness of the proposed method. Towards compliance interactions with the environment, accurate modelling or prediction of nonlinear friction forces is a nontrivial whilst challenging task. Frictional instabilities are typically required to be eliminated or compensated through efficiently designed controllers. In this work, a prediction and analysis framework is designed for the self-propelled vibro-driven system, whose locomotion greatly relies on the dynamic interactions with the nonlinear frictions. This thesis proposes a combined physics-based and analytical-based approach, in a manner that non-reversible characteristic for static friction, presliding as well as pure sliding regimes are revealed, and the frictional limit boundaries are identified. Nonlinear dynamic analysis and simulation results demonstrate good captions of experimentally observed frictional characteristics, quenching of friction-induced vibrations and satisfaction of energy requirements. The thesis also performs elaborative studies on trajectory tracking. Control schemes are designed and extended for a class of underactuated systems with concrete considerations on uncertainties and disturbances. They include a collocated partial feedback control scheme, and an adaptive variable structure control scheme with an elaborately designed auxiliary control variable. Generically, adaptive control schemes using neural networks are designed to ensure trajectory tracking. Theoretical background of these methods is presented with rigorous analysis and developed in detail for particular examples. The schemes promote the utilization of linear filters in the control input to improve the system robustness. Asymptotic stability and convergence of time-varying reference trajectories for the system dynamics are shown by means of Lyapunov synthesis

Intelligent model-based control of complex multi-link mechanisms

Complex under-actuated multilink mechanism involves a system whose number of control inputs is smaller than the dimension of the configuration space. The ability to control such a system through the manipulation of its natural dynamics would allow for the design of more energy-efficient machines with the ability to achieve smooth motions similar to those found in the natural world. This research aims to understand the complex nature of the Robogymnast, a triple link underactuated pendulum built at Cardiff University with the purpose of studying the behaviour of non-linear systems and understanding the challenges in developing its control system. A mathematical model of the robot was derived from the Euler-Lagrange equations. The design of the control system was based on the discrete-time linear model around the downward position and a sampling time of 2.5 milliseconds. Firstly, Invasive Weed Optimization (IWO) was used to optimize the swing-up motion of the robot by determining the optimum values of parameters that control the input signals of the Robogymnast’s two motors. The values obtained from IWO were then applied to both simulation and experiment. The results showed that the swing-up motion of the Robogymnast from the stable downward position to the inverted configuration to be successfully achieved. Secondly, due to the complex nature and nonlinearity of the Robogymnast, a novel approach of modelling the Robogymnast using a multi-layered Elman neural ii network (ENN) was proposed. The ENN model was then tested with various inputs and its output were analysed. The results showed that the ENN model to be capable of providing a better representation of the actual system compared to the mathematical model. Thirdly, IWO is used to investigate the optimum Q values of the Linear Quadratic Regulator (LQR) for inverted balance control of the Robogymnast. IWO was used to obtain the optimal Q values required by the LQR to maintain the Robogymnast in an upright configuration. Two fitness criteria were investigated: cost function J and settling time T. A controller was developed using values obtained from each fitness criteria. The results showed that LQRT performed faster but LQRJ was capable of stabilizing the Robogymnast from larger deflection angles. Finally, fitness criteria J and T were used simultaneously to obtain the optimal Q values for the LQR. For this purpose, two multi-objective optimization methods based on the IWO, namely the Weighted Criteria Method IWO (WCMIWO) and the Fuzzy Logic IWO Hybrid (FLIWOH) were developed. Two LQR controllers were first developed using the parameters obtained from the two optimization methods. The same process was then repeated with disturbance applied to the Robogymnast states to develop another two LQR controllers. The response of the controllers was then tested in different scenarios using simulation and their performance was evaluated. The results showed that all four controllers were able to balance the Robogymnast with the fastest settling time achieved by WMCIWO with disturbance followed by in the ascending order: FLIWOH with disturbance, FLIWOH, and WCMIWO

Advanced Strategies for Robot Manipulators

Amongst the robotic systems, robot manipulators have proven themselves to be of increasing importance and are widely adopted to substitute for human in repetitive and/or hazardous tasks. Modern manipulators are designed complicatedly and need to do more precise, crucial and critical tasks. So, the simple traditional control methods cannot be efficient, and advanced control strategies with considering special constraints are needed to establish. In spite of the fact that groundbreaking researches have been carried out in this realm until now, there are still many novel aspects which have to be explored

Modeling and control of nonlinear underactuated systems

Tato práce je zaměřena na návrh řízení nelineárních systémů. Předpokladem je nejen zajistit správnou funkčnost v okolí určitého pracovního bodu, ale především řešit přechod systému mezi dvěma stavy. Při přesouvání systému ve stavovém prostoru se často výrazně projevuje jeho nelineární chování. Návrh řízení je rozebírán jak ve variantě, kdy je požadováno pouhé splnění převodu mezi stavy, tak v podobě, u které se pomocí účelové funkce specifikují požadované vlastnosti daného přechodu a hledá se optimální řešení. V celém procesu návrhu řízení i při jeho ověřování se využívá v určité podobě model systému (model based design), tudíž modelování je nedílnou součástí této práce. Cílovou skupinou soustav, kterou se práce zabývá, jsou nelineární podaktuované systémy, byť většinu uvedených metod je možné použít obecně. Jako případová studie byl vybrán typický systém reprezentující tuto třídu – jednoramenné inverzní kyvadlo. Ověřování řízení pro realizaci jeho výšvihu probíhá nejen v simulaci, ale také na reálném laboratorním modelu. V závěrečné části práce probíhá návrh řízení pro víceramenná inverzní kyvadla, pomocí čehož se ověřuje univerzálnost celého návrhu a použitelnost metod pro extrémně složité systémy.This thesis focuses on the design of nonlinear system control. The idea is not only to ensure correct functionality around a certain operating point, but also to solve the transition of the system between two states. When moving the system in the state space, its nonlinear behavior is often significantly manifested. The control design is discussed both in a variant where the transition between states is only required and in a form where the desired properties of the transition are specified using an objective function and an optimal solution is searched for. A model of the system is used in some form throughout the control design and verification process (model based design), so modelling is an integral part of this thesis. The target group of systems addressed in this thesis are nonlinear underactuated systems, although most of the methods presented can be applied in general. A typical system representing this class, the single-arm inverted pendulum, was chosen as a case study. Verification of the control to realize its swing-up is carried out not only in simulation but also using a real laboratory model. In the final part of the thesis, the design of the control for multi-arm inverted pendulums is performed, through which the universality of the overall design and the applicability of the methods to extremely complex systems are verified.450 - Katedra kybernetiky a biomedicínského inženýrstvívyhově