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ArticleModel free sliding mode stabilizing control of a real rotary inverted pendulum _ Ilhami Yigit Abstract Inverted pendulum systems, because of highly nonlinear, coupled, and unstable dynamic behaviour, are excellent experimental platforms for testing new developed control algorithms. This study explores nonlinear modelling, simulation and sliding mode stabilizing control of a real rotary inverted pendulum in detail. For simulation purposes only, the system was modelled in a nonlinear state space form including the servomotor dynamics. In the light of the simulation results, a rotary inverted pendulum system was designed and manufactured. For a certain quality level of desired output, benefits of the sliding mode control of the system without using an equivalent control signal by selecting a proper smoothing function were shown. This model free approach can be used to satisfy a need especially for practical control applications in industry to a certain level, encouraging practical control engineers to use sliding mode control, who have no ability to model a system or no sufficient time for this, or encounter very complex nonlinear system models in many cases. Comparisons of the theoretical and experimental results demonstrate that the state equations describe the dynamics of the system satisfactorily, and that robust and accurate balancing of the pendulum can be achieved by using model free sliding mode control with sigmoid smoothing function.

In this study, cavity pressure control of a computer controlled powder injection moulding setup driven by an electro-hydraulic servovalve was investigated both theoretically and experimentally. For this purpose, a detailed system model of a powder injection moulding machine was developed and the important parameters that affect the system behaviour were determined by carrying out computer simulations. In light of the simulation results, a closed-loop control system was designed and manufactured. The control system was implemented to a specially designed powder injection moulding setup. Comparisons of the theoretical and experimental results demonstrate that the developed system model describes the dynamic behaviour of the system satisfactorily. The results of experiments show that accurate control of the cavity pressure can be achieved by the proposed control system. A 1 Area of the right-hand side of the hydraulic piston [m 2 ] A 2 Injection piston (screw piston) area [m 2 ] A 3 Area of the left-hand side of the hydraulic piston [m 2 ] A i Cross-sectional area of the ith passage [m 2 ] A c , b Coefficients which describe the feedstock properties b mh Damping coefficent [N.s/m] C ai Circumference of the ith passage [m] C d Discharge coefficent of the servovalve ports C lh Coefficient of leakage around the hydraulic piston [m 3 /s/Pa] C lm Coefficient of leakage around the injection piston [m 3 /s/Pa] d hi Hydraulic diameter of the ith passage at a given time [m] I v Servovalve input current [mA] K v Gain of the servovalve [m/mA] L ei Length of the ith passage at a given time [m] P 2 Injection pressure [Pa] P c Cavity pressure [Pa] P s Supply pressure [Pa] Q m Flow rate into the mould [m 3 /s] R Total resistance [N.s/m 5 ] T mi Feedstock temperature in the ith passage [ C] T 0 Initial temperature of the feedstock [ C] V 1 Oil volume in the right-hand side of the hydraulic cylinder [m 3 ] V 2 Feedstock volume in the injection cylinder [m 3 ] V 3 Oil volume in the left-hand side of the hydraulic cylinder [m 3 ] V fi Volume of the filled part of the ith passage [m 3 ] q h Density of the hydraulic oil [kg/m 3 ] b h Bulk modulus of the hydraulic oil [Pa] b m Bulk modulus of the feedstock [Pa] l i Absolute viscosity of the feedstock flowing through the ith passage [N.s/m 2 ] w Peripheral length of the servovalve ports [m] _ c c i Shear rate in the ith passage [s À1 ] x v Natural frequency of the valve [rad/s] n v Damping coefficient of the second-stage valve x v Servovalve spool position [m]

ÖZETKayan kipli kontrol, uygun şartlar yerine geldiğinde, dış bozucular ve belirsizliklere rağmen istenilen dinamik davranışı sağlayabilen gürbüz bir kontrol yöntemidir. Kayan kipli kontrol yöntemi, uygulama basitliği ve gürbüzlüğünden dolayı, son yıllarda gözde hale gelmiş, çok sayıda kayan kipli kontrol tekniği geliştirilmiş, mühendislik uygulamalarda yerini almıştır. Ancak, açık literatürde bu kontrol tekniklerinin çeşitli gerçek sistemler üzerinde aynı anda uygulandığı kapsamlı bir çalışma bulunmadığı görülmüştür. Bu çalışmada, pratikte kullanılan bazı kayan kipli kontrol teknikleri çeşitli gerçek sistemler üzerinde teorik ve deneysel olarak incelenmiştir. Bu amaçla, tek giriş tek çıkışlı doğru akım motoru tahrikli doğrusal bilyalı kızak sistemi, doğrusal olmayan basit ters sarkaç ve tek giriş çok çıkışlı dolaylı tahrikli doğrusal olmayan arabalı ters sarkaç sistemi olmak üzere üç farklı gerçek sistem kullanılmıştır. Bu sistemlerin kontrolleri, hem teorik hem de deneysel olarak tatmin edici düzeyde gerçekleştirilmiş, elde edilen çok sayıda simülasyon ve deney sonuçları değerlendirilerek karşılaştırmalar yapılmış, çeşitli sonuçlar çıkarılmış, ileriye dönük çalışmalar için önerilerde bulunulmuştur.Anahtar Kelimeler: kayan kipli kontrol, doğrusal olmayan sistem, ters sarkaç, modelleme, simülasyon, deney THEORETICAL AND EXPERIMENTAL INVESTIGATION OF SOME SLIDING MODE CONTROL TECHNIQUES USED IN PRACTICE ABSTRACTSliding mode control is a robust control technique which is able to provide a desired dynamic behaviour in spite of disturbances and uncertainties under matching conditions. In recent years, because of simplicity and robustness, sliding mode control has become popular and various sliding mode control techniques have been developed and taken place in engineering practices. However, it is found that a comprehensive study dealing with the application of these control techniques on various real systems is not available in open literature. In this study, some commonly used sliding mode control techniques are investigated theoretically, and experimentally applying on various real systems. For this purpose, three different types of real systems are used: a single input single output direct current motor driven linear recirculating ball bearing system; a nonlinear simple inverted pendulum; and a single input multiple output underactuated nonlinear cart type inverted pendulum. Control of the systems with various control techniques are implemented satisfactorily both theoretically and experimentally. Results of simulations and experiments are compared with each other, and various inferences are made and recommendations for further studies are presented.